Plato: Phaedo

The Phaedo is one of the most widely read dialogues written by the ancient Greek philosopher Plato. It claims to recount the events and conversations that occurred on the day that Plato’s teacher, Socrates (469-399 B.C.E.), was put to death by the state of Athens. It is the final episode in the series of dialogues recounting Socrates’ trial and death. The earlier Euthyphro dialogue portrayed Socrates in discussion outside the court where he was to be prosecuted on charges of impiety and corrupting the youth; the Apology described his defense before the Athenian jury; and the Crito described a conversation during his subsequent imprisonment. The Phaedo now brings things to a close by describing the moments in the prison cell leading up to Socrates’ death from poisoning by use of hemlock.

Among these “trial and death” dialogues, the Phaedo is unique in that it presents Plato’s own metaphysical, psychological, and epistemological views; thus it belongs to Plato’s middle period rather than with his earlier works detailing Socrates’ conversations regarding ethics. Known to ancient commentators by the title On the Soul, the dialogue presents no less than four arguments for the soul’s immortality. It also contains discussions of Plato’s doctrine of knowledge as recollection, his account of the soul’s relationship to the body, and his views about causality and scientific explanation. Most importantly of all, Plato sets forth his most distinctive philosophical theory—the theory of Forms—for what is arguably the first time. So, the Phaedo merges Plato’s own philosophical worldview with an enduring portrait of Socrates in the hours leading up to his death.

Objections from Simmias and Cebes, and Socrates’ Response (84c-107b)

References and Further Reading

1. The Place of the Phaedo within Plato’s works

Plato wrote approximately thirty dialogues. The Phaedo is usually placed at the beginning of his “middle” period, which contains his own distinctive views about the nature of knowledge, reality, and the soul, as well as the implications of these views for human ethical and political life. Its middle-period classification puts it after “early” dialogues such as the Apology, Euthyphro, Crito, Protagoras, and others which present Socrates’ search—usually inconclusive—for ethical definitions, and before “late” dialogues like the Parmenides, Theaetetus, Sophist, and Statesman. Within the middle dialogues, it is uncontroversial that the Phaedo was written before the Republic, and most scholars think it belongs before the Symposium as well. Thus, in addition to being an account of what Socrates said and did on the day he died, the Phaedo contains what is probably Plato’s first overall statement of his own philosophy. His most famous theory, the theory of Forms, is presented in four different places in the dialogue.

2. Drama and Doctrine

In addition to its central role in conveying Plato’s philosophy, the Phaedo is widely agreed to be a masterpiece of ancient Greek literature. Besides philosophical argumentation, it contains a narrative framing device that resembles the chorus in Greek tragedy, references to the Greek myth of Theseus and the fables of Aesop, Plato’s own original myth about the afterlife, and in its opening and closing pages, a moving portrait of Socrates in the hours leading up to his death. Plato draws attention (at 59b) to the fact that he himself was not present during the events retold, suggesting that he wants the dialogue to be seen as work of fiction.

Contemporary commentators have struggled to put together the dialogue’s dramatic components with its lengthy sections of philosophical argumentation—most importantly, with the four arguments for the soul’s immortality, which tend to strike even Plato’s charitable interpreters as being in need of further defense. (Socrates himself challenges his listeners to provide such defense at 84c-d.) How seriously does Plato take these arguments, and what does the surrounding context contribute to our understanding of them? While this article will concentrate on the philosophical aspects of the Phaedo, readers are advised to pay close attention to the interwoven dramatic features as well.

3. Outline of the Dialogue

The dialogue revolves around the topic of death and immortality: how the philosopher is supposed to relate to death, and what we can expect to happen to our souls after we die. The text can be divided, rather unevenly, into five sections:

(1) an initial discussion of the philosopher and death (59c-69e)

(2) three arguments for the soul’s immortality (69e-84b)

(3) some objections to these arguments from Socrates’ interlocutors and his response, which includes a fourth argument (84c-107b)

(4) a myth about the afterlife (107c-115a)

(5) a description of the final moments of Socrates’ life (115a-118a)

The dialogue commences with a conversation (57a-59c) between two characters, Echecrates and Phaedo, occurring sometime after Socrates’ death in the Greek city of Phlius. The former asks the latter, who was present on that day, to recount what took place. Phaedo begins by explaining why some time had elapsed between Socrates’ trial and his execution: the Athenians had sent their annual religious mission to Delos the day before the trial, and executions are forbidden until the mission returns. He also lists the friends who were present and describes their mood as “an unaccustomed mixture of pleasure and pain,” since Socrates appeared happy and without fear but his friends knew that he was going to die. He agrees to tell the whole story from the beginning; within this story the main interlocutors are Socrates, Simmias, and Cebes. Some commentators on the dialogue have taken the latter two characters to be followers of the philosopher Pythagoras (570-490 B.C).

a. The Philosopher and Death (59c-69e)

Socrates’ friends learn that he will die on the present day, since the mission from Delos has returned. They go in to the prison to find Socrates with his wife Xanthippe and their baby, who are then sent away. Socrates, rubbing the place on his leg where his just removed bonds had been, remarks on how strange it is that a man cannot have both pleasure and pain at the same time, yet when he pursues and catches one, he is sure to meet with the other as well. Cebes asks Socrates about the poetry he is said to have begun writing, since Evenus (a Sophist teacher, not present) was wondering about this. Socrates relates how certain dreams have caused him to do so, and says that he is presently putting Aesop’s fables into verse. He then asks Cebes to convey to Evenus his farewell, and to tell him that—even though it would be wrong to take his own life—he, like any philosopher, should be prepared to follow Socrates to his death.

Here the conversation turns toward an examination of the philosopher’s attitude toward death. The discussion starts with the question of suicide. If philosophers are so willing to die, asks Cebes, why is it wrong for them to kill themselves? Socrates’ initial answer is that the gods are our guardians, and that they will be angry if one of their possessions kills itself without permission. As Cebes and Simmias immediately point out, however, this appears to contradict his earlier claim that the philosopher should be willing to die: for what truly wise man would want to leave the service of the best of all masters, the gods?

In reply to their objection, Socrates offers to “make a defense” of his view, as if he were in court, and submits that he hopes this defense will be more convincing to them than it was to the jury. (He is referring here, of course, to his defense at his trial, which is recounted in Plato’s Apology.) The thesis to be supported is a generalized version of his earlier advice to Evenus: that “the one aim of those who practice philosophy in the proper manner is to practice for dying and death” (64a3-4).

Socrates begins his defense of this thesis, which takes up the remainder of the present section, by defining death as the separation of body and soul. This definition goes unchallenged by his interlocutors, as does its dualistic assumption that body and soul are two distinct entities. (The Greek word psuchē is only roughly approximate to our word “soul”; the Greeks thought of psuchē as what makes something alive, and Aristotle talks about non-human animals and even plants as having souls in this sense.) Granted that death is a soul/body separation, Socrates sets forth a number of reasons why philosophers are prepared for such an event. First, the true philosopher despises bodily pleasures such as food, drink, and sex, so he more than anyone else wants to free himself from his body (64d-65a). Additionally, since the bodily senses are inaccurate and deceptive, the philosopher’s search for knowledge is most successful when the soul is “most by itself.”

The latter point holds especially for the objects of philosophical knowledge that Plato later on in the dialogue (103e) refers to as “Forms.” Here Forms are mentioned for what is perhaps the first time in Plato’s dialogues: the Just itself, the Beautiful, and the Good; Bigness, Health, and Strength; and “in a word, the reality of all other things, that which each of them essentially is” (65d). They are best approached not by sense perception but by pure thought alone. These entities are granted again without argument by Simmias and Cebes, and are discussed in more detail later. .

All told, then, the body is a constant impediment to philosophers in their search for truth: “It fills us with wants, desires, fears, all sorts of illusions and much nonsense, so that, as it is said, in truth and in fact no thought of any kind ever comes to us from the body” (66c). To have pure knowledge, therefore, philosophers must escape from the influence of the body as much as is possible in this life. Philosophy itself is, in fact, a kind of “training for dying” (67e), a purification of the philosopher’s soul from its bodily attachment.

Thus, Socrates concludes, it would be unreasonable for a philosopher to fear death, since upon dying he is most likely to obtain the wisdom which he has been seeking his whole life. Both the philosopher’s courage in the face of death and his moderation with respect to bodily pleasures which result from the pursuit of wisdom stand in stark contrast to the courage and moderation practiced by ordinary people. (Wisdom, courage, and moderation are key virtues in Plato’s writings, and are included in his definition of justice in the Republic.) Ordinary people are only brave in regard to some things because they fear even worse things happening, and only moderate in relation to some pleasures because they want to be immoderate with respect to others. But this is only “an illusory appearance of virtue”—for as it happens, “moderation and courage and justice are a purging away of all such things, and wisdom itself is a kind of cleansing or purification” (69b-c). Since Socrates counts himself among these philosophers, why wouldn’t he be prepared to meet death? Thus ends his defense.

b. Three Arguments for the Soul’s Immortality (69e-84b)

But what about those, says Cebes, who believe that the soul is destroyed when a person dies? To persuade them that it continues to exist on its own will require some compelling argument. Readers should note several important features of Cebes’ brief objection (70a-b). First, he presents the belief in the immortality of the soul as an uncommon belief (“men find it hard to believe . . .”). Secondly, he identifies two things which need to be demonstrated in order to convince those who are skeptical: (a) that the soul continues to exist after a person’s death, and (b) that it still possesses intelligence. The first argument that Socrates deploys appears to be intended to respond to (a), and the second to (b).

i. The Cyclical Argument (70c-72e)

Socrates mentions an ancient theory holding that just as the souls of the dead in the underworld come from those living in this world, the living souls come back from those of the dead (70c-d). He uses this theory as the inspiration for his first argument, which may be reconstructed as follows:

1. All things come to be from their opposite states: for example, something that comes to be “larger” must necessarily have been “smaller” before (70e-71a).

2. Between every pair of opposite states there are two opposite processes: for example, between the pair “smaller” and “larger” there are the processes “increase” and “decrease” (71b).

3. If the two opposite processes did not balance each other out, everything would eventually be in the same state: for example, if increase did not balance out decrease, everything would keep becoming smaller and smaller (72b).

4. Since “being alive” and “being dead” are opposite states, and “dying” and “coming-to-life” are the two opposite processes between these states, coming-to-life must balance out dying (71c-e).

5. Therefore, everything that dies must come back to life again (72a).

A main question that arises in regard to this argument is what Socrates means by “opposites.” We can see at least two different ways in which this term is used in reference to the opposed states he mentions. In a first sense, it is used for “comparatives” such as larger and smaller (and also the pairs weaker/stronger and swifter/slower at 71a), opposites which admit of various degrees and which even may be present in the same object at once (on this latter point, see 102b-c). However, Socrates also refers to “being alive” and “being dead” as opposites—but this pair is rather different from comparative states such as larger and smaller, since something can’t be deader, but only dead. Being alive and being dead are what logicians call “contraries” (as opposed to “contradictories,” such as “alive” and “not-alive,” which exclude any third possibility). With this terminology in mind, some contemporary commentators have maintained that the argument relies on covertly shifting between these different kinds of opposites.

Clever readers may notice other apparent difficulties as well. Does the principle about balance in (3), for instance, necessarily apply to living things? Couldn’t all life simply cease to exist at some point, without returning? Moreover, how does Plato account for adding new living souls to the human population? While these questions are perhaps not unanswerable from the point of view of the present argument, we should keep in mind that Socrates has several arguments remaining, and he later suggests that this first one should be seen as complementing the second (77c-d).

ii. The Argument from Recollection (72e-78b)

Cebes mentions that the soul’s immortality also is supported by Socrates’ theory that learning is “recollection” (a theory which is, by most accounts, distinctively Platonic, and one that plays a role in his dialogues Meno and Phaedrus as well). As evidence of this theory he mentions instances in which people can “recollect” answers to questions they did not previously appear to possess when this knowledge is elicited from them using the proper methods. This is likely a reference to the Meno (82b ff.), where Socrates elicits knowledge about basic geometry from a slave-boy by asking the latter a series of questions to guide him in the right direction. Asked by Simmias to elaborate further upon this doctrine, Socrates explains that recollection occurs “when a man sees or hears or in some other way perceives one thing and not only knows that thing but also thinks of another thing of which the knowledge is not the same but different . . .” (73c). For example, when a lover sees his beloved’s lyre, the image of his beloved comes into his mind as well, even though the lyre and the beloved are two distinct things.

Based on this theory, Socrates now commences a second proof for the soul’s immortality—one which is referred to with approval in later passages in the dialogue (77a-b, 87a, 91e-92a, and 92d-e). The argument may be reconstructed as follows:

1. Things in the world which appear to be equal in measurement are in fact deficient in the equality they possess (74b, d-e).

2. Therefore, they are not the same as true equality, that is, “the Equal itself” (74c).

3. When we see the deficiency of the examples of equality, it helps us to think of, or “recollect,” the Equal itself (74c-d).

4. In order to do this, we must have had some prior knowledge of the Equal itself (74d-e).

5. Since this knowledge does not come from sense-perception, we must have acquired it before we acquired sense-perception, that is, before we were born (75b ff.).

6. Therefore, our souls must have existed before we were born. (76d-e)

With regard to premise (1), in what respect are this-worldly instances of equality deficient? Socrates mentions that two apparently equal sticks, for example, “fall short” of true equality and are thus “inferior” to it (74e). Why? His reasoning at 74b8-9—that the sticks “sometimes, while remaining the same, appear to one to be equal and another to be unequal”—is notoriously ambiguous, and has been the subject of much scrutiny. He could mean that the sticks may appear as equal or unequal to different observers, or perhaps they appear as equal when measured against one thing but not another. In any case, the notion that the sensible world is imperfect is a standard view of the middle dialogues (see Republic 479b-c for a similar example), and is emphasized further in his next argument.

By “true equality” and “the Equal itself” in premises (2)-(4), Socrates is referring to the Form of Equality. It is this entity with respect to which the sensible instances of equality fall short—and indeed, Socrates says that the Form is “something else beyond all these.” His brief argument at 74a-c that true equality is something altogether distinct from any visible instances of equality is of considerable interest, since it is one of few places in the middle dialogues where he makes an explicit argument for why there must be Forms. The conclusion of the second argument for the soul’s immortality extends what has been said about equality to other Forms as well: “If those realities we are always talking about exist, the Beautiful and the Good and all that kind of reality, and we refer all the things we perceive to that reality, discovering that it existed before and is ours, and we compare these things with it, then, just as they exist, so our soul must exist before we are born” (76d-e). The process of recollection is initiated not just when we see imperfectly equal things, then, but when we see things that appear to be beautiful or good as well; experience of all such things inspires us to recollect the relevant Forms. Moreover, if these Forms are never available to us in our sensory experience, we must have learned them even before we were capable of having such experience.

Simmias agrees with the argument so far, but says that this still does not prove that our souls exist after death, but only before birth. This difficulty, Socrates suggests, can be resolved by combining the present argument with the one from opposites: the soul comes to life from out of death, so it cannot avoid existing after death as well. He does not elaborate on this suggestion, however, and instead proceeds to offer a third argument.

iii. The Affinity Argument (78b-84b)

The third argument for the soul’s immortality is referred to by commentators as the “affinity argument,” since it turns on the idea that the soul has a likeness to a higher level of reality:

1. There are two kinds of existences: (a) the visible world that we perceive with our senses, which is human, mortal, composite, unintelligible, and always changing, and (b) the invisible world of Forms that we can access solely with our minds, which is divine, deathless, intelligible, non-composite, and always the same (78c-79a, 80b).

2. The soul is more like world (b), whereas the body is more like world (a) (79b-e).

3. Therefore, supposing it has been freed of bodily influence through philosophical training, the soul is most likely to make its way to world (b) when the body dies (80d-81a). (If, however, the soul is polluted by bodily influence, it likely will stay bound to world (a) upon death (81b-82b).)

Note that this argument is intended to establish only the probability of the soul’s continued existence after the death of the body—“what kind of thing,” Socrates asks at the outset, “is likely to be scattered [after the death of the body]?” (78b; my italics) Further, premise (2) appears to rest on an analogy between the soul and body and the two kinds of realities mentioned in (1), a style of argument that Simmias will criticize later (85e ff.). Indeed, since Plato himself appends several pages of objections by Socrates’ interlocutors to this argument, one might wonder how authoritative he takes it to be.

Yet Socrates’ reasoning about the soul at 78c-79a states an important feature of Plato’s middle period metaphysics, sometimes referred to as his “two-world theory.” In this picture of reality, the world perceived by the senses is set against the world of Forms, with each world being populated by fundamentally different kinds of entities:

The World of the Senses	The World of Forms
Composites (that is, things with parts)	Non-composites
Things that never remain the same from one moment to the next	Things that always remain the same and don’t tolerate any change
Any particular thing that is equal, beautiful, and so forth	The Equal, the Beautiful, and what each thing is in itself
That which is visible	That which is grasped by the mind and invisible

Since the body is like one world and the soul like the other, it would be strange to think that even though the body lasts for some time after a person’s death, the soul immediately dissolves and exists no further. Given the respective affinities of the body and soul, Socrates spends the rest of the argument (roughly 80d-84b) expanding on the earlier point (from his “defense”) that philosophers should focus on the latter. This section has some similarities to the myth about the afterlife, which he narrates near the dialogue’s end; note that some of the details of the account here of what happens after death are characterized as merely “likely.” A soul which is purified of bodily things, Socrates says, will make its way to the divine when the body dies, whereas an impure soul retains its share in the visible after death, becoming a wandering phantom. Of the impure souls, those who have been immoderate will later become donkeys or similar animals, the unjust will become wolves or hawks, those with only ordinary non-philosophical virtue will become social creatures such as bees or ants.

The philosopher, on the other hand, will join the company of the gods. For philosophy brings deliverance from bodily imprisonment, persuading the soul “to trust only itself and whatever reality, existing by itself, the soul by itself understands, and not to consider as true whatever it examines by other means, for this is different in different circumstances and is sensible and visible, whereas what the soul itself sees is intelligible and indivisible” (83a6-b4). The philosopher thus avoids the “greatest and most extreme evil” that comes from the senses: that of violent pleasures and pains which deceive one into thinking that what causes them is genuine. Hence, after death, his soul will join with that to which it is akin, namely, the divine.

c. Objections from Simmias and Cebes, and Socrates’ Response (84c-107b)

After a long silence, Socrates tells Simmias and Cebes not to worry about objecting to any of what he has just said. For he, like the swan that sings beautifully before it dies, is dedicated to the service of Apollo, and thus filled with a gift of prophecy that makes him hopeful for what death will bring.

i. The Objections (85c-88c)

Simmias prefaces his objection by making a remark about methodology. While certainty, he says, is either impossible or difficult, it would show a weak spirit not to make a complete investigation. If at the end of this investigation one fails to find the truth, one should adopt the best theory and cling to it like a raft, either until one dies or comes upon something sturdier.

This being said, he proceeds to challenge Socrates’ third argument. For one might put forth a similar argument which claims that the soul is like a harmony and the body is like a lyre and its strings. In fact, Simmias claims that “we really do suppose the soul to be something of this kind,” that is, a harmony or proper mixture of bodily elements like the hot and cold or dry and moist (86b-c). (Some commentators think the “we” here refers to followers of Pythagoras.) But even though a musical harmony is invisible and akin to the divine, it will cease to exist when the lyre is destroyed. Following the soul-as-harmony thesis, the same would be true of the soul when the body dies.

Next Socrates asks if Cebes has any objections. The latter says that he is convinced by Socrates’ argument that the soul exists before birth, but still doubts whether it continues to exist after death. In support of his doubt, he invokes a metaphor of his own. Suppose someone were to say that since a man lasts longer than his cloak, it follows that if the cloak is still there the man must be there too. We would certainly think this statement was nonsense. (He appears to be refering to Socrates’ argument at 80c-e here.) Just as a man might wear out many cloaks before he dies, the soul might use up many bodies before it dies. So even supposing everything else is granted, if “one does not further agree that the soul is not damaged by its many births and is not, in the end, altogether destroyed in one of those deaths, he might say that no one knows which death and dissolution of the body brings about the destruction of the soul, since not one of us can be aware of this” (88a-b). In light of this uncertainty, one should always face death with fear.

ii. Interlude on Misology (89b-91c)

After a short exchange in the meta-dialogue in which Phaedo and Echecrates praise Socrates’ pleasant attitude throughout this discussion, Socrates begins his response with a warning that they not become misologues. Misology, he says, arises in much the same way that misanthropy does: when someone with little experience puts his trust in another person, but later finds him to be unreliable, his first reaction is to blame this on the depraved nature of people in general. If he had more knowledge and experience, however, he would not be so quick to make this leap, for he would realize that most people fall somewhere in between the extremes of good and bad, and he merely happened to encounter someone at one end of the spectrum. A similar caution applies to arguments. If someone thinks a particular argument is sound, but later finds out that it is not, his first inclination will be to think that all arguments are unsound; yet instead of blaming arguments in general and coming to hate reasonable discussion, we should blame our own lack of skill and experience.

iii. Response to Simmias (91e-95a)

Socrates then puts forth three counter-arguments to Simmias’ objection. To begin, he gets both Simmias and Cebes to agree that the theory of recollection is true. But if this is so, then Simmias is not able to “harmonize” his view that the soul is a harmony dependent on the body with the recollection view that the soul exists before birth. Simmias admits this inconsistency, and says that he in fact prefers the theory of recollection to the other view. Nonetheless, Socrates proceeds to make two additional points. First, if the soul is a harmony, he contends, it can have no share in the disharmony of wickedness. But this implies that all souls are equally good. Second, if the soul is never out of tune with its component parts (as shown at 93a), then it seems like it could never oppose these parts. But in fact it does the opposite, “ruling over all the elements of which one says it is composed, opposing nearly all of them throughout life, directing all their ways, inflicting harsh and painful punishment on them, . . . holding converse with desires and passions and fears, as if it were one thing talking to a different one . . .” (94c9-d5). A passage in Homer, wherein Odysseus beats his breast and orders his heart to endure, strengthens this picture of the opposition between soul and bodily emotions. Given these counter-arguments, Simmias agrees that the soul-as-harmony thesis cannot be correct.

iv. Response to Cebes (95a-107b)

1. Socrates’ Intellectual History (96a-102a)

After summarizing Cebes’ objection that the soul may outlast the body yet not be immortal, Socrates says that this problem requires “a thorough investigation of the cause of generation and destruction” (96a; the Greek word aitia, translated as “cause,” has the more general meaning of “explanation”). He now proceeds to relate his own examinations into this subject, recalling in turn his youthful puzzlement about the topic, his initial attraction to a solution given by the philosopher Anaxagoras (500-428 B.C.), and finally his development of his own method of explanation involving Forms. It is debated whether this account is meant to describe Socrates’ intellectual autobiography or Plato’s own, since the theory of Forms generally is described as the latter’s distinctive contribution. (Some commentators have suggested that it may be neither, but instead just good storytelling on Plato’s part.)

When Socrates was young, he says, he was excited by natural science, and wanted to know the explanation of everything from how living things are nourished to how things occur in the heavens and on earth. But then he realized that he had no ability for such investigations, since they caused him to unlearn many of the things he thought he had previously known. He used to think, for instance, that people grew larger by various kinds of external nourishment combining with the appropriate parts of our bodies, for example, by food adding flesh to flesh. But what is it which makes one person larger than another? Or for that matter, which makes one and one add up to two? It seems like it can’t be simply the two things coming near one another. Because of puzzles like these, Socrates is now forced to admit his ignorance: “I do not any longer persuade myself that I know why a unit or anything else comes to be, or perishes or exists by the old method of investigation, and I do not accept it, but I have a confused method of my own” (97b).

This method came about as follows. One day after his initial setbacks Socrates happened to hear of Anaxagoras’ view that Mind directs and causes all things. He took this to mean that everything was arranged for the best. Therefore, if one wanted to know the explanation of something, one only had to know what was best for that thing. Suppose, for instance, that Socrates wanted to know why the heavenly bodies move the way they do. Anaxagoras would show him how this was the best possible way for each of them to be. And once he had taught Socrates what the best was for each thing individually, he then would explain the overall good that they all share in common. Yet upon studying Anaxagoras further, Socrates found these expectations disappointed. It turned out that Anaxagoras did not talk about Mind as cause at all, but rather about air and ether and other mechanistic explanations. For Socrates, however, this sort of explanation was simply unacceptable:

To call those things causes is too absurd. If someone said that without bones and sinews and all such things, I should not be able to do what I decided, he would be right, but surely to say that they are the cause of what I do, and not that I have chosen the best course, even though I act with my mind, is to speak very lazily and carelessly. Imagine not being able to distinguish the real cause from that without which the cause would not be able to act as a cause. (99a-b)

Frustrated at finding a teacher who would provide a teleological explanation of these phenomena, Socrates settled for what he refers to as his “second voyage” (99d). This new method consists in taking what seems to him to be the most convincing theory—the theory of Forms—as his basic hypothesis, and judging everything else in accordance with it. In other words, he assumes the existence of the Beautiful, the Good, and so on, and employs them as explanations for all the other things. If something is beautiful, for instance, the “safe answer” he now offers for what makes it such is “the presence of,” or “sharing in,” the Beautiful (100d). Socrates does not go into any detail here about the relationship between the Form and object that shares in it, but only claims that “all beautiful things are beautiful by the Beautiful” (100d). In regard to the phenomena that puzzled him as a young man, he offers the same answer. What makes a big thing big, or a bigger thing bigger, is the Form Bigness. Similarly, if one and one are said to be two, it is because they share in Twoness, whereas previously each shared in Oneness.

2. The Final Argument (102b-107b)

When Socrates has finished describing this method, both Simmias and Cebes agree that what he has said is true. Their accord with his view is echoed in another brief interlude by Echecrates and Phaedo, in which the former says that Socrates has “made these things wonderfully clear to anyone of even the smallest intelligence,” and Phaedo adds that all those present agreed with Socrates as well. Returning again to the prison scene, Socrates now uses this as the basis of a fourth argument that the soul is immortal. One may reconstruct this argument as follows:

1. Nothing can become its opposite while still being itself: it either flees away or is destroyed at the approach of its opposite. (For example, “tallness” cannot become “shortness” while still being “hot.”) (102d-103a)

2. This is true not only of opposites, but in a similar way of things that contain opposites. (For example, “fire” and “snow” are not themselves opposites, but “fire” always brings “hot” with it, and “snow” always brings “cold” with it. So “fire” will not become “cold” without ceasing to be “fire,” nor will “snow” become “hot” without ceasing to be “snow.”) (103c-105b)

3. The “soul” always brings “life” with it. (105c-d)

4. Therefore “soul” will never admit the opposite of “life,” that is, “death,” without ceasing to be “soul.” (105d-e)

5. But what does not admit death is also indestructible. (105e-106d)

6. Therefore, the soul is indestructible. (106e-107a)

When someone objects that premise (1) contradicts his earlier statement (at 70d-71a) about opposites arising from one another, Socrates responds that then he was speaking of things with opposite properties, whereas here is talking about the opposites themselves. Careful readers will distinguish three different ontological items at issue in this passage:

(a) the thing (for example, Simmias) that participates in a Form (for example, that of Tallness), but can come to participate in the opposite Form (of Shortness) without thereby changing that which it is (namely, Simmias)

(b) the Form (for example, of Tallness), which cannot admit its opposite (Shortness)

(c) the Form-in-the-thing (for example, the tallness in Simmias), which cannot admit its opposite (shortness) without fleeing away of being destroyed

Premise (2) introduces another item:

(d) a kind of entity (for example, fire) that, even though it does not share the same name as a Form, always participates in that Form (for example, Hotness), and therefore always excludes the opposite Form (Coldness) wherever it (fire) exists

This new kind of entity puts Socrates beyond the “safe answer” given before (at 100d) about how a thing participates in a Form. His new, “more sophisticated answer” is to say that what makes a body hot is not heat—the safe answer—but rather an entity such as fire. In like manner, what makes a body sick is not sickness but fever, and what makes a number odd is not oddness but oneness (105b-c). Premise (3) then states that the soul is this sort of entity with respect to the Form of Life. And just as fire always brings the Form of Hotness and excludes that of Coldness, the soul will always bring the Form of Life with it and exclude its opposite.

However, one might wonder about premise (5). Even though fire, to return to Socrates’ example, does not admit Coldness, it still may be destroyed in the presence of something cold—indeed, this was one of the alternatives mentioned in premise (1). Similarly, might not the soul, while not admitting death, nonetheless be destroyed by its presence? Socrates tries to block this possibility by appealing to what he takes to be a widely shared assumption, namely, that what is deathless is also indestructible: “All would agree . . . that the god, and the Form of Life itself, and anything that is deathless, are never destroyed” (107d). For readers who do not agree that such items are deathless in the first place, however, this sort of appeal is unlikely to be acceptable.

Simmias, for his part, says he agrees with Socrates’ line of reasoning, although he admits that he may have misgivings about it later on. Socrates says that this is only because their hypotheses need clearer examination—but upon examination they will be found convincing.

d. The Myth about the Afterlife (107c-115a)

The issue of the immortality of the soul, Socrates says, has considerable implications for morality. If the soul is immortal, then we must worry about our souls not just in this life but for all time; if it is not, then there are no lasting consequences for those who are wicked. But in fact, the soul is immortal, as the previous arguments have shown, and Socrates now begins to describe what happens when it journeys to the underworld after the death of the body. The ensuing tale tells us of

(1) the judgment of the dead souls and their subsequent journey to the underworld (107d-108c)

(2) the shape of the earth and its regions (108c-113c)

(3) the punishment of the wicked and the reward of the pious philosophers (113d-114c)

Commentators commonly refer to this story as a “myth,” and Socrates himself describes it this way (using the Greek word muthos at 110b, which earlier on in the dialogue (61b) he has contrasted with logos, or “argument.”). Readers should be aware that for the Greeks myth did not have the negative connotations it often carries today, as when we say, for instance, that something is “just a myth” or when we distinguish myth from fact. While Plato’s relation to traditional Greek mythology is a complex one—see his critique of Homer and Hesiod in Republic Book II, for instance—he himself uses myths to bolster his doctrines not only in the Phaedo, but in dialogues such as the Gorgias, Republic, and Phaedrus as well.

At the end of his tale, Socrates says that what is important about his story is not its literal details, but rather that we “risk the belief” that “this, or something like this, is true about our souls and their dwelling places,” and repeat such a tale to ourselves as though it were an “incantation” (114d). Doing so will keep us in good spirits as we work to improve our souls in this life. The myth thus reinforces the dialogue’s recommendation of the practice of philosophy as care for one’s soul.

e. Socrates’ Death (115a-118a)

The depiction of Socrates’ death that closes the Phaedo is rich in dramatic detail. It also is complicated by a couple of difficult interpretative questions.

After Socrates has finished his tale about the afterlife, he says that it is time for him to prepare to take the hemlock poison required by his death sentence. When Crito asks him what his final instructions are for his burial, Socrates reminds him that what will remain with them after death is not Socrates himself, but rather just his body, and tells him that they can bury it however they want. Next he takes a bath—so that his corpse will not have to be cleaned post-mortem—and says farewell to his wife and three sons. Even the officer sent to carry out Socrates’ punishment is moved to tears at this point, and describes Socrates as “the noblest, the gentlest and the best man” who has ever been at the prison.

Crito tells Socrates that some condemned men put off taking the poison for as long as possible, in order to enjoy their last moments in feasting or sex. Socrates, however, asks for the poison to be brought immediately. He drinks it calmly and in good cheer, and chastises his friends for their weeping. When his legs begin to feel heavy, he lies down; the numbness in his body travels upward until eventually it reaches his heart.

Some contemporary scholars have challenged Plato’s description of hemlock-poisoning, arguing that in fact the symptoms would have been much more violent than the relatively gentle death he depicts. If these scholars are right, why does Plato depict the death scene the way he does? There is also a dispute about Socrates’ last words, which invoke a sacrificial offering made by the sick to the god of medicine: “Crito, we owe a cock to Asclepius; make this offering to him and do not forget.” Did Socrates view life as a kind of sickness?

4. References and Further Reading

a. General Commentaries

Bostock, D. Plato’s Phaedo. Oxford, 1986.

In-depth yet accessible discussion of the dialogue’s arguments (does not include text of the Phaedo). Includes a helpful chapter on the theory of Forms.

Dorter, K. Plato’s Phaedo: An Interpretation. University of Toronto Press, 1982.

Reading of the dialogue that combines both dramatic and doctrinal approaches (does not include text of the Phaedo).

Gallop, D. Plato: Phaedo. Oxford, 1975.

English translation with separate commentary that focuses on the dialogue’s argumentation.

Hackforth, R. Plato’s Phaedo: Translated with an Introduction and Commentary. Cambridge, 1955.

English translation with running commentary.

Rowe, C.J. Plato: Phaedo. Cambridge, 1993.

Original Greek text (no English) with introduction and detailed textual commentary.

b. The Philosopher and Death (59c-69e)

Pakaluk, M. “Degrees of Separation in the ‘Phaedo.’” Phronesis 48 (2003) 89-115.

Discusses Plato’s notion of the soul-body distinction at 63a-69e.

Warren, J. “Socratic Suicide.” The Journal of Hellenic Studies 121 (2001) 91-106.

On the Platonic philosopher’s attitude toward suicide in the 61e-69e passage.

Weiss, R. "The Right Exchange: Phaedo 69a6-c3". Ancient Philosophy 7 (1987) 57-66.

Examines the notion that wisdom is the highest goal of the philosopher.

c. Three Arguments for the Soul’s Immortality (69e-84b)

Ackrill, J.L. “Anamnēsis in the Phaedo,” in E.N. Lee and A.P.D. Mourelatos (eds.) Exegesis and Argument: Studies in Greek Philosophy Presented to Gregory Vlastos. Assen, 1973. 177-95.

On the theory of recollection (73c-75).

Apolloni, D. “Plato’s Affinity Argument for the Immortality of the Soul.” Journal of the History of Philosophy 34 (1996) 5-32.

A study of the argument at 78b-80d.

Gallop, D. “Plato’s ‘Cyclical Argument’ Recycled.” Phronesis 27 (1982) 207-222.

On the first argument for the soul’s immortality (69e-72e) and its relation to the other arguments.

Matthen, M. “Forms and Participants in Plato’s Phaedo.” Noûs 18:2 (1984) 281-297.

Discusses Plato’s argument concerning equals at 74b7-c6.

Nehamas, A. “Plato on the Imperfection of the Sensible World,” in G. Fine, ed., Plato 1: Metaphysics and Epistemology. Oxford, 1999. 171-191.

On Plato’s view of sensible particulars, especially at 72e-78b.

d. Objections from Simmias and Cebes, and Socrates’ Response (84c-107b)

Frede, D. “The Final Proof of the Immortality of the Soul in Plato’s Phaedo 102a-107a.” Phronesis 23 (1978) 27-41.

A defense of Plato’s argument and examination of its underlying assumptions regarding the soul.

Gottschalk, H.D. “Soul as Harmonia.” Phronesis 16 (1971) 179-198.

Discusses Simmias’ account of the soul beginning at 85e.

Vlastos, G. “Reasons and Causes in the Phaedo,” in Plato: A Collection of Critical Essays, Vol. I: Metaphysics and Epistemology. Garden City, NY: Anchor Books, 1971.

Are Forms causes? An examination of 95e-105c.

Wiggins, D. “Teleology and the Good in Plato’s Phaedo.” Oxford Studies in Ancient Philosophy 4 (1986) 1-18.

On Socrates’ “second voyage” beginning at 99c2-d1.

e. The Myth about the Afterlife (107c-115a)

Annas, J. “Plato’s Myths of Judgment.” Phronesis 27 (1982) 119-43.

A study of Plato’s myths in the Gorgias, Phaedo, and Republic.

Morgan, K.A. Myth and Philosophy from the pre-Socratics to Plato. Cambridge, 2000.

Includes extensive background on myth in Plato, as well as discussion of the Phaedo myth in particular.

Sedley, D. “Teleology and Myth in the Phaedo.” Proceedings of the Boston Area Colloquium in Ancient Philosophy 5 (1990) 359–83.

f. Socrates’ Death (115a-118a)

Crook, J. “Socrates’ Last Words: Another Look at an Ancient Riddle.” Classical Quarterly 48 (1998) 117-125.

The papers by Crook and Most (cited below) consider some puzzles regarding Socrates’ final words at the dialogue’s end.

Gill, C. “The Death of Socrates.” Classical Quarterly 23 (1973) 25-25.

On the finer details of hemlock-poisoning.

Most, G.W. “A Cock for Asclepius.” Classical Quarterly 43 (1993) 96-111.
Stewart, D. “Socrates’ Last Bath.” Journal of the History of Philosophy 10 (1972) 253-9.

Looks at the deeper meaning of Socrates’ bath at 116a.

Wilson, E. The Death of Socrates. Harvard University Press, 2007.

Includes discussion of the death scene in the Phaedo, as well as its subsequent reception in Western philosophy, art, and culture.

Author Information

Tim Connolly
Email: tconnolly@po-box.esu.edu
East Stroudsburg University
U. S. A.

Plato: Political Philosophy

Plato (c. 427-347 B.C.E.) developed such distinct areas of philosophy as epistemology, metaphysics, ethics, and aesthetics. His deep influence on Western philosophy is asserted in the famous remark of Alfred North Whitehead: “the safest characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.” He was also the prototypical political philosopher whose ideas had a profound impact on subsequent political theory. His greatest impact was Aristotle, but he influenced Western political thought in many ways. The Academy, the school he founded in 385 B.C.E., became the model for other schools of higher learning and later for European universities.The philosophy of Plato is marked by the usage of dialectic, a method of discussion involving ever more profound insights into the nature of reality, and by cognitive optimism, a belief in the capacity of the human mind to attain the truth and to use this truth for the rational and virtuous ordering of human affairs. Plato believes that conflicting interests of different parts of society can be harmonized. The best, rational and righteous, political order, which he proposes, leads to a harmonious unity of society and allows each of its parts to flourish, but not at the expense of others. The theoretical design and practical implementation of such order, he argues, are impossible without virtue.

1. Life - from Politics to Philosophy

Plato was born in Athens in c. 427 B.C.E. Until his mid-twenties, Athens was involved in a long and disastrous military conflict with Sparta, known as the Peloponnesian War. Coming from a distinguished family - on his father’s side descending from Codrus, one of the early kings of Athens, and on his mother’s side from Solon, the prominent reformer of the Athenian constitution - he was naturally destined to take an active role in political life. But this never happened. Although cherishing the hope of assuming a significant place in his political community, he found himself continually thwarted. As he relates in his autobiographical Seventh Letter, he could not identify himself with any of the contending political parties or the succession of corrupt regimes, each of which brought Athens to further decline (324b-326a). He was a pupil of Socrates, whom he considered the most just man of his time, and who, although did not leave any writings behind, exerted a large influence on philosophy. It was Socrates who, in Cicero’s words, “called down philosophy from the skies.” The pre-Socratic philosophers were mostly interested in cosmology and ontology; Socrates’ concerns, in contrast, were almost exclusively moral and political issues. In 399 when a democratic court voted by a large majority of its five hundred and one jurors for Socrates’ execution on an unjust charge of impiety, Plato came to the conclusion that all existing governments were bad and almost beyond redemption. “The human race will have no respite from evils until those who are really philosophers acquire political power or until, through some divine dispensation, those who rule and have political authority in the cities become real philosophers” (326a-326b).

It was perhaps because of this opinion that he retreated to his Academy and to Sicily for implementing his ideas. He visited Syracuse first in 387, then in 367, and again in 362-361, with the general purpose to moderate the Sicilian tyrants with philosophical education and to establish a model political rule. But this adventure with practical politics ended in failure, and Plato went back to Athens. His Academy, which provided a base for succeeding generations of Platonic philosophers until its final closure in C.E. 529, became the most famous teaching institution of the Hellenistic world. Mathematics, rhetoric, astronomy, dialectics, and other subjects, all seen as necessary for the education of philosophers and statesmen, were studied there. Some of Plato’s pupils later became leaders, mentors, and constitutional advisers in Greek city-states. His most renowned pupil was Aristotle. Plato died in c. 347 B.C.E. During his lifetime, Athens turned away from her military and imperial ambitions and became the intellectual center of Greece. She gave host to all the four major Greek philosophical schools founded in the course of the fourth century: Plato’s Academy, Aristotle’s Lyceum, and the Epicurean and Stoic schools.

2. The Threefold Task of Political Philosophy

Although the Republic, the Statesman, the Laws and a few shorter dialogues are considered to be the only strictly political dialogues of Plato, it can be argued that political philosophy was the area of his greatest concern. In the English-speaking world, under the influence of twentieth century analytic philosophy, the main task of political philosophy today is still often seen as conceptual analysis: the clarification of political concepts. To understand what this means, it may be useful to think of concepts as the uses of words. When we use general words, such as “table,” “chair,” “pen,” or political terms, such as “state,” “power,” “democracy,” or “freedom,” by applying them to different things, we understand them in a certain way, and hence assign to them certain meanings. Conceptual analysis then is a mental clearance, the clarification of a concept in its meaning. As such it has a long tradition and is first introduced in Platonic dialogues. Although the results are mostly inconclusive, in “early” dialogues especially, Socrates tries to define and clarify various concepts. However, in contrast to what it is for some analytic philosophers, for Plato conceptual analysis is not an end to itself, but a preliminary step. The next step is critical evaluation of beliefs, deciding which one of the incompatible ideas is correct and which one is wrong. For Plato, making decisions about the right political order are, along with the choice between peace and war, the most important choices one can make in politics. Such decisions cannot be left solely to public opinion, he believes, which in many cases does not have enough foresight and gets its lessons only post factum from disasters recorded in history. In his political philosophy, the clarification of concepts is thus a preliminary step in evaluating beliefs, and right beliefs in turn lead to an answer to the question of the best political order. The movement from conceptual analysis, through evaluation of beliefs, to the best political order can clearly be seen in the structure of Plato’s Republic.

3. The Quest for Justice in The Republic

One of the most fundamental ethical and political concepts is justice. It is a complex and ambiguous concept. It may refer to individual virtue, the order of society, as well as individual rights in contrast to the claims of the general social order. In Book I of the Republic, Socrates and his interlocutors discuss the meaning of justice. Four definitions that report how the word “justice” (dikaiosune) is actually used, are offered. The old man of means Cephalus suggests the first definition. Justice is “speaking the truth and repaying what one has borrowed” (331d). Yet this definition, which is based on traditional moral custom and relates justice to honesty and goodness; i.e. paying one’s debts, speaking the truth, loving one’s country, having good manners, showing proper respect for the gods, and so on, is found to be inadequate. It cannot withstand the challenge of new times and the power of critical thinking. Socrates refutes it by presenting a counterexample. If we tacitly agree that justice is related to goodness, to return a weapon that was borrowed from someone who, although once sane, has turned into a madman does not seem to be just but involves a danger of harm to both sides. Cephalus’ son Polemarchus, who continues the discussion after his father leaves to offer a sacrifice, gives his opinion that the poet Simonides was correct in saying that it was just “to render to each his due” (331e). He explains this statement by defining justice as “treating friends well and enemies badly” (332d). Under the pressure of Socrates’ objections that one may be mistaken in judging others and thus harm good people, Polemarchus modifies his definition to say that justice is “to treat well a friend who is good and to harm an enemy who is bad” (335a). However, when Socrates finally objects that it cannot be just to harm anyone, because justice cannot produce injustice, Polemarchus is completely confused. He agrees with Socrates that justice, which both sides tacitly agree relates to goodness, cannot produce any harm, which can only be caused by injustice. Like his father, he withdraws from the dialogue. The careful reader will note that Socrates does not reject the definition of justice implied in the saying of Simonides, who is called a wise man, namely, that “justice is rendering to each what befits him” (332b), but only its explication given by Polemarchus. This definition is, nevertheless, found unclear.

The first part of Book I of the Republic ends in a negative way, with parties agreeing that none of the definitions provided stands up to examination and that the original question “What is justice?” is more difficult to answer than it seemed to be at the outset. This negative outcome can be seen as a linguistic and philosophical therapy. Firstly, although Socrates’ objections to given definitions can be challenged, it is shown, as it stands, that popular opinions about justice involve inconsistencies. They are inconsistent with other opinions held to be true. The reportive definitions based on everyday usage of the word “justice” help us perhaps to understand partially what justice means, but fail to provide a complete account of what is justice. These definitions have to be supplied by a definition that will assist clarity and establish the meaning of justice. However, to propose such an adequate definition one has to know what justice really is. The way people define a given word is largely determined by the beliefs which they hold about the thing referred to by this word. A definition that is merely arbitrary or either too narrow or too broad, based on a false belief about justice, does not give the possibility of communication. Platonic dialogues are expressions of the ultimate communication that can take place between humans; and true communication is likely to take place only if individuals can share meanings of the words they use. Communication based on false beliefs, such as statements of ideology, is still possible, but seems limited, dividing people into factions, and, as history teaches us, can finally lead only to confusion. The definition of justice as “treating friends well and enemies badly” is for Plato not only inadequate because it is too narrow, but also wrong because it is based on a mistaken belief of what justice is, namely, on the belief grounded in factionalism, which Socrates does not associate with the wise ones but with tyrants (336a). Therefore, in the Republic, as well as in other Platonic dialogues, there is a relationship between conceptual analysis and critical evaluation of beliefs. The goals of these conversations are not merely linguistic, to arrive at an adequate verbal definition, but also substantial, to arrive at a right belief. The question “what is justice” is not only about linguistic usage of the word “justice,” but primarily about the thing to which the word refers. The focus of the second part of Book I is no longer clarification of concepts, but evaluation of beliefs.

In Platonic dialogues, rather than telling them what they have to think, Socrates is often getting his interlocutors to tell him what they think. The next stage of the discussion of the meaning of justice is taken over by Thrasymachus, a sophist, who violently and impatiently bursts into the dialogue. In the fifth and fourth century B.C.E., the sophists were paid teachers of rhetoric and other practical skills, mostly non-Athenians, offering courses of instruction and claiming to be best qualified to prepare young men for success in public life. Plato describes the sophists as itinerant individuals, known for their rhetorical abilities, who reject religious beliefs and traditional morality, and he contrasts them with Socrates, who as a teacher would refuse to accept payment and instead of teaching skills would commit himself to a disinterested inquiry into what is true and just. In a contemptuous manner, Thrasymachus asks Socrates to stop talking nonsense and look into the facts. As a clever man of affairs, he gives an answer to the question of “what is justice” by deriving justice from the city’s configuration of power and making it relative to the interests of the dominant social or political group. “Justice is nothing else than the interest of the stronger” (338c). Now, by contrast to what some commentators say, the statement that Thrasymachus offers as an answer to Socrates’ question about justice is not a definition. The careful reader will notice that Thrasymachus identifies justice with either maintenance or observance of law. His statement is an expression of his belief that, in the world imperfect as it is, the ruling element in the city, or as we would say today the dominant political or social group, institutes laws and governs for its own benefit (338d). The democrats make laws in support of democracy; the aristocrats make laws that support the government of the well-born; the propertied make laws that protect their status and keep their businesses going; and so on. This belief implies, firstly, that justice is not a universal moral value but a notion relative to expediency of the dominant status quo group; secondly, that justice is in the exclusive interest of the dominant group; thirdly, that justice is used as a means of oppression and thus is harmful to the powerless; fourthly, that there is neither any common good nor harmony of interests between those who are in a position of power and those who are not. All there is, is a domination by the powerful and privileged over the powerless. The moral language of justice is used merely instrumentally to conceal the interests of the dominant group and to make these interests appear universal. The powerful “declare what they have made - what is to their own advantage - to be just” (338e). The arrogance with which Thrasymachus makes his statements suggests that he strongly believes that to hold a different view from his own would be to mislead oneself about the world as it is.

After presenting his statement, Thrasymachus intends to leave as if he believed that what he said was so compelling that no further debate about justice was ever possible (344d). In the Republic he exemplifies the power of a dogma. Indeed he presents Socrates with a powerful challenge. Yet, whether or not what he said sounds attractive to anyone, Socrates is not convinced by the statement of his beliefs. Beliefs shape our lives as individuals, nations, ages, and civilizations. Should we really believe that “justice [obeying laws] is really the good of another, the advantage of the stronger and the ruler, harmful to the one who obeys, while injustice [disobeying laws] is in one’s own advantage” (343c)? The discussion between Socrates and his interlocutors is no longer about the meaning of “justice.” It is about fundamental beliefs and “concerns no ordinary topic but the way we ought to live” (352d). Although in Book I Socrates finally succeeds in showing Thrasymachus that his position is self-contradictory and Thrasymachus withdraws from the dialogue, perhaps not fully convinced, yet red-faced, in Book II Thrasymachus’ argument is taken over by two young intellectuals, Plato’s brothers, Glaucon and Adeimantus, who for the sake of curiosity and a playful intellectual exercise push it to the limit (358c-366d). Thrasymachus withdraws, but his statement: moral skepticism and relativism, predominance of power in human relations, and non-existence of the harmony of interests, hovers over the Western mind. It takes whole generations of thinkers to struggle with Thrasymachus’ beliefs, and the debate still continues. It takes the whole remainder of the Republic to present an argument in defense of justice as a universal value and the foundation of the best political order.

4. The Best Political Order

Although large parts of the Republic are devoted to the description of an ideal state ruled by philosophers and its subsequent decline, the chief theme of the dialogue is justice. It is fairly clear that Plato does not introduce his fantastical political innovation, which Socrates describes as a city in speech, a model in heaven, for the purpose of practical implementation (592a-b). The vision of the ideal state is used rather to illustrate the main thesis of the dialogue that justice, understood traditionally as virtue and related to goodness, is the foundation of a good political order, and as such is in everyone’s interest. Justice, if rightly understood, Plato argues, is not to the exclusive advantage of any of the city’s factions, but is concerned with the common good of the whole political community, and is to the advantage of everyone. It provides the city with a sense of unity, and thus, is a basic condition for its health. “Injustice causes civil war, hatred, and fighting, while justice brings friendship and a sense of common purpose” (351d). In order to understand further what justice and political order are for Plato, it is useful to compare his political philosophy with the pre-philosophical insights of Solon, who is referred to in a few dialogues. Biographical information about Plato is fairly scarce. The fact that he was related through his mother to this famous Athenian legislator, statesman and poet, regarded as one of the “Seven Sages,” may be treated as merely incidental. On the other hand, taking into consideration that in Plato’s times education would have been passed on to children informally at home, it seems highly probable that Plato was not only well acquainted with the deeds and ideas of Solon, but that these deeply influenced him.

The essence of the constitutional reform which Solon made in 593 B.C.E., over one hundred and fifty years before Plato’s birth, when he became the Athenian leader, was the restoration of righteous order, eunomia. In the early part of the sixth century Athens was disturbed by a great tension between two parties: the poor and the rich, and stood at the brink of a fierce civil war. On the one hand, because of an economic crisis, many poorer Athenians were hopelessly falling into debt, and since their loans were often secured by their own persons, thousands of them were put into serfdom. On the other hand, lured by easy profits from loans, the rich stood firmly in defense of private property and their ancient privileges. The partisan strife, which seemed inevitable, would make Athens even more weak economically and defenseless before external enemies. Appointed as a mediator in this conflict, Solon enacted laws prohibiting loans on the security of the person. He lowered the rate of interest, ordered the cancellation of all debts, and gave freedom to serfs. He acted so moderately and impartially that he became unpopular with both parties. The rich felt hurt by the reform. The poor, unable to hold excess in check, demanded a complete redistribution of landed property and the dividing of it into equal shares. Nevertheless, despite these criticisms from both sides, Solon succeeded in gaining social peace. Further, by implementing new constitutional laws, he set up a “mighty shield against both parties and did not allow either to win an unjust victory” (Aristotle, The Athenian Constitution). He introduced a system of checks and balances which would not favor any side, but took into consideration legitimate interests of all social groups. In his position, he could easily have become the tyrant over the city, but he did not seek power for himself. After he completed his reform, he left Athens in order to see whether it would stand the test of time, and returned to his country only ten years later. Even though in 561 Pisistratus seized power and became the first in a succession of Athenian tyrants, and in 461 the democratic leader Ephialtes abolished the checks upon popular sovereignty, Solon’s reform provided the ancient Greeks with a model of both political leadership and order based on impartiality and fairness. Justice for Solon is not an arithmetical equality: giving equal shares to all alike irrespective of merit, which represents the democratic concept of distributive justice, but it is equity or fairness based on difference: giving shares proportionate to the merit of those who receive them. The same ideas of political order, leadership, and justice can be found in Plato’s dialogues.

For Plato, like for Solon, the starting point for the inquiry about the best political order is the fact of social diversity and conflicting interests, which involve the danger of civil strife. The political community consists of different parts or social classes, such as the noble, the rich, and the poor, each representing different values, interests, and claims to rule. This gives rise to the controversy of who should rule the community, and what is the best political system. In both the Republic and the Laws, Plato asserts not only that factionalism and civil war are the greatest dangers to the city, more dangerous even than war against external enemies, but also that peace obtained by the victory of one part and the destruction of its rivals is not to be preferred to social peace obtained through the friendship and cooperation of all the city’s parts (Republic 462a-b, Laws 628a-b). Peace for Plato is, unlike for Marxists and other radical thinkers, not a status quo notion, related to the interest of the privileged group, but a value that most people usually desire. He does not stand for war and the victory of one class, but for peace in social diversity. “The best is neither war nor faction - they are things we should pray to be spared from - but peace and mutual good will” (628c). Building on the pre-philosophical insights of Solon and his concept of balancing conflicting interests, in both the Republic and the Laws, Plato offers two different solutions to the same problem of social peace based on the equilibrium and harmonious union of different social classes. If in the Republic it is the main function of the political leadership of philosopher-rulers to make the civil strife cease, in the Laws this mediating function is taken over by laws. The best political order for Plato is that which promotes social peace in the environment of cooperation and friendship among different social groups, each benefiting from and each adding to the common good. The best form of government, which he advances in the Republic, is a philosophical aristocracy or monarchy, but that which he proposes in his last dialogue the Laws is a traditional polity: the mixed or composite constitution that reconciles different partisan interests and includes aristocratic, oligarchic, and democratic elements.

5. The Government of Philosopher Rulers

It is generally believed today that democracy, “government of the people by the people and for the people,” is the best and only fully justifiable political system. The distinct features of democracy are freedom and equality. Democracy can be described as the rule of the free people who govern themselves, either directly or though their representatives, in their own interest. Why does Plato not consider democracy the best form of government? In the Republic he criticizes the direct and unchecked democracy of his time precisely because of its leading features (557a-564a). Firstly, although freedom is for Plato a true value, democracy involves the danger of excessive freedom, of doing as one likes, which leads to anarchy. Secondly, equality, related to the belief that everyone has the right and equal capacity to rule, brings to politics all kinds of power-seeking individuals, motivated by personal gain rather than public good. Democracy is thus highly corruptible. It opens gates to demagogues, potential dictators, and can thus lead to tyranny. Hence, although it may not be applicable to modern liberal democracies, Plato’s main charge against the democracy he knows from the ancient Greek political practice is that it is unstable, leading from anarchy to tyranny, and that it lacks leaders with proper skill and morals. Democracy depends on chance and must be mixed with competent leadership (501b). Without able and virtuous leaders, such as Solon or Pericles, who come and go by chance, it is not a good form of government. But even Pericles, who as Socrates says made people “wilder” rather than more virtuous, is considered not to be the best leader (Gorgias, 516c). If ruling a state is a craft, indeed statecraft, Plato argues, then politics needs expert rulers, and they cannot come to it merely by accident, but must be carefully selected and prepared in the course of extensive training. Making political decisions requires good judgment. Politics needs competence, at least in the form of today’s civil servants. Who then should the experts be and why? Why does Plato in the Republic decide to hand the steering wheel of the state to philosophers?

In spite of the idealism with which he is usually associated, Plato is not politically naive. He does not idealize, but is deeply pessimistic about human beings. Most people, corrupted as they are, are for him fundamentally irrational, driven by their appetites, egoistic passions, and informed by false beliefs. If they choose to be just and obey laws, it is only because they lack the power to act criminally and are afraid of punishment (Republic, 359a). Nevertheless, human beings are not vicious by nature. They are social animals, incapable of living alone (369a-b). Living in communities and exchanging products of their labor is natural for them, so that they have capacities for rationality and goodness. Plato, as later Rousseau, believes that once political society is properly ordered, it can contribute to the restoration of morals. A good political order, good education and upbringing can produce “good natures; and [these] useful natures, who are in turn well educated, grow up even better than their predecessors” (424a). Hence, there are in Plato such elements of the idealistic or liberal world view as the belief in education and progress, and a hope for a better future. The quality of human life can be improved if people learn to be rational and understand that their real interests lie in harmonious cooperation with one another, and not in war or partisan strife. However, unlike Rousseau, Plato does not see the best social and political order in a democratic republic. Opinions overcome truth in everyday life. Peoples’ lives and the lives of communities are shaped by the prevailing beliefs. If philosophers are those who can distinguish between true and false beliefs, who love knowledge and are motivated by the common good, and finally if they are not only master-theoreticians, but also the master-practitioners who can heal the ills of their society, then they, and not democratically elected representatives, must be chosen as leaders and educators of the political community and guide it to proper ends. They are required to counteract the destabilizing effects of false beliefs on society. Are philosophers incorruptible? In the ideal city there are provisions to minimize possible corruption, even among the good-loving philosophers. They can neither enjoy private property nor family life. Although they are the rulers, they receive only a modest remuneration from the state, dine in common dining halls, and have wives and children in common. These provisions are necessary, Plato believes, because if the philosopher-rulers were to acquire private land, luxurious homes, and money themselves, they would soon become hostile masters of other citizens rather than their leaders and allies (417a-b). The ideal city becomes a bad one, described as timocracy, precisely when the philosophers neglect music and physical exercise, and begin to gather wealth (547b).

To be sure, Plato’s philosophers, among whom he includes both men and women, are not those who can usually be found today in departments of philosophy and who are described as the “prisoners who take refuge in a temple” (495a). Initially chosen from among the brightest, most stable, and most courageous children, they go through a sophisticated and prolonged educational training which begins with gymnastics, music and mathematics, and ends with dialectic, military service and practical city management. They have superior theoretical knowledge, including the knowledge of the just, noble, good and advantageous, but are not inferior to others in practical matters as well (484d, 539e). Being in the final stage of their education illuminated by the idea of the good, they are those who can see beyond changing empirical phenomena and reflect on such timeless values as justice, beauty, truth, and moderation (501b, 517b). Goodness is not merely a theoretical idea for them, but the ultimate state of their mind. If the life of the philosopher-rulers is not of private property, family or wealth, nor even of honor, and if the intellectual life itself seems so attractive, why should they then agree to rule? Plato’s answer is in a sense a negative one. Philosophical life, based on contemplative leisure and the pleasure of learning, is indeed better and happier than that of ruling the state (519d). However, the underlying idea is not to make any social class in the city the victorious one and make it thus happy, but “to spread happiness throughout the city by bringing the citizens into harmony with each other ... and by making them share with each other the benefits that each class can confer on the community” (519e). Plato assumes that a city in which the rulers do not govern out of desire for private gain, but are least motivated by personal ambition, is governed in the way which is the finest and freest from civil strife (520d). Philosophers will rule not only because they will be best prepared for this, but also because if they do not, the city will no longer be well governed and may fall prey to economic decline, factionalism, and civil war. They will approach ruling not as something really enjoyable, but as something necessary (347c-d).

Objections against the government of philosopher-rulers can be made. Firstly, because of the restrictions concerning family and private property, Plato is often accused of totalitarianism. However, Plato’s political vision differs from a totalitarian state in a number of important aspects. Especially in the Laws he makes clear that freedom is one of the main values of society (701d). Other values for which Plato stands include justice, friendship, wisdom, courage, and moderation, and not factionalism or terror that can be associated with a totalitarian state. The restrictions which he proposes are placed on the governors, rather than on the governed. Secondly, one can argue that there may obviously be a danger in the self-professed claim to rule of the philosophers. Individuals may imagine themselves to be best qualified to govern a country, but in fact they may lose contact with political realities and not be good leaders at all. If philosopher-rulers did not have real knowledge of their city, they would be deprived of the essential credential that is required to make their rule legitimate, namely, that they alone know how best to govern. Indeed, at the end of Book VII of the Republic where philosophers’ education is discussed, Socrates says: “I forgot that we were only playing, and so I spoke too vehemently” (536b), as if to imply that objections can be made to philosophical rule. As in a few other places in the dialogue, Plato throws his political innovation open to doubt. However, in Plato’s view, philosopher-rulers do not derive their authority solely from their expert knowledge, but also from their love of the city as a whole and their impartiality and fairness. Their political authority is not only rational but also substantially moral, based on the consent of the governed. They regard justice as the most important and most essential thing (540e). Even if particular political solutions presented in the Republic may be open to questioning, what seems to stand firm is the basic idea that underlies philosophers’ governance and that can be traced back to Solon: the idea of fairness based on difference as the basis of the righteous political order. A political order based on fairness leads to friendship and cooperation among different parts of the city.

For Plato, as for Solon, government exists for the benefit of all citizens and all social classes, and must mediate between potentially conflicting interests. Such a mediating force is exercised in the ideal city of the Republic by the philosopher-rulers. They are the guarantors of the political order that is encapsulated in the norm that regulates just relations of persons and classes within the city and is expressed by the phrase: “doing one’s own work and not meddling with what isn’t one’s own” (433a-b). If justice is related to equality, the notion of equality is indeed preserved in Plato’s view of justice expressed by this norm as the impartial, equal treatment of all citizens and social groups. It is not the case that Plato knew that his justice meant equality but really made inequality, as Karl Popper (one of his major critics) believed. In the ideal city all persons and social groups are given equal opportunities to be happy, that is, to pursue happiness, but not at the expense of others. Their particular individual, group or class happiness is limited by the need of the happiness for all. The happiness of the whole city is not for Plato the happiness of an abstract unity called the polis, or the happiness of the greatest number, but rather the happiness of all citizens derived from a peaceful, harmonious, and cooperative union of different social classes. According to the traditional definition of justice by Simonides from Book I, which is reinterpreted in Book IV, as “doing one’s own work,” each social class receives its proper due in the distribution of benefits and burdens. The philosopher-rulers enjoy respect and contemplative leisure, but not wealth or honors; the guardian class, the second class in the city, military honors, but not leisure or wealth; and the producer class, family life, wealth, and freedom of enterprise, but not honors or rule. Then, the producers supply the city with goods; the guardians, defend it; and the philosophers, attuned to virtue and illuminated by goodness, rule it impartially for the common benefit of all citizens. The three different social classes engage in mutually beneficial enterprise, by which the interests of all are best served. Social and economic differences, i.e. departures from equality, bring about benefits to people in all social positions, and therefore, are justified. In the Platonic vision of the Republic, all social classes get to perform what they are best fit to do and are unified into a single community by mutual interests. In this sense, although each are different, they are all friends.

6. Politics and the Soul

It can be contended that the whole argument of the Republic is made in response to the denial of justice as a universal moral value expressed in Thrasymachus’ statement: “Justice is nothing else than the interest of the stronger.” Moral relativism, the denial of the harmony of interests, and other problems posed by this statement are a real challenge for Plato for whom justice is not merely a notion relative to the existing laws instituted by the victorious factions in power. In the Laws a similar statement is made again (714c), and it is interpreted as the right of the strong, the winner in a political battle (715a). By such interpretation, morality is denied and the right to govern, like in the “Melian Dialogue” of Thucydides, is equated simply with might. The decisions about morals and justice which we make are for Plato “no trifle, but the foremost thing” (714b). The answer to the question of what is right and what is wrong can entirely determine our way of life, as individuals and communities. If Plato’s argument about justice presented in both the Republic and the Laws can be summarized in just one sentence, the sentence will say: “Justice is neither the right of the strong nor the advantage of the stronger, but the right of the best and the advantage of the whole community.” The best, as explained in the Republic, are the expert philosophical rulers. They, the wise and virtuous, free from faction and guided by the idea of the common good, should rule for the common benefit of the whole community, so that the city will not be internally divided by strife, but one in friendship (Republic, 462a-b). Then, in the Laws, the reign of the best individuals is replaced by the reign of the finest laws instituted by a judicious legislator (715c-d). Throughout this dialogue Plato’s guiding principle is that the good society is a harmonious union of different social elements that represent two key values: wisdom and freedom (701d). The best laws assure that all the city’s parts: the democratic, the oligarchic, and the aristocratic, are represented in political institutions: the popular Assembly, the elected Council, and the Higher Council, and thus each social class receives its due expression. Still, a democratic skeptic can feel dissatisfied with Plato’s proposal to grant the right to rule to the best, either individuals or laws, even on the basis of tacit consent of the governed. The skeptic may believe that every adult is capable of exercising the power of self-direction, and should be given the opportunity to do so. He will be prepared to pay the costs of eventual mistakes and to endure an occasional civil unrest or even a limited war rather than be directed by anyone who may claim superior wisdom. Why then should Plato’s best constitution be preferable to democracy? In order to fully explain the Platonic political vision, the meaning of “the best” should be further clarified.

In the short dialogue Alcibiades I, little studied today and thought by some scholars as not genuine, though held in great esteem by the Platonists of antiquity, Socrates speaks with Alcibiades. The subject of their conversation is politics. Frequently referred to by Thucydides in the History of the Peloponnesian War, Alcibiades, the future leader of Athens, highly intelligent and ambitious, largely responsible for the Athenian invasion of Sicily, is at the time of conversation barely twenty years old. The young, handsome, and well-born Alcibiades of the dialogue is about to begin his political career and to address the Assembly for the first time (105a-b). He plans to advise the Athenians on the subject of peace and war, or some other important affair (107d). His ambitions are indeed extraordinary. He does not want just to display his worth before the people of Athens and become their leader, but to rule over Europe and Asia as well (105c). His dreams resemble that of the future Alexander the Great. His claim to rule is that he is the best. However, upon Socrates’ scrutiny, it becomes apparent that young Alcibiades knows neither what is just, nor what is advantageous, nor what is good, nor what is noble, beyond what he has learned from the crowd (110d-e, 117a). His world-view is based on unexamined opinions. He appears to be the worst type of ignorant person who pretends that he knows something but does not. Such ignorance in politics is the cause of mistakes and evils (118a). What is implied in the dialogue is that noble birth, beautiful looks, and even intelligence and power, without knowledge, do not give the title to rule. Ignorance, the condition of Alcibiades, is also the condition of the great majority of the people (118b-c). Nevertheless, Socrates promises to guide Alcibiades, so that he becomes excellent and renowned among the Greeks (124b-c). In the course of further conversation, it turns out that one who is truly the best does not only have knowledge of political things, rather than an opinion about them, but also knows one’s own self and is a beautiful soul. He or she is perfect in virtue. The riches of the world can be entrusted only to those who “take trouble over” themselves (128d), who look “toward what is divine and bright” (134d), and who following the supreme soul, God, the finest mirror of their own image (133c), strive to be as beautiful and wealthy in their souls as possible (123e, 131d). The best government can be founded only on beautiful and well-ordered souls.

In a few dialogues, such as Phaedo, the Republic, Phaedrus, Timaeus, and the Laws, Plato introduces his doctrine of the immortality of the soul. His ultimate answer to the question “Who am I?” is not an “egoistic animal” or an “independent variable,” as the twentieth century behavioral researcher blatantly might say, but an “immortal soul, corrupted by vice and purified by virtue, of whom the body is only an instrument” (129a-130c). Expert political knowledge for him should include not only knowledge of things out there, but also knowledge of oneself. This is because whoever is ignorant of himself will also be ignorant of others and of political things, and, therefore, will never be an expert politician (133e). Those who are ignorant will go wrong, moving from one misery to another (134a). For them history will be a tough teacher, but as long they do not recognize themselves and practice virtue, they will learn nothing. Plato’s good society is impossible without transcendence, without a link to the perfect being who is God, the true measure of all things. It is also impossible without an ongoing philosophical reflection on whom we truly are. Therefore, democracy would not be a good form of government for him unless, as it is proposed in the Laws, the element of freedom is mixed with the element of wisdom, which includes ultimate knowledge of the self. Unmixed and unchecked democracy, marked by the general permissiveness that spurs vices, makes people impious, and lets them forget about their true self, is only be the second worst in the rank of flawed regimes after tyranny headed by a vicious individual. This does not mean that Plato would support a theocratic government based on shallow religiosity and religious hypocrisy. There is no evidence for this. Freedom of speech, forming opinions and expressing them, which may be denied in theocracy, is a true value for Plato, along with wisdom. It is the basic requirement for philosophy. In shallow religiosity, like in atheism, there is ignorance and no knowledge of the self either. In Book II of the Republic, Plato criticizes the popular religious beliefs of the Athenians, who under the influence of Homer and Hesiod attribute vices to the gods and heroes (377d-383c). He tries to show that God is the perfect being, the purest and brightest, always the same, immortal and true, to whom we should look in order to know ourselves and become pure and virtuous (585b-e). God, and not human beings, is the measure of political order (Laws, 716c).

7. Plato’s Achievement

Plato’s greatest achievement may be seen firstly in that he, in opposing the sophists, offered to decadent Athens, which had lost faith in her old religion, traditions, and customs, a means by which civilization and the city’s health could be restored: the recovery of order in both the polis and the soul.

The best, rational and righteous political order leads to the harmonious unity of a society and allows all the city’s parts to pursue happiness but not at the expense of others. The characteristics of a good political society, of which most people can say “it is mine” (462c), are described in the Republic by four virtues: justice, wisdom, moderation, and courage. Justice is the equity or fairness that grants each social group its due and ensures that each “does one’s own work” (433a). The three other virtues describe qualities of different social groups. Wisdom, which can be understood as the knowledge of the whole, including both knowledge of the self and political prudence, is the quality of the leadership (428e-429a). Courage is not merely military courage but primarily civic courage: the ability to preserve the right, law-inspired belief, and stand in defense of such values as friendship and freedom on which a good society is founded. It is the primary quality of the guardians (430b). Finally, moderation, a sense of the limits that bring peace and happiness to all, is the quality of all social classes. It expresses the mutual consent of both the governed and the rulers as to who should rule (431d-432a). The four virtues of the good society describe also the soul of a well-ordered individual. Its rational part, whose quality is wisdom, nurtured by fine words and learning, should together with the emotional or spirited part, cultivated by music and rhythm, rule over the volitional or appetitive part (442a). Under the leadership of the intellect, the soul must free itself from greed, lust, and other degrading vices, and direct itself to the divine. The liberation of the soul from vice is for Plato the ultimate task of humans on earth. Nobody can be wicked and happy (580a-c). Only a spiritually liberated individual, whose soul is beautiful and well ordered, can experience true happiness. Only a country ordered according to the principles of virtue can claim to have the best system of government.

Plato’s critique of democracy may be considered by modern readers as not applicable to liberal democracy today. Liberal democracies are not only founded on considerations of freedom and equality, but also include other elements, such as the rule of law, multiparty systems, periodic elections, and a professional civil service. Organized along the principle of separation of powers, today’s Western democracy resembles more a revised version of mixed government, with a degree of moderation and competence, rather than the highly unstable and unchecked Athenian democracy of the fourth and fifth century B.C.E., in which all governmental policies were directly determined by the often changing moods of the people. However, what still seems to be relevant in Plato’s political philosophy is that he reminds us of the moral and spiritual dimension of political life. He believes that virtue is the lifeblood of any good society.

Moved by extreme ambitions, the Athenians, like the mythological Atlantians described in the dialogue Critias, became infected by “wicked coveting and the pride of power” (121b). Like the drunken Alcibiades from the Symposium, who would swap “bronze for gold” and thus prove that he did not understand the Socratic teaching, they chose the “semblance of beauty,” the shining appearance of power and material wealth, rather than the “thing itself,” the being of perfection (Symposium, 218e). “To the seen eye they now began to seem foul, for they were losing the fairest bloom from their precious treasure, but to such who could not see the truly happy life, they would appear fair and blessed” (Critias, 121b). They were losing their virtuous souls, their virtue by which they could prove themselves to be worthy of preservation as a great nation. Racked by the selfish passions of greed and envy, they forfeited their conception of the right order. Their benevolence, the desire to do good, ceased. “Man and city are alike,” Plato claims (Republic, 577d). Humans without souls are hollow. Cities without virtue are rotten. To those who cannot see clearly they may look glorious but what appears bright is only exterior. To see clearly what is visible, the political world out there, Plato argues, one has first to perceive what is invisible but intelligible, the soul. One has to know oneself. Humans are immortal souls, he claims, and not just independent variables. They are often egoistic, but the divine element in them makes them more than mere animals. Friendship, freedom, justice, wisdom, courage, and moderation are the key values that define a good society based on virtue, which must be guarded against vice, war, and factionalism. To enjoy true happiness, humans must remain virtuous and remember God, the perfect being.

Plato’s achievement as a political philosopher may be seen in that he believed that there could be a body of knowledge whose attainment would make it possible to heal political problems, such as factionalism and the corruption of morals, which can bring a city to a decline. The doctrine of the harmony of interests, fairness as the basis of the best political order, the mixed constitution, the rule of law, the distinction between good and deviated forms of government, practical wisdom as the quality of good leadership, and the importance of virtue and transcendence for politics are the political ideas that can rightly be associated with Plato. They have profoundly influenced subsequent political thinkers.

Author Information

W. J. Korab-Karpowicz
Email: Sopot_Plato@hotmail.com
Anglo-American University of Prague
Czech Republic

Plato: The Republic

Since the mid-nineteenth century, the Republic has been Plato’s most famous and widely read dialogue. As in most other Platonic dialogues the main character is Socrates. It is generally accepted that the Republic belongs to the dialogues of Plato’s middle period. In Plato’s early dialogues, Socrates refutes the accounts of his interlocutors and the discussion ends with no satisfactory answer to the matter investigated. In the Republic however, we encounter Socrates developing a position on justice and its relation to eudaimonia (happiness). He provides a long and complicated, but unified argument, in defense of the just life and its necessary connection to the happy life.

The dialogue explores two central questions. The first question is “what is justice?” Socrates addresses this question both in terms of political communities and in terms of the individual person or soul. He does this to address the second and driving question of the dialogue: “is the just person happier than the unjust person?” or “what is the relation of justice to happiness?” Given the two central questions of the discussion, Plato’s philosophical concerns in the dialogue are ethical and political. In order to address these two questions, Socrates and his interlocutors construct a just city in speech, the Kallipolis. They do this in order to explain what justice is and then they proceed to illustrate justice by analogy in the human soul. On the way to defending the just life, Socrates considers a tremendous variety of subjects such as several rival theories of justice, competing views of human happiness, education, the nature and importance of philosophy and philosophers, knowledge, the structure of reality, the Forms, the virtues and vices, good and bad souls, good and bad political regimes, the family, the role of women in society, the role of art in society, and even the afterlife. This wide scope of the dialogue presents various interpretative difficulties and has resulted in thousands of scholarly works. In order to attempt to understand the dialogue’s argument as a whole one is required to grapple with these subjects.

Synopsis of the Republic

1. Synopsis of the Republic

a. Book I

Socrates and Glaucon visit the Piraeus to attend a festival in honor of the Thracian goddess Bendis (327a). They are led to Polemarchus’ house (328b). Socrates speaks to Cephalus about old age, the benefits of being wealthy, and justice (328e-331d). One would not claim that it is just to return weapons one owes to a mad friend (331c), thus justice is not being truthful and returning what one owes as Cephalus claims. The discussion between Socrates and Polemarchus follows (331d-336b).

Polemarchus claims that justice is helping one’s friends and harming one’s enemies and that this is what one owes people (332c). Socrates’ objections to Polemarchus’ definition are as follows: (i) Is this appropriate in medicine or cooking? So in what context is this the case? (332d)? (ii) The just person will also be good at useless things and at being unjust (333e). (iii) We often do not know who our friends and enemies are. Thus, we may treat those whom we only think are our friends or enemies well or badly. Would this be justice? (334c). (iv) It does not seem to be just to treat anyone badly, not even an enemy (335b). Discussion between Socrates and Thrasymachus follows (336b-354c).

Thrasymachus defines justice as the advantage or what is beneficial to the stronger (338c). Justice is different under different political regimes according to the laws, which are made to serve the interests of the strong (the ruling class in each regime, 338e-339a). Socrates requires clarification of the definition: does it mean that justice is what the stronger think is beneficial to them or what is actually beneficial to them (339b)? And don’t the strong rulers make mistakes and sometimes create laws that do not serve their advantage (339c)? Thrasymachus points out that the stronger are really only those who do not make mistakes as to what is to their advantage (340d). Socrates responds with a discussion of art or craft and points out that its aim is to do what is good for its subjects, not what is good for the practitioner (341c). Thrasymachus suggests that some arts, such as that of shepherds, do not do this but rather aim at the advantage of the practitioner (343c). He also adds the claim that injustice is in every way better than justice and that the unjust person who commits injustice undetected is always happier than the just person (343e-344c). The paradigm of the happy unjust person is the tyrant who is able to satisfy all his desires (344a-b). Socrates points out that the shepherd’s concern for his sheep is different from his concern to make money, which is extraneous to the art (345c) and that no power or art provides what is beneficial to itself (346e). Socrates claims that the best rulers are reluctant to rule but do so out of necessity: they do not wish to be ruled by someone inferior (347a-c).

Socrates offers three argument in favor of the just life over the unjust life: (i) the just man is wise and good, and the unjust man is ignorant and bad (349b); (ii) injustice produces internal disharmony which prevents effective actions (351b); (iii) virtue is excellence at a thing’s function and the just person lives a happier life than the unjust person, since he performs the various functions of the human soul well (352d). Socrates is dissatisfied with the discussion since an adequate account of justice is necessary before they can address whether the just life is better than the unjust life (354b).

b. Book II

Glaucon is not persuaded by the arguments in the previous discussion (357a). He divides good things into three classes: things good in themselves, things good both in themselves and for their consequences, and things good only for their consequences (357b-d). Socrates places justice in the class of things good in themselves and for their consequences.

Glaucon renews Thrasymachus’ argument to challenge Socrates to defend justice by itself without any consideration of what comes from it (358b ff.). Glaucon gives a speech defending injustice: (i) justice originates as a compromise between weak people who are afraid that suffering injustice is worse than doing it (358e-359a); (ii) people act justly because this is necessary and unavoidable, so justice is good only for its consequences (story of the ring of Gyges’ ancestor, 359c-360d); (iii) the unjust person with the reputation for justice is happier than the just person with the reputation for injustice (360d-362c).

Adeimantus expands Glaucon’s defense of injustice and attack on justice by asserting: the reputation of justice is better than justice itself, so the unjust person who is able to keep the reputation of being just will be happier than the just person; discussion of various ways that the unjust can acquire the reputation for justice (362d-366d).

Socrates is asked to defend justice for itself, not for the reputation it allows for (367b). He proposes to look for justice in the city first and then to proceed by analogy to find justice in the individual (368c-369a). This approach will allow for a clearer judgment on the question of whether the just person is happier than the unjust person. Socrates begins by discussing the origins of political life and constructs a just city in speech that satisfies only basic human necessities (369b-372c). Socrates argues that humans enter political life since each is not self-sufficient by nature. Each human has certain natural abilities (370a) and doing only the single job one is naturally suited for, is the most efficient way to satisfy the needs of all the citizens (370c). Glaucon objects that Socrates’ city is too simple and calls it “a city of pigs” (372d). Socrates describes a city that allows for luxuries (“a feverish city,” 372e-373e). Socrates points out that the luxurious city will require an army to guard the city (373e). The army will be composed of professional soldiers, the guardians, who, like dogs, must be gentle to fellow citizens and harsh to enemies (375c). The guardians need to be educated very carefully to be able to do their job of protecting the city’s citizens, laws, and customs well (376d). Poetry and stories need to be censored to guarantee such an education (377b). Poetry should: (i) present the gods as good and only as causes of good (379a); (ii) as unchanging in form (380d); (iii) as beings who refrain from lies and deception (381e).

c. Book III

Socrates continues the political measures of the censorship of poetry: (iv) the underworld should not be portrayed as a bad place so that the guardians will not be too afraid of death (386b); (v) the heroes and gods should not be presented lamenting so that the guardians can develop courage (387e); (vi) poetry should prevent people from laughing violently (388e); (vii) poetry should promote the guardian’s sense of truth-telling but with the willingness to lie when this is conducive to the good of the city (389b); (viii) it should promote self-discipline and obedience (389c-d); (ix) it should not include stories that contribute to avarice (390d); (x) it should not include stories that contribute to hubris or impiety (391a). Socrates moves on to discuss the manner in which stories should be told (392d). He divides such manners into simple narration (in third person) and imitative narration (in first person, 392d). To keep the guardians doing only their job, Socrates argues that the guardians may imitate only what is appropriate for this (394e-395d). The just city should allow only modes and rhythms that fit the content of poetry allowed in the just city (398b-399c). Socrates explains how good art can lead to the formation of good character and make people more likely to follow their reason (400e-402c). Socrates turns to the physical education of the guardians and says that it should include physical training that prepares them for war, a careful diet, and habits that contribute to the avoidance of doctors (403c-405b). Physical education should be geared to benefit the soul rather than the body, since the body necessarily benefits when the soul is in a good condition, whereas the soul does not necessarily benefit when the body is in a good condition (410b-c).

Socrates begins to describe how the rulers of the just city are to be selected from the class of the guardians: they need to be older, strong, wise, and wholly unwilling to do anything other than what is advantageous to the city (412b-414b). Socrates suggests that they need to tell the citizens a myth that should be believed by subsequent generations in order for everyone to accept his position in the city (414b-415d). The myth of metals portrays each human as having a precious metal in them: those naturally suited to be rulers have gold, those suited to be guardians have silver, and those suited for farming and the other crafts have bronze.

Socrates proceeds to discuss the living and housing conditions of the guardians: they will not have private property, they will have little privacy, they will receive what they need from the city via taxation of the other classes, and they will live communally and have common messes (415e-416e).

d. Book IV

Adeimantus complains that the guardians in the just city will not be very happy (419a). Socrates points out that the aim is to make the whole city, and not any particular class, as happy as possible (420b). Socrates discusses several other measures for the city as a whole in order to accomplish this. There should be neither too much wealth nor too much poverty in the city since these cause social strife (421d-422a). The just city should be only as large in size as would permit it to be unified and stable (423b). Socrates reemphasizes the importance of the guardian’s education and suggests that the guardians will possess wives and children in common (423e). He suggests that they should only allow very limited ways by which innovations may be introduced to education or change in the laws (424b-425e). The just city will follow traditional Greek religious customs (427b).

With the founding of the just city completed, Socrates proceeds to discuss justice (427d). He claims that the city they have founded is completely good and virtuous and thus it is wise, courageous, moderate, and just (427e). Justice will be what remains once they find the other three virtues in it, namely wisdom, courage, and moderation (428a). The wisdom of the just city is found in its rulers and it is the type of knowledge that allows them to rule the city well (428b-d). The courage of the just city is found in its military and it is correct and lawful belief about what to fear and what not to fear (429a-430b). The city’s moderation or self-discipline is its unanimity in following the just city’s structure in terms of who should rule and who should be ruled (430d-432a). The city’s justice consists in each class performing its proper function (433a-b).

Socrates then proceeds to find the corresponding four virtues in the individual (434d). Socrates defends the analogy of the city and the individual (435a-b) and proceeds to distinguish three analogous parts in the soul with their natural functions (436b). By using instances of psychological conflict, he distinguishes the function of the rational part from that of the appetitive part of the soul (439a). Then he distinguishes the function of the spirited part from the functions of the two other parts (439e-440e). The function of the rational part is thinking, that of the spirited part the experience of emotions, and that of the appetitive part the pursuit of bodily desires. Socrates explains the virtues of the individual’s soul and how they correspond to the virtues of the city (441c-442d). Socrates points out that one is just when each of the three parts of the soul performs its function (442d). Justice is a natural balance of the soul’s parts and injustice is an imbalance of the parts of the soul (444e). Socrates is now ready to answer the question of whether justice is more profitable than injustice that goes unpunished (444e-445a). To do so he will need to examine the various unjust political regimes and the corresponding unjust individuals in each (445c-e).

e. Book V

Socrates is about to embark on a discussion of the unjust political regimes and the corresponding unjust individuals when he is interrupted by Adeimantus and Polemarchus (449a-b). They insist that he needs to address the comment he made earlier that the guardians will possess the women and the children of the city in common (449b-d). Socrates reluctantly agrees (450a-451b) and begins with the suggestion that the guardian women should perform the same job as the male guardians (451c-d). Some may follow convention and object that women should be given different jobs because they differ from men by nature (453a-c). Socrates responds by indicating that the natural differences between men and women are not relevant when it comes to the jobs of protecting and ruling the city. Both sexes are naturally suited for these tasks (454d-e). Socrates goes on to argue that the measure of allowing the women to perform the same tasks as the men in this way is not only feasible but also best. This is the case since the most suited people for the job will be performing it (456c).

Socrates also proposes that there should be no separate families among the members of the guardian class: the guardians will possess all the women and children in common (457c-d). Socrates proceeds to discuss how this measure is for the best and Glaucon allows him to skip discussing its feasibility (458a-c). The best guardian men are to have sex with the best guardian women to produce offspring of a similar nature (458d-459d). Socrates describes the system of eugenics in more detail. In order to guarantee that the best guardian men have sex with the best guardian women, the city will have marriage festivals supported by a rigged lottery system (459e-460a). The best guardian men will also be allowed to have sex with as many women as they desire in order to increase the likelihood of giving birth to children with similar natures (460a-b). Once born, the children will be taken away to a rearing pen to be taken care of by nurses and the parents will not be allowed to know who their own children are (460c-d). This is so that the parents think of all the children as their own. Socrates recognizes that this system will result in members of the same family having intercourse with each other (461c-e).

Socrates proceeds to argue that these arrangements will ensure that unity spreads throughout the city (462a-465d). Responding to Adeimantus’ earlier complaint that the guardians would not be happy, Socrates indicates that the guardians will be happy with their way of life; they will have their needs satisfied and will receive sufficient honor from the city (465d-e). Thereafter, Socrates discusses how the guardians will conduct war (466e).

Glaucon interrupts him and demands an account explaining how such a just city can come into being (471c-e). Socrates admits that this is the most difficult criticism to address (472a). Then he explains that the theoretical model of the just city they constructed remains valid for discussing justice and injustice even if they cannot prove that such a city can come to exist (472b-473b). Socrates claims that the model of the just city cannot come into being until philosophers rule as kings or kings become philosophers (473c-d). He also points out that this is the only possible route by which to reach complete happiness in both public and private life (473e). Socrates indicates that they to, discuss philosophy and philosophers to justify these claims (474b-c). Philosophers love and pursue all of wisdom (475b-c) and they especially love the sight of truth (475e). Philosophers are the only ones who recognize and find pleasure in what is behind the multiplicity of appearances, namely the single Form (476a-b). Socrates distinguishes between those who know the single Forms that are and those who have opinions (476d). Those who have opinions do not know, since opinions have becoming and changing appearances as their object, whereas knowledge implies that the objects thereof are stable (476e-477e).

f. Book VI

Socrates goes on to explain why philosophers should rule the city. They should do so since they are better able to know the truth and since they have the relevant practical knowledge by which to rule. The philosopher’s natural abilities and virtues prove that they have what is necessary to rule well: they love what is rather than what becomes (485a-b), they hate falsehood (485c), they are moderate (485d-e), they are courageous (486a-b), they are quick learners (486c), they have a good memory (486c-d), they like proportion since the truth is like it, and they have a pleasant nature (486d-487a).

Adeimantus objects that actual philosophers are either useless or bad people (487a-d). Socrates responds with the analogy of the ship of state to show that philosophers are falsely blamed for their uselessness (487e-489a). Like a doctor who does not beg patients to heal them, the philosopher should not plead with people to rule them (489b-c). To the accusation that philosophers are bad, Socrates responds that those with the philosopher’s natural abilities and with outstanding natures often get corrupted by a bad education and become outstandingly bad (491b-e). Thus, someone can only be a philosopher in the true sense if he receives the proper kind of education. After a discussion of the sophists as bad teachers (492a-493c), Socrates warns against various people who falsely claim to be philosophers (495b-c). Since current political regimes lead to either the corruption or the destruction of the philosopher, he should avoid politics and lead a quiet private life (496c-d).

Socrates then addresses the question of how philosophy can come to play an important role in existing cities (497e). Those with philosophical natures need to practice philosophy all their lives, especially when they are older (498a-c). The only way to make sure that philosophy is properly appreciated and does not meet hostility is to wipe an existing city clean and begin it anew (501a). Socrates concludes that the just city and the measures proposed are both for the best and not impossible to bring about (502c).

Socrates proceeds to discuss the education of philosopher kings (502c-d). The most important thing philosophers should study is the Form of the Good (505a). Socrates considers several candidates for what the Good is, such as pleasure and knowledge and he rejects them (505b-d). He points out that we choose everything with a view to the good (505e). Socrates attempts to explain what the Form of the Good is through the analogy of the sun (507c-509d). As the sun illuminates objects so the eye can see them, the Form of the Good renders the objects of knowledge knowable to the human soul. As the sun provides things with their ability to be, to grow, and with nourishment, the Form of the Good provides the objects of knowledge with their being even though it itself is higher than being (509b).

Socrates offers the analogy of the divided line to explain the Form of the Good even further (509d-511d). He divides a line into two unequal sections once and then into two unequal sections again. The lowest two parts represent the visible realm and the top two parts the intelligible realm. In the first of the four sections of the line, Socrates places images/shadows, in the second section visible objects, in the third section truths arrived at via hypotheses as mathematicians do, and in the last section the Forms themselves. Corresponding to each of these, there is a capacity of the human soul: imagination, belief, thought, and understanding. The line also represents degrees of clarity and opacity as the lowest sections are more opaque and the higher sections clearer.

g. Book VII

Socrates continues his discussion of the philosopher and the Forms with a third analogy, the analogy of the cave (514a-517c). This represents the philosopher’s education from ignorance to knowledge of the Forms. True education is the turning around of the soul from shadows and visible objects to true understanding of the Forms (518c-d). Philosophers who accomplish this understanding will be reluctant to do anything other than contemplate the Forms but they must be forced to return to the cave (the city) and rule it.

Socrates proceeds to outline the structure of the philosopher king’s education so that they can reach an understanding of the Forms (521d). Those who eventually become philosopher kings will initially be educated like the other guardians in poetry, music, and physical education (521d-e). Then they will receive education in mathematics: arithmetic and number (522c), plane geometry (526c), and solid geometry (528b). Following these, they will study astronomy (528e), and harmonics (530d). Then they will study dialectic which will lead them to understand the Forms and the Form of the Good (532a). Socrates gives a partial explanation of the nature of dialectic and leaves Glaucon with no clear explanation of its nature or how it may lead to understanding (532a-535a). Then they discuss who will receive this course of education and how long they are to study these subjects (535a-540b). The ones receiving this type of education need to exhibit the natural abilities suited to a philosopher discussed earlier. After the training in dialectic the education system will include fifteen years of practical political training (539e-540c) to prepare philosopher kings for ruling the city. Socrates concludes by suggesting that the easiest way to bring the just city into being would be to expel everyone over the age of ten out of an existing city (540e-541b).

h. Book VIII

Socrates picks up the argument that was interrupted in Book V. Glaucon remembers that Socrates was about to describe the four types of unjust regime along with their corresponding unjust individuals (543c-544b). Socrates announces that he will begin discussing the regimes and individual that deviate the least from the just city and individual and proceed to discuss the ones that deviate the most (545b-c). The cause of change in regime is lack of unity in the rulers (545d). Assuming that the just city could come into being, Socrates indicates that it would eventually change since everything which comes into being must decay (546a-b). The rulers are bound to make mistakes in assigning people jobs suited to their natural capacities and each of the classes will begin to be mixed with people who are not naturally suited for the tasks relevant to each class (546e). This will lead to class conflicts (547a).

The first deviant regime from just kingship or aristocracy will be timocracy, that emphasizes the pursuit of honor rather than wisdom and justice (547d ff.). The timocratic individual will have a strong spirited part in his soul and will pursue honor, power, and success (549a). This city will be militaristic. Socrates explains the process by which an individual becomes timocratic: he listens to his mother complain about his father’s lack of interest in honor and success (549d). The timocratic individual’s soul is at a middle point between reason and spirit.

Oligarchy arises out of timocracy and it emphasizes wealth rather than honor (550c-e). Socrates discusses how it arises out of timocracy and its characteristics (551c-552e): people will pursue wealth; it will essentially be two cities, a city of wealthy citizens and a city of poor people; the few wealthy will fear the many poor; people will do various jobs simultaneously; the city will allow for poor people without means; it will have a high crime rate. The oligarchic individual comes by seeing his father lose his possessions and feeling insecure he begins to greedily pursue wealth (553a-c). Thus he allows his appetitive part to become a more dominant part of his soul (553c). The oligarchic individual’s soul is at middle point between the spirited and the appetitive part.

Socrates proceeds penultimately, to discuss democracy. It comes about when the rich become too rich and the poor too poor (555c-d). Too much luxury makes the oligarchs soft and the poor revolt against them (556c-e). In democracy most of the political offices are distributed by lot (557a). The primary goal of the democratic regime is freedom or license (557b-c). People will come to hold offices without having the necessary knowledge (557e) and everyone is treated as an equal in ability (equals and unequals alike, 558c). The democratic individual comes to pursue all sorts of bodily desires excessively (558d-559d) and allows his appetitive part to rule his soul. He comes about when his bad education allows him to transition from desiring money to desiring bodily and material goods (559d-e). The democratic individual has no shame and no self-discipline (560d).

Tyranny arises out of democracy when the desire for freedom to do what one wants becomes extreme (562b-c). The freedom or license aimed at in the democracy becomes so extreme that any limitations on anyone’s freedom seem unfair. Socrates points out that when freedom is taken to such an extreme it produces its opposite, slavery (563e-564a). The tyrant comes about by presenting himself as a champion of the people against the class of the few people who are wealthy (565d-566a). The tyrant is forced to commit a number of acts to gain and retain power: accuse people falsely, attack his kinsmen, bring people to trial under false pretenses, kill many people, exile many people, and purport to cancel the debts of the poor to gain their support (565e-566a). The tyrant eliminates the rich, brave, and wise people in the city since he perceives them as threats to his power (567c). Socrates indicates that the tyrant faces the dilemma to either live with worthless people or with good people who may eventually depose him and chooses to live with worthless people (567d). The tyrant ends up using mercenaries as his guards since he cannot trust any of the citizens (567d-e). The tyrant also needs a very large army and will spend the city’s money (568d-e), and will not hesitate to kill members of his own family if they resist his ways (569b-c).

i. Book IX

Socrates is now ready to discuss the tyrannical individual (571a). He begins by discussing necessary and unnecessary pleasures and desires (571b-c). Those with balanced souls ruled by reason are able to keep their unnecessary desires from becoming lawless and extreme (571d-572b). The tyrannical individual comes out of the democratic individual when the latter’s unnecessary desires and pleasures become extreme; when he becomes full of Eros or lust (572c-573b). The tyrannical person is mad with lust (573c) and this leads him to seek any means by which to satisfy his desires and to resist anyone who gets in his way (573d-574d). Some tyrannical individuals eventually become actual tyrants (575b-d). Tyrants associate themselves with flatterers and are incapable of friendship (575e-576a). Applying the analogy of the city and the soul, Socrates proceeds to argue that the tyrannical individual is the most unhappy individual (576c ff.). Like the tyrannical city, the tyrannical individual is enslaved (577c-d), least likely to do what he wants (577d-e), poor and unsatisfiable (579e-578a), fearful and full of wailing and lamenting (578a). The individual who becomes an actual tyrant of a city is the unhappiest of all (578b-580a). Socrates concludes this first argument with a ranking of the individuals in terms of happiness: the more just one is the happier (580b-c).

He proceeds to a second proof that the just are happier than the unjust (580d). Socrates distinguishes three types of persons: one who pursues wisdom, another who pursues honor, and another who pursues profit (579d-581c). He argues that we should trust the wisdom lover’s judgment in his way of life as the most pleasant, since he is able to consider all three types of life clearly (581c-583a).

Socrates proceeds to offer a third proof that the just are happier than the unjust (583b). He begins with an analysis of pleasure: relief from pain may seem pleasant (583c) and bodily pleasures are merely a relief from pain but not true pleasure (584b-c). The only truly fulfilling pleasure is that which comes from understanding since the objects it pursues are permanent (585b-c). Socrates adds that only if the rational part rules the soul, will each part of the soul find its proper pleasure (586d-587a). He concludes the argument with a calculation of how many times the best life is more pleasant than the worst: seven-hundred and twenty nine (587a-587e). Socrates discusses an imaginary multi-headed beast to illustrate the consequences of justice and injustice in the soul and to support justice (588c ff.).

j. Book X

Thereafter, Socrates returns to the subject of poetry and claims that the measures introduced to exclude imitative poetry from the just city seem clearly justified now (595a). Poetry is to be censored since the poets may not know which is; thus may lead the soul astray (595b). Socrates proceeds to discuss imitation. He explains what it is by distinguishing several levels of imitation through the example of a couch: there is the Form of the couch, the particular couch, and a painting of a couch (596a-598b). The products of imitation are far removed from the truth (597e-598c). Poets, like painters are imitators who produce imitations without knowledge of the truth (598e-599a). Socrates argues that if poets had knowledge of the truth they would want to be people who do great things rather than remain poets (599b). Socrates doubts the poet’s capacity to teach virtue since he only imitates images of it (599c-601a). The poet’s knowledge is inferior to that of the maker of other products and the maker’s knowledge is inferior to that of the user’s (601c-602b).

Now Socrates considers how imitators affect their audiences (602c). He uses a comparison with optical illusions (602c) to argue that imitative poetry causes the parts of the soul to be at war with each other and this leads to injustice (603c-605b). The most serious charge against imitative poetry is that it even corrupts decent people (605c). He concludes that the just city should not allow such poetry in it but only poetry that praises the gods and good humans (606e-607a). Imitative poetry prevents the immortal soul from attaining its greatest reward (608c-d).

Glaucon wonders if the soul is immortal and Socrates launches into an argument proving its immortality: things that are destroyed, are destroyed by their own evil; the body’s evil is disease and this can destroy it; the soul’s evils are ignorance, injustice and the other vices but these do not destroy the soul; thus, the soul is immortal (608d-611a). Socrates points out that we cannot understand the nature of the soul if we only consider its relation to the body as the present discussion has (611b-d).

Socrates finally describes the rewards of justice by first having Glaucon allow that he can discuss the rewards of reputation for justice (612b-d). Glaucon allows this since Socrates has already defended justice by itself in the soul. Socrates indicates justice and injustice do not escape the notice of the gods, that the gods love the just and hate the unjust, and that good things come to those whom the gods love (612e-613a). Socrates lists various rewards for the just and punishments for the unjust in this life (613a-e). He proceeds to tell the Myth of Er that is supposed to illustrate reward and punishment in the afterlife (614b). The souls of the dead go up through an opening on the right if they were just, or below through an opening on the left if they were unjust (614d). The various souls discuss their rewards and punishments (614e-615a). Socrates explains the multiples by which people are punished and rewarded (615a-b). The souls of the dead are able to choose their next lives (617d) and then they are reincarnated (620e). Socrates ends the discussion by prompting Glaucon and the others to do well both in this life and in the afterlife (621c-d).

2. Ethics or Political Philosophy?

The Republic has acquired the recognition of a classic and seminal work in political philosophy. It is often taught in courses that focus on political theory or political philosophy. Moreover, in the dialogue Socrates seems primarily concerned with what is an ethical issue, namely whether the just life is better than the unjust life for the individual. These two observations raise two issues. The first is whether the Republic is primarily about ethics or about politics. If it is primarily about ethics then perhaps its recognition as a seminal political work is unwarranted. Moreover, considering it a political work would be somewhat mistaken. The second issue is that even if thinking of it as a classic in political philosophy is warranted, it is very difficult to situate it in terms of its political position.

Interpreters of the Republic have presented various arguments concerning the issue of whether the dialogue is primarily about ethics or about politics. As is evident from Books I and II, Socrates’ main aim in the dialogue is to prove that the just person is better off than the unjust person. In Book II, he proposes to construct the just city in speech in order to find justice in it and then to proceed to find justice in the individual (368a). Thus, he seems to use a discussion in political matters as a means by which to answer what is essentially an ethical question. But, Socrates also spends a lot of time in the dialogue on political matters in relation to the question of political justice such as education, the positions and relations among political classes, war, property, the causes of political strife and change of regimes, and several other matters. Each of these could provide important contributions to political philosophy.

One argument, suggesting that the dialogue is primarily concerned with the ethical question, focuses on Socrates’ presentation of the political discussion of justice as instrumental to discovering justice in the individual. Another relevant consideration is that there are several indications in the dialogue that the aim in the discussion is more pressing than the means (the just city). Thus, the argument goes, Socrates does not seem primarily interested in discussing political philosophy but ethics instead. Another related argument indicates that the discussion entails great doubts about whether the just city is even possible. Socrates claims this along with the idea that the function of the just city in the argument is to enable the individual to get a better idea of justice and injustice (472b-d, 592a-b). Thus, it is very difficult for us to conclude that Socrates takes the political discussion as seriously as he does the moral question (see Annas, Julia. Platonic Ethics, Old and New).

Other interpreters indicate that the Republic is essentially about both ethics and politics (among others see Santas, Gerasimos. Understanding Plato’s Republic; Schofield, Malcolm. Plato: Political Philosophy; Reeve C.D.C. Philosopher Kings). Some emphasize that many of Socrates’ proposals for social reform (education, property, the role of women, the family) go beyond what is needed to be able to argue that the just person is better off than the unjust person. Thus, these social reforms seem to be developed for their own sake.

Some indicate that Socrates’ discussion of political matters is meant, in part, to provide us with Plato’s critique of Greek political life. In Book VIII he criticizes democracy as an unjust regime and thus he seems to launch a critique against Athenian democracy. He also adopts several measures in the just city, which were part of the Spartan constitution. Like Spartan citizens, the guardians of the just city are professional soldiers whose aim is the protection of the city, the guardians eat together, and they have their needs provided for by other classes. But unlike Sparta, the just city has philosophers as rulers, a rigorous system of education in intellectual matters, and it is not timocratic or honor loving. These differences may be construed as a critique of Sparta’s political life. Thus, the argument suggests, in addition to the main ethical question the dialogue is also about political philosophy.

Another position is that even though the discussion of political matters is instrumental to addressing the main ethical question of the dialogue, Socrates makes several important contributions to political philosophy. One such contribution is his description of political regimes in Book VIII and his classification of them on a scale of more or less just. Another such contribution is his consideration of the causes of political change from one political regime to another. Moreover, Socrates seems to raise and address a number of questions that seem necessary in order to understand political life clearly. He raises the issues of the role of women in the city, the role of the family, the role of art, the issue of class relations, of political stability, of the limitation of people’s freedoms and several others. Thus, according to this view, it is warranted to regard the Republic as a work on political philosophy and as a seminal work in that area.

A further relevant consideration has to do with how one understands the nature of ethics and political philosophy and their relation. Since modernity, it becomes much easier to treat these as separate subjects. Modern ethics is more focused on determining whether an action is morally permissible or not whereas ancient ethics is more focused on happiness or the good life. Many ancient thinkers want to address the question “what is the happy life?” and in order to do this they think that it is warranted to address political matters. Humans live their lives in political communities and the kind of political community they live in can be conducive or detrimental to one’s happiness. Thus, ethics and political philosophy are more closely linked for ancient thinkers than they may be for us since modernity. Ethics and political philosophy seem to be different sides of the same coin.

The second issue has to do with situating the Republic’s political stance. There are several competing candidates. The Republic entails elements of socialism as when Socrates expresses the desire to achieve happiness for the whole city not for any particular group of it (420b) and when he argues against inequalities in wealth (421d). There are also elements of fascism or totalitarianism. Among others, there is extreme censorship of poetry, lying to maintain good behavior and political stability, restriction of power to a small elite group, eugenic techniques, centralized control of the citizen’s lives, a strong military group that enforces the laws, and suppression of freedom of expression and choice. Several commentators focused on these elements to dismiss the Republic as a proto-totalitarian text (see Popper, Karl. The Open Society and Its Enemies). There are also some strong elements of communism such as the idea that the guardian class ought to possess things in common. Despite, Socrates’ emphasis on the individual and the condition of his soul, the Republic does not entail the kernels of what becomes modern liberalism. Socrates seems to argue against allowing much freedom to individuals and to criticize the democratic tendency to treat humans as equals. Some have argued that the Republic is neither a precursor of these political positions nor does it fit any of them. They find that the Republic has been such a seminal work in the history of political philosophy precisely because it raises such issues as its political stance while discussing many of the features of such political positions.

3. The Analogy of the City and the Soul

The analogy of the city and the soul, is Socrates proposed and accepted method by which to argue that the just person is better off than the unjust person (Book II, 368c-369a). If Socrates is able to show how a just city is always happier than unjust cities, then he can have a model by which to argue that a just person is always happier than an unjust one. He plausibly assumes that there is an interesting, intelligible, and non-accidental relation between the structural features and values of a city and an individual. But commentators have found this curious approach one of the most puzzling features of the Republic. The city/soul analogy is quite puzzling since Socrates seems to apply it in different ways, thus there is much controversy about the exact extent of the analogy. Moreover, there is much controversy concerning its usefulness in the attempt to discover and to defend justice in terms of the individual.

In several passages Socrates seems to say that the same account of justice must apply to both cities (justice is the right order of classes) and to individuals (justice is the right order of the soul). But even though he says this he seems to think that this ought to be the case for different reasons. For example, at (435a), he seems to say that the same account of justice ought to apply to the city and to the individual since the same account of any predicate X must apply to all things that are X. So, if a city or an individual is just then the same predicates must apply to both. In other passages Socrates seems to mean that same account of justice ought to apply to the city and to the individual since the X-ness of the whole is due to the X-ness of the parts (435d). So, if the people in the city are just, then this will cause the city to be just as well. Yet still in other passages he seems to say that if a city is just and this causes it to have certain features such as wisdom or courage, then we can deduce that the individual’s being just will also cause him to be wise and courageous. So if a city’s X-ness entails certain predicates, then the individual’s X-ness must entail the same predicates. In other passages still, he seems to claim that the justice of the city can be used as a heuristic device by which to look for justice in the individual, thus the relation between the two seems quite loose (368e-369a). (For a thorough discussion of these issues and the various interpretations of the city/soul analogy see Ferrari, G.R.F. City and Soul in Plato’s Republic.)

4. Plato’s Defense of Justice

In response to Thrasymachus, Glaucon, and Adeimantus, Socrates seeks to show that it is always in an individual’s interest to be just, rather than unjust. Thus, one of the most pressing issues regarding the Republic is whether Socrates defends justice successfully or not. David Sachs, in his influential article “A Fallacy in Plato’s Republic”, argues that Socrates’ defense of justice entails a crucial problem which renders the defense problematic. Sachs argues that Socrates commits the fallacy of irrelevance. Socrates sets out to defend the idea that it is always in one’s interest to be just and to act justly and he presents the just person as one who has a balanced soul. Sachs observes that what Socrates defends is psychic health or rationality which may lead one to be happy but he fails to defend justice. Socrates fails to show why having a balanced soul will lead one to act justly or why psychic health amounts to justice. Sachs implies that justice, as this is traditionally understood, includes actions in relation to others, it includes considerations of other people’s good, and also includes strong motivations not to act unjustly. According to Sachs, Socrates’ defense of justice does not include compelling reasons to think that a person with a balanced soul will refrain from acts that are traditionally thought to be unjust such as say, theft, murder, or adultery. Thus, Plato presents Socrates defending psychic health rather than justice.

Sachs’ critique indicates that as Socrates presents the just person, the person’s balanced soul does not entail a sufficient causal or logical connection to performing socially just actions. In order to save Socrates’ defense of justice one needs to show that there is a logical and a causal connection between having a balanced soul and performing socially just actions. Otherwise, the problem of being psychically just but socially unjust remains

Given Sachs’ critique, several commentators have come to Socrates’ defense to bridge the gap between a just soul and just actions (these are discussed in detail by Singpurwalla, Rachel G. K. “Plato’s Defense of Justice in the Republic”). One approach to bridging the gap between a just soul and just actions has been to show that the just person with a balanced soul operates according to certain values and desires which cannot lead to unjust actions (see Kraut, Richard “The Defense of Justice in Plato’s Republic”). The just person’s soul entails desires for certain kinds of objects the most important of which is knowledge. Socrates indicates the difficulty and extreme effort required to attain knowledge of the forms and the form of the Good, thus the just person will pursue learning and not spend time indulging in the satisfaction of desires that typically lead to unjust actions. This approach of bridging the gap between a just soul and just actions may have some drawbacks. One drawback may be that several unjust actions may be motivated by desires that are compatible with the desire for knowledge. For example, why wouldn’t a person with a great desire for knowledge steal a book if this would contribute to his knowledge.

A second approach to bridging the gap between the just soul and just actions has been to show that the just person’s knowledge of the good, directly motivates him to perform just actions and to refrain from unjust ones (see Cooper, John “The Psychology of Justice in Plato’s Republic” and White, N. A Companion to Plato’s Republic). A crucial piece of evidence for this approach is Socrates’ presentation of the philosopher who agrees to rule the city even though this will interfere with his desire to learn. The proponents of this approach argue that the philosopher agrees to rule since his knowledge of the good directly motivates him to act against his interests and to do something that is good objectively and for others. This approach has met at least one serious objection: the just person’s knowledge of the good may motivate him to do what is good for others but Socrates seeks to also argue that it is always in one’s interest to be just, thus this approach may suggest that just actions may not always be in the just person’s interests (for a discussion of this see Singpurwalla). This objection amounts to the claim that the second approach may show that the just person will do just actions but it does this by sacrificing Socrates’ claim that being just is always in one’s interest.

Given the problems of the first two approaches, a third one attempts to show that the just person will do what is just in relation to others while at the same time doing what is in the just person’s interests. In other words, this approach seeks to show that the just person’s own good is realized in doing what is also good for others. According to this approach, the just person has a value that motivates him to do what is just, in relation to others and this value is the just person’s love of the forms (see Dahl, Norman “Plato’s Defense of Justice”). The just person’s love of the forms is the desire to contemplate and also imitate or instantiate these in the world. Thus, the philosopher regards ruling as something in his interest despite the fact that it interferes with his pursuit of knowledge, since in ruling he will be imitating the forms. Even though this approach seems to bridge the gap between the just person and just actions and the gap between just actions and such actions being in the just person’s interest (this was the problem with the second approach) a criticism remains. Singpurwalla points out that only very few people can acquire such knowledge of the forms so as to be just persons, thus for most people Socrates offers no good reason to be just. This third approach may save Socrates’ defense of justice only for people capable of knowing the forms, but falls short of showing that everyone has a reason to be just.

Singpurwalla suggests a fourth approach which can defend Socrates contra Sachs and which will avoid the criticisms launched against the other approaches. She aims to show that Socrates has a good reason to think that it is in everyone’s interest to act justly because doing so satisfies a deeply ingrained human need, namely, the need to be unified with others. Singpurwalla attempts to make her case by showing the following: (1) that according to Socrates our happiness largely resides in being unified with others (she cites the tyrant’s unhappiness due to bad relations with others as evidence for this, 567a-580a); (2) that being unified with others entails considering their own good when we act (she cites Socrates’ claims that when people are unified they share in each other’s pleasures and successes and failures as evidence for this, 462b-e, 463e-464d); (3) thus, behaving unjustly, which involves disregarding another’s good, is incompatible with being unified with others and with our happiness. Singpurwalla’s position tries to show that even though the average person may not be able to attain the knowledge of the form of the good, he can still be motivated to act justly since this is in his interest. Thus, Socrates’ defense of justice may be compelling for the philosopher as well as the average person.

5. References and Further Reading

a. Standard Greek Text

Slings, S.R. (ed.), Platonis Rempublicam (Oxford: Oxford Classical Texts, 2003).

b. English Translations

Shorey, Paul. Plato. Republic (2 vols. Loeb, 137-1937). This translation includes an introduction and notes.
Bloom, Allan. The Republic of Plato. (New York: Basic Books, 1968). This translation includes notes and an interpretative essay.
Ferrari, G.R.F. (ed.), Griffith, Tom (trans.). Plato. The Republic. (Cambridge: Cambridge University Press, 2000). This translation includes an introduction.
Reeve, C.D.C. Plato. The Republic. (Indianapolis: Hackett, 2004).

c. General Discussions of the Republic

(all attempt to provide a unified interpretation of the dialogue).

Murphy, N.R. The Interpretation of Plato’s Republic (Oxford: Clarendon Press, 1951).
Cross, R.C. and Woozley, A.D. Plato’s Republic: A Philosophical Commentary (New York: St. Martin’s Press, 1964).
White, Nicholas P. A Companion to Plato’s Republic (Indianapolis: Hackett, 1979).
Annas, Julia. An Introduction to Plato’s Republic (Oxford: Oxford University Press, 1981).
Reeve, C.D.C. Philosopher Kings: The Argument of Plato’s Republic (Princeton: Princeton University Press, 1988).
Howland, Jacob. The Republic: The Odyssey of Philosophy (Philadelphia: Paul Dry Books, 2004).
Rosen, Stanley. Plato’s Republic: A Study (New Haven: Yale University Press, 2005).
Santas, Gerasimos. Understanding Plato’s Republic (Wiley-Blackwell, 2010).

d. Discussions on Plato’s Ethics and Political Philosophy

(all entail a systematic discussion of ethics and/or political philosophy in the Republic).

Irwin, T.H. Plato’s Ethics (Oxford: Oxford University Press, 1995).
Annas, Julia. Platonic Ethics Old and New (Ithaca: Cornell University Press, 1999).
Monoson, Sara. Plato’s Democratic Entanglements (Princeton: Princeton University Press, 2000).
Bobonich, Christopher. Plato’s Utopia Recast (Oxford: Oxford University Press, 2002).
Schofield, Malcolm. Plato: Political Philosophy (Oxford: Oxford University Press, 2006).
Rowe, Christopher. “The Place of the Republic in Plato’s Political Thought” in Ferrari, G.R.F. The Canbridge Companion to Plato’s Republic. (Cambridge: Cambridge University Press, 2007).

e. Discussions on the City/Soul Analogy.

Williams, Bernard. “The Analogy of City and Soul in Plato’s Republic”, in Kraut, Richard (ed.). Plato’s Republic: Critical Essays (New York: Rowman and Littlefield, 1997).
Lear, Jonathan. “Inside and Outside the Republic”, in Kraut, Richard (ed.). Plato’s Republic: Critical Essays (New York: Rowman and Littlefield, 1997).
Ferrari, G.R.F. City and Soul in Plato’s Republic (Chicago: The University of Chicago Press, 2005).
Blossner, Norbert. “The City-Soul Analogy”, in Ferrari, G.R.F. The Canbridge Companion to Plato’s Republic. (Cambridge: Cambridge University Press, 2007).

f. Discussions of Plato’s Defense of Justice in the Republic

(in chronological order; these essays discuss how Socrates defends justice and examine how well he does in doing so).

Sachs, David. “A Fallacy in Plato’s Republic”, in The Philosophical Review 72 (1963): 141-58.
Dahl, Norman O. “Plato’s Defense of Justice”, in Philosophy and Phenomenological Research. Vol. 51, No. 4 (Dec. 1991).
Kraut, Richard. “The Defense of Justice in Plato’s Republic”, in Kraut, Richard (ed.) Plato’s Republic: Critical Essays (New York: Rowman and Littlefield, 1997).
Singpurwalla, Rachel G.K. “Plato’s Defense of Justice in the Republic”, in Santas, Gerasimos (ed.). The Blackwell Guide to Plato’s Republic (Oxford: Blackwell Publishing, 2006).

g. Discussions of Political Measures Introduced in the Just City

i. Discussions of the Role of Women in the Just City

Discussions of the Role of Women in the Just City
Vlastos, Gregory. “Was Plato a Feminist?”, Times Literary Supplement, No. 4, 485, Mar. 17, 1989, 276, 288-89.
Saxonhouse, Arlene. “The philosopher and the Female in the Political Thought of Plato”, in Kraut, Richard (ed.) Plato’s Republic: Critical Essays (New York: Rowman and Littlefield, 1997).
Reeve. C.D.C. “The Naked Old Women in the Palaestra”, in Kraut, Richard (ed.) Plato’s Republic: Critical Essays (New York: Rowman and Littlefield, 1997).

ii. Discussions of Poetry in the Just City

Urmson, James O. “Plato and the Poets”, in Kraut, Richard (ed.) Plato’s Republic: Critical Essays (New York: Rowman and Littlefield, 1997).
O’Connor, David K. “Rewriting the Poets in Plato’s Characters”, in Ferrari, G.R.F. The Canbridge Companion to Plato’s Republic. (Cambridge: Cambridge University Press, 2007).
Moss, Jessica. “What is Imitative Poetry and Why is it Bad?”, in Ferrari, G.R.F. The Canbridge Companion to Plato’s Republic. (Cambridge: Cambridge University Press, 2007).

iii. Discussions on the Soul in the Republic

Lorenz, Hendrik. “The Analysis of the Soul in Plato’s Republic” in Santas, Gerasimos (ed.). The Blackwell Guide to Plato’s Republic (Oxford: Blackwell Publishing, 2006).
Ferrari, G.R.F., “The Three-Part Soul”, in Ferrari, G.R.F. The Cambridge Companion to Plato’s Republic. (Cambridge: Cambridge University Press, 2007).

iv. Discussions on Plato’s Moral Psychology in the Republic

Cooper, John M. “The Psychology of Justice in Plato” in Kraut, Richard (ed.) Plato’s Republic: Critical Essays (New York: Rowman and Littlefield, 1997).
Anagnostopoulos, Mariana. “The Divided Soul and the Desire for Good in Plato’s Republic” in Santas, Gerasimos (ed.). The Blackwell Guide to Plato’s Republic (Oxford: Blackwell Publishing, 2006).

Author Information

Antonis Coumoundouros
Email: acoumoundouros@adrian.edu
Adrian College
U. S. A.

Plato: Theaetetus

The Theaetetus is one of the middle to later dialogues of the ancient Greek philosopher Plato. Plato was Socrates’ student and Aristotle’s teacher. As in most of Plato’s dialogues, the main character is Socrates. In the Theaetetus, Socrates converses with Theaetetus, a boy, and Theodorus, his mathematics teacher. Although this dialogue features Plato’s most sustained discussion on the concept of knowledge, it fails to yield an adequate definition of knowledge, thus ending inconclusively. Despite this lack of a positive definition, the Theaetetus has been the source of endless scholarly fascination. In addition to its main emphasis on the nature of cognition, it considers a wide variety of philosophical issues: the Socratic Dialectic, Heraclitean Flux, Protagorean Relativism, rhetorical versus philosophical life, and false judgment. These issues are also discussed in other Platonic dialogues.

The Theaetetus poses a special difficulty for Plato scholars trying to interpret the dialogue: in light of Plato’s metaphysical and epistemological commitments, expounded in earlier dialogues such as the Republic, the Forms are the only suitable objects of knowledge, and yet the Theaetetus fails explicitly to acknowledge them. Might this failure mean that Plato has lost faith in the Forms, as the Parmenides suggests, or is this omission of the Forms a calculated move on Plato’s part to show that knowledge is indeed indefinable without a proper acknowledgement of the Forms? Scholars have also been puzzled by the picture of the philosopher painted by Socrates in the digression: there the philosopher emerges as a man indifferent to the affairs of the city and concerned solely with “becoming as much godlike as possible.” What does this version of the philosophic life have to do with a city-bound Socrates whose chief concern was to benefit his fellow citizens? These are only two of the questions that have preoccupied Plato scholars in their attempt to interpret this highly complex dialogue.

References and Further Reading

1. The Characters of Plato’s Theaetetus

In the Theaetetus, Socrates converses with two mathematicians, Theaetetus and Theodorus. Theaetetus is portrayed as a physically ugly but extraordinarily astute boy, and Theodorus is his mathematics teacher. According to the Oxford Classical Dictionary, Theaetetus lived in Athens (c. 415–369 BCE) and was a renowned geometer. He is credited with the theory of irrational lines, a contribution of fundamental importance for Euclid’s Elements X. He also worked out constructions of the regular solids like those in Elements XIII. Theodorus lived in Cyrene in the late fifth century BCE. In the dialogue, he is portrayed as a friend of Protagoras, well-aware of the Sophist’s teachings, and quite unfamiliar with the intricacies of Socratic Dialectic. As far as his scientific work is concerned, the only existing source is Plato’s Theaetetus: In the dialogue, Theodorus is portrayed as having shown the irrationality of the square roots of 3, 5, 6, 7, ... ,17. Irrational numbers are numbers equal to an ordinary fraction, a fraction that has whole numbers in its numerator and denominator. The passage has been interpreted in many different ways, and its historical accuracy has been disputed.

2. Date of Composition

The introduction of the dialogue informs the reader that Theaetetus is being carried home dying of wounds and dysentery after a battle near Corinth. There are two known battles that are possibly the one referred to in the dialogue: the first one took place at about 394 BCE, and the other occurred at around 369 BCE. Scholars commonly prefer the battle of 369 BCE as the battle referred to in the dialogue. The dialogue is a tribute to Theaetetus’ memory and was probably written shortly after his death, which most scholars date around 369 – 367 BCE. It is uncontroversial that the Theaetetus, the Sophist and the Statesman were written in that order. The primary evidence for this order is that the Sophist begins with a reference back to the Theaetetus and a reference forward to the Statesman. In addition, there is a number of thematic continuities between the Theaetetus and the Sophist (for instance, the concept of “false belief,” and the notions of “being,” “sameness,” and “difference”) and between the Sophist and the Statesman (such as the use of the method of “collection and division”).

3. Outline of the Dialogue

The dialogue examines the question, “What is knowledge (episteme)?” For heuristic purposes, it can be divided into four sections, in which a different answer to this question is examined: (i) Knowledge is the various arts and sciences; (ii) Knowledge is perception; (iii) Knowledge is true judgment; and (iv) Knowledge is true judgment with an “account” (Logos). The dialogue itself is prefaced by a conversation between Terpsion and Euclid, in the latter’s house in Megara. From this conversation we learn about Theaetetus’ wounds and impending death and about Socrates’ prophecy regarding the future of the young man. In addition, we learn about the dialogue’s recording method: Euclid had heard the entire conversation from Socrates, he then wrote down his memoirs of the conversation, while checking the details with Socrates on subsequent visits to Athens. Euclid’s role did not consist simply in writing down Socrates’ memorized version of the actual dialogue; he also chose to cast it in direct dialogue, as opposed to narrative form, leaving out such connecting sentences as “and I said” and “he agreed.” Finally, Euclid’s product is read for him and for Terpsion by a slave. This is the only Platonic dialogue which is being read by a slave.

a. Knowledge as Arts and Sciences (146c – 151d)

To Socrates’ question, “What is knowledge?,” Theaetetus responds by giving a list of examples of knowledge, namely geometry, astronomy, harmonics, and arithmetic, as well as the crafts or skills (technai) of cobbling and so on (146c–d). These he calls “knowledges,” presumably thinking of them as the various branches of knowledge. As Socrates correctly observes, Theaetetus’ answer provides a list of instances of things of which there is knowledge. Socrates states three complaints against this response: (a) what he is interested in is the one thing common to all the various examples of knowledge, not a multiplicity of different kinds of knowledge; (b) Theaetetus’ response is circular, because even if one knows that, say, cobbling is “knowledge of how to make shoes,” one cannot know what cobbling is, unless one knows what knowledge is; (c) The youth’s answer is needlessly long-winded, a short formula is all that is required. The definition of clay as “earth mixed with water,” which is also evoked by Aristotle in Topics 127a, is representative of the type of definition needed here. Theaetetus offers the following mathematical example to show that he understands Socrates’ definitional requirements: the geometrical equivalents of what are now called “surds” could be grouped in one class and given a single name (“powers”) by dint of their common characteristic of irrationality or incommensurability. When he tries to apply the same method to the question about knowledge, however, Theaetetus does not know how to proceed. In a justly celebrated image, Socrates, like an intellectual midwife, undertakes to assist him in giving birth to his ideas and in judging whether or not they are legitimate children. Socrates has the ability to determine who is mentally pregnant, by knowing how to use “medicine” and “incantations” to induce mental labor. Socrates also has the ability to tell in whose company a young man may benefit academically. This latter skill is not one that ordinary midwives seem to have, but Socrates insists that they are the most reliable matchmakers, and in order to prove his assertion he draws upon an agricultural analogy: just as the farmer not only tends and harvests the fruits of the earth, but also knows which kind of earth is best for planting various kinds of seed, so the midwife’s art should include a knowledge of both “sowing” and “harvesting.” But unlike common midwives, Socrates’ art deals with the soul and enables him to distinguish and embrace true beliefs rather than false beliefs. By combining the technê of the midwife with that of the farmer, Socrates provides in the Theaetetus the most celebrated analogy for his own philosophical practice.

b. Knowledge as Perception (151d – 186e)

Encouraged by Socrates’ maieutic intervention, Theaetetus comes up with a serious proposal for a definition: knowledge is perception. Satisfied with at least the form of this definition, Socrates immediately converts it into Protagoras’ homo-mensura doctrine, “Man is the measure of all things, of the things that are that [or how] they are, of the things that are not that [or how] they are not.” The Protagorean thesis underscores the alleged fact that perception is not only an infallible but also the sole form of cognition, thereby bringing out the implicit assumptions of Theaetetus’ general definition. Socrates effects the complete identity between knowledge and perception by bringing together two theses: (a) the interpretation of Protagoras’ doctrine as meaning “how things appear to an individual is how they are for that individual” (e.g., “if the wind appears cold to X, then it is cold for X”); and (b) the equivalence of “Y appears F to X” with “X perceives Y as F” (e.g., “the wind appears cold to Socrates” with “Socrates perceives the wind as cold”). His next move is to build the ontological foundation of a world that guarantees perceptual infallibility. For that, Socrates turns to the Heraclitean postulate of Radical Flux, which he attributes to Protagoras as his Secret Doctrine. Nearly all commentators acknowledge that Protagoras’ secret teaching is unlikely to be a historically accurate representation of either Protagoras’ ontological commitments or Heraclitus’ Flux doctrine. The notion of Universal Flux makes every visual event—for example the visual perception of whiteness—the private and unique product of interaction between an individual’s eyes and an external motion. Later this privacy is explained with the metaphor of the perceiver and the perceived object as parents birthing a twin offspring, the object’s whiteness and the subject’s corresponding perception of it. Both parents and offspring are unique and unrepeatable: there can be no other, identical interaction between either the same parents or different parents able to produce the same offspring. No two perceptions can thus ever be in conflict with each other, and no one can ever refute anyone else’s perceptual judgments, since these are the products of instantaneous perceptual relations, obtaining between ever-changing perceiving subjects and ever-changing perceived objects. Although the assimilation of Protagorean Relativism to Theaetetus’ definition requires the application of the doctrine to Perceptual Relativism—which explains Socrates’ extensive focus on the mechanics of perception—one should bear in mind that the man-as-measure thesis is broader in scope, encompassing all judgments, especially judgments concerning values, such as “the just” and “the good,” and not just narrowly sensory impressions. Socrates launches a critique against both interpretations of Protagoreanism, beginning with its broad—moral and epistemological—dimensions, and concluding with its narrow, perceptual aspects.

Socrates attacks broad Protagoreanism from within the standpoint afforded him by three main arguments. First, Socrates asks how, if people are each a measure of their own truth, some, among whom is Protagoras himself, can be wiser than others. The same argument appears in Cratylus 385e–386d as a sufficient refutation of the homo-mensura doctrine. The Sophists’ imagined answer evinces a new conceptualization of wisdom: the wisdom of a teacher like Protagoras has nothing to do with truth, instead it lies in the fact that he can better the way things appear to other people, just as the expert doctor makes the patient feel well by making his food taste sweet rather than bitter, the farmer restores health to sickly plants by making them feel better, and the educator “changes a worse state into a better state” by means of words (167a).

The second critique of Protagoras is the famous self-refutation argument. It is essentially a two-pronged argument: the first part revolves around false beliefs, while the second part, which builds on the findings of the first, threatens the validity of the man-as-measure doctrine. The former can be sketched as follows: (1) many people believe that there are false beliefs; therefore, (2) if all beliefs are true, there are [per (1)] false beliefs; (3) if not all beliefs are true, there are false beliefs; (4) therefore, either way, there are false beliefs (169d–170c). The existence of false beliefs is inconsistent with the homo-mensura doctrine, and hence, if there are false beliefs, Protagoras’ “truth” is false. But since the homo-mensura doctrine proclaims that all beliefs are true, if there are false beliefs, then the doctrine is manifestly untenable. The latter part of Socrates’ second critique is much bolder—being called by Socrates “the most subtle argument”—as it aims to undermine Protagoras’ own commitment to relativism from within the relativist framework itself (170e–171c). At the beginning of this critique Socrates asserts that, according to the doctrine under attack, if you believe something to be the case but thousands disagree with you about it, that thing is true for you but false for the thousands. Then he wonders what the case for Protagoras himself is. If not even he believed that man is the measure, and the many did not either (as indeed they do not), this “truth” that he wrote about is true for no one. If, on the other hand, he himself believed it, but the masses do not agree, the extent to which those who do not think so exceed those who do, to that same extent it is not so more than it is so. Subsequently, Socrates adds his “most subtle” point: Protagoras agrees, regarding his own view, that the opinion of those who think he is wrong is true, since he agrees that everybody believes things that are so. On the basis of this, he would have to agree that his own view is false. On the other hand, the others do not agree that they are wrong, and Protagoras is bound to agree, on the basis of his own doctrine, that their belief is true. The conclusion, Socrates states, inevitably undermines the validity of the Protagorean thesis: if Protagoras’ opponents think that their disbelief in the homo-mensura doctrine is true and Protagoras himself must grant the veracity of that belief, then the truth of the Protagorean theory is disputed by everyone, including Protagoras himself.

In the famous digression (172a–177c), which separates the second from the third argument against broad Protagoreanism, Socrates sets up a dichotomy between the judicial and the philosophical realm: those thought of as worldly experts in issues of justice are blind followers of legal practicalities, while the philosophical mind, being unrestricted by temporal or spatial limitations, is free to investigate the true essence of justice. Civic justice is concerned with the here-and-now and presupposes a mechanical absorption of rules and regulations, whereas philosophical examination leads to an understanding of justice as an absolute, non-relativistic value. This dichotomy between temporal and a-temporal justice rests on a more fundamental conceptual opposition between a civic morality and a godlike distancing from civic preoccupations. Godlikeness, Socrates contends, requires a certain degree of withdrawal from earthly affairs and an attempt to emulate divine intelligence and morality. The otherworldliness of the digression has attracted the attention of, among others, Aristotle, in Nicomachean Ethics X 7, and Plotinus, who in Enneads I 2, offers an extended commentary of the text.

In his third argument against broad Protagoreanism, Socrates exposes the flawed nature of Protagoras’ definition of expertise, as a skill that points out what is beneficial, by contrasting sensible properties—such as hot, which may indeed be immune to interpersonal correction—and values, like the good and the beneficial, whose essence is independent from individual appearances. The reason for this, Socrates argues, is that the content of value-judgments is properly assessed by reference to how things will turn out in the future. Experts are thus people who have the capacity to foresee the future effects of present causes. One may be an infallible judge of whether one is hot now, but only the expert physician is able accurately to tell today whether one will be feverish tomorrow. Thus the predictive powers of expertise cast the last blow on the moral and epistemological dimensions of Protagorean Relativism.

In order to attack narrow Protagoreanism, which fully identifies knowledge with perception, Socrates proposes to investigate the doctrine’s Heraclitean underpinnings. The question he now poses is: how radical does the Flux to which the Heracliteans are committed to must be in order for the definition of knowledge as perception to emerge as coherent and plausible? His answer is that the nature of Flux that sanctions Theaetetus’ account must be very radical, indeed too radical for the definition itself to be either expressible or defensible. As we saw earlier, the Secret Doctrine postulated two kinds of motion: the parents of the perceptual event undergo qualitative change, while its twin offspring undergoes locomotive change. To the question whether the Heracliteans will grant that everything undergoes both kinds of change, Socrates replies in the affirmative because, were that not the case, both change and stability would be observed in the Heraclitean world of Flux. If then everything is characterized by all kinds of change at all times, what can we say about anything? The answer is “nothing” because the referents of our discourse would be constantly shifting, and thus we would be deprived of the ability to formulate any words at all about anything. Consequently, Theaetetus’ identification of knowledge with perception is deeply problematic because no single act can properly be called “perception” rather than “non perception,” and the definiendum is left with no definiens.

After Socrates has shown that narrow Protagoreanism, from within the ontological framework of radical Heracliteanism, is untenable, he proceeds to reveal the inherent faultiness of Theaetetus’ definition of knowledge as perception. In his final and most decisive argument, Socrates makes the point that perhaps the most basic thought one can have about two perceptible things, say a color and a sound, is that they both “are.” This kind of thought goes beyond the capacity of any one sense: sight cannot assess the “being” of sound, nor can hearing assess that of color. Among these “common” categories, i.e., categories to which no single sensual organ can afford access, Socrates includes “same,” “different,” “one,” and “two,” but also values, such as “fair” and “foul.” All of these are ascertained by the soul through its own resources, with no recourse to the senses. Theaetetus adds that the soul “seems to be making a calculation within itself of past and present in relation to future” (186b). This remark ties in with Socrates’ earlier attribution to expertise of the ability to predict the future outcome of present occurrences. But it also transcends that assertion in the sense that now a single unified entity, the soul, is given cognitive supremacy, in some cases with the assistance of the senses whereas in other cases the soul “itself by itself.” Perception is thus shown to be an inadequate candidate for knowledge, and the discussion needs to foreground the activity of the soul when “it is busying itself over the things-which-are” (187a). The name of that activity is judging, and it is to this that the second part of the conversation now turns.

c. Knowledge as True Judgment (187a – 201c)

While true judgment, as the definiens of knowledge, is the ostensible topic of the discussants’ new round of conversation, the de facto topic turns out to be false judgment. Judgment, as the soul’s internal reasoning function, is introduced into the discussion at this juncture, which leads Theaetetus to the formulation of the identification of knowledge with true judgment. But Socrates contends that one cannot make proper sense of the notion of “true judgment,” unless one can explain what a false judgment is, a topic that also emerges in such dialogues as Euthydemus, Cratylus, Sophist, Philebus, and Timaeus. In order to examine the meaning of “false judgment,” he articulates five essentially abortive ways of looking at it: (a) false judgment as “mistaking one thing for another” (188a–c); (b) false judgment as “thinking what is not” (188c–189b); (c) false judgment as “other-judgment” (189b–191a); (d) false judgment as the inappropriate linkage of a perception to a memory – the mind as a wax tablet (191a–196c); and (e) potential and actual knowledge – the mind as an aviary (196d–200c).

The impossibility of false judgment as “mistaking one thing for another” is demonstrated by the apparent plausibility of the following perceptual claim: one cannot judge falsely that one person is another person, whether one knows one of them, or both of them, or neither one nor the other. The argument concerning false judgment as “thinking what is not” rests on an analogy between sense-perception and judgment: if one hears or feels something, there must be something which one hears or feels. Likewise, if one judges something, there must be something that one judges. Hence, one cannot judge “what is not,” for one’s judgment would in that case have no object, one would judge nothing, and so would make no judgment at all. This then cannot be a proper account of false judgment. The interlocutors’ failure prompts a third attempt at solving the problem: perhaps, Socrates suggests, false judgment occurs “when a man, in place of one of the things that are, has substituted in his thought another of the things that are and asserts that it is. In this way, he is always judging something which is, but judges one thing in place of another; and having missed the thing which was the object of his consideration, he might fairly be called one who judges falsely” (189c). False judgment then is not concerned with what-is-not, but with interchanging one of the things-which-are with some other of the things-which-are, for example beautiful with ugly, just with unjust, odd with even, and cow with horse. The absurdity of this substitution is reinforced by Socrates’ definition of judgment as the final stage of the mind’s conversing with itself. How is it possible, then, for one to conclude one’s silent, internal dialogue with the preposterous equation of two mutually exclusive attributes, and actually to say to oneself, “an odd number is even,” or “oddness is evenness”?

The next attempt at explaining false judgment invokes the mental acts of remembering and forgetting and the ways in which they are implicated in perceptual events. Imagine the mind as a wax block, Socrates asks Theaetetus, on which we stamp what we perceive or conceive. Whatever is impressed upon the wax we remember and know, so long as the image remains in the wax; whatever is obliterated or cannot be impressed, we forget and do not know (191d-e). False judgment consists in matching the perception to the wrong imprint, e.g., seeing at a distance two men, both of whom we know, we may, in fitting the perceptions to the memory imprints, transpose them; or we may match the sight of a man we know to the memory imprint of another man we know, when we only perceive one of them. Theaetetus accepts this model enthusiastically but Socrates dismisses it because it leaves open the possibility of confusing unperceived concepts, such as numbers. One may wrongly think that 7+5 = 11, and since 7+5 = 12, this amounts to thinking that 12 is 11. Thus arithmetical errors call for the positing of a more comprehensive theoretical account of false judgment.

Socrates’ next explanatory model, the aviary, is meant to address this particular kind of error. What Aristotle later called a distinction between potentiality and actuality becomes the conceptual foundation of this model. Socrates invites us to think of the mind as an aviary full of birds of all sorts. The owner possesses them, in the sense that he has the ability to enter the aviary and catch them, but does not have them, unless he literally has them in his hands. The birds are pieces of knowledge, to hand them over to someone else is to teach, to stock the aviary is to learn, to catch a particular bird is to remember a thing once learned and thus potentially known. The possibility of false judgment emerges when one enters the aviary in order to catch, say, a pigeon but instead catches, say, a ring-dove. To use an arithmetical example, one who has learned the numbers knows, in the sense that he possesses the knowledge of, both 11 and 12. If, when asked what is 7+5, one replies 11, one has hunted in one’s memory for 12 but has activated instead one’s knowledge of 11. Although the aviary’s distinction between potential and actual knowledge improves our understanding of the nature of episteme, it is soon rejected by Socrates on the grounds that it explains false judgment as “the interchange of pieces of knowledge” (199c). Even if one, following Theaetetus’ suggestion, were willing to place in the aviary not only pieces of knowledge but also pieces of ignorance—thereby making false judgment be the apprehension of a piece of ignorance—the question of false judgment would not be answered satisfactorily; for in that case, as Socrates says, the man who catches a piece of ignorance would still believe that he has caught a piece of knowledge, and therefore would behave as if he knew. To go back to the arithmetical example mentioned earlier, Theaetetus suggests that the mistaking of 11 for 12 happens because the man making the judgment mistakes a piece of ignorance for a piece of knowledge but acts as if he has activated his capacity for knowing. The problem is, as Socrates says, that we would need to posit another aviary to explain how the judgment-maker mistakes a piece of ignorance for a piece of knowledge.

Socrates attributes their failure to explain false judgment to their attempting to do so before they have settled the question of the nature of knowledge. Theaetetus repeats his definition of knowledge as true judgment but Socrates rejects it by means of the following argument: suppose, he says, the members of a jury are “justly persuaded of some matter, which only an eye-witness could know and which cannot otherwise be known; suppose they come to their decision upon hearsay, forming a true judgment. Hence, they have decided the case without knowledge, but, granted they did their job well, they were correctly persuaded” (201b-c). This argument shows that forming a true opinion about something by means of persuasion is different from knowing it by an appeal to the only method by means of which it can be known—in this case by seeing it—and thus knowledge and true judgment cannot be the same. After the failure of this attempt, Socrates and Theaetetus proceed to their last attempt to define knowledge.

d. Knowledge as True Judgment with Logos (201c – 210d)

Theaetetus remembers having heard that knowledge is true judgment accompanied by Logos (account), adding that only that which has Logos can be known. Since Theaetetus remembers no more, Socrates decides to help by offering a relevant theory that he once heard.

According to the Dream Theory (201d-206b), the world is composed of complexes and their elements. Complexes have Logos, while elements have none, but can only be named. It is not even possible to say of an element that “it is” or “it is not,” because adding Being or non-Being to it would be tantamount to making it a complex. Elements cannot be accounted for or known, but are perceptible. Complexes, on the contrary, can be known because one can have a true belief about them and give an account of them, which is “essentially a complex of names” (202b).

After Theaetetus concedes that this is the theory he has in mind, he and Socrates proceed to examine it. In order to pinpoint the first problematic feature of the theory, Socrates uses the example of letters and syllables: the Logos of the syllable “so” – the first syllable of Socrates’ name – is “s and o”; but one cannot give a similar Logos of the syllable’s elements, namely of “s” and “o,” since they are mere noises. In that case, Socrates wonders, how can a complex of unknowable elements be itself knowable? For if the complex is simply the sum of its elements, then the knowledge of it is predicated on knowledge of its elements, which is impossible; if, on the other hand, the complex is a “single form” produced out of the collocation of its elements, it will still be an indefinable simple. The only reasonable thing to say then is that the elements are much more clearly known than the complexes.

Now, turning to the fourth definition of knowledge as true judgment accompanied by Logos, Socrates wishes to examine the meaning of the term Logos, and comes up with three possible definitions. First, giving an account of something is “making one’s thought apparent vocally by means of words and verbal expressions” (206c). The problem with this definition is that Logos becomes “a thing that everyone is able to do more or less readily,” unless one is deaf or dumb, so that anyone with a true opinion would have knowledge as well. Secondly, to give an account of a thing is to enumerate all its elements (207a). Hesiod said that a wagon contains a hundred timbers. If asked what a wagon is, the average person will most probably say, “wheels, axle, body, rails, yoke.” But that would be ridiculous, Socrates says, because it would be the same as giving the syllables of a name to someone’s asking for an account of it. The ability to do that does not preclude the possibility that a person identifies now correctly and now incorrectly the elements of the same syllable in different contexts. Finally, giving an account is defined as “being able to tell some mark by which the object you are asked about differs from all other things” (208c). As an example, Socrates uses the definition of the sun as the brightest of the heavenly bodies that circle the earth. But here again, the definition of knowledge as true judgment with Logos is not immune to criticism. For if someone, who is asked to tell what distinguishes, say, Theaetetus, a man of whom he has a correct judgment, from all other things, were to say that he is a man, and has a nose, mouth, eyes, and so on, his account would not help to distinguish Theaetetus from all other men. But if he had not already in his mind the means of differentiating Theaetetus from everyone else, he could not judge correctly who Theaetetus was and could not recognize him the next time he saw him. So to add Logos in this sense to true judgment is meaningless, because Logos is already part of true judgment, and so cannot itself be a guarantee of knowledge. To say that Logos is knowledge of the difference does not solve the problem, since the definition of knowledge as “true judgment plus knowledge of the difference” begs the question of what knowledge is.

The definition of knowledge as “true judgment plus Logos” cannot be sustained on any of the three interpretations of the term Logos. Theaetetus has nothing else to say, and the dialogue ends inconclusively. Its achievement, according to Socrates, has been to rid Theaetetus of several false beliefs so that “if ever in the future [he] should attempt to conceive or should succeed in conceiving other theories, they will be better ones as the result of this enquiry” (210b–c).

Despite its failure to produce a viable definition of knowledge, the Theaetetus has exerted considerable influence on modern philosophical thought. Socrates’ blurring of the distinction between sanity and madness in his examination of knowledge as perception was picked up in the first of Descartes’ Meditations (1641); echoes of Protagorean Relativism have appeared in important works of modern philosophy, such as Quine’s Ontological Relativity and Other Essays (1969) and Kuhn’s The Structure of Scientific Revolutions (1970); In Siris: A Chain of Philosophical Reflexions and Inquiries Concerning the Virtues of Tar-Water (1744), Bishop Berkeley thought that the dialogue anticipated the central tenets of his own theory of knowledge; in Studies in Humanism (1907), the English pragmatist F.C.S. Schiller saw in the section 166a ff. the pragmatist account of truth, first expounded and then condemned; and L. Wittgenstein, in Philosophical Investigations (1953), found in the passage 201d–202b the seed of his Logical Atomism, espoused also by Russell, and found it reminiscent of certain theses of his Tractatus Logico-Philosophicus.

4. References and Further Reading

a. General Commentaries

Bostock, D. Plato's Theaetetus. Oxford, 1988.
Burnyeat, M. F. The Theaetetus of Plato. Trans. M.J. Levett. Indianapolis and Cambridge, 1990.
Campbell, L. The Theaetetus of Plato. 2nd Ed. Oxford, 1883.
Cornford, F. M. Plato’s Theory of Knowledge. The Theaetetus and the Sophist of Plato. Trans. F. M. Cornford. London, 1935.
McDowell, J. Plato: Theaetetus. Trans. J. McDowell. Oxford, 1973.
Polansky, R. Philosophy and Knowledge: A Commentary on Plato's Theaetetus. Lewisburg, 1992.
Sedley, D. N. The Midwife of Platonism: Text and Subtext in Plato's Theaetetus. Oxford, 2004.

b. Knowledge as Arts and Sciences

Burnyeat, M. F. “The Philosophical Sense of Theaetetus’ Mathematics.” Isis 69 (1978). 489–513.
Burnyeat, M. F. “Socratic Midwifery, Platonic Inspiration.” Bulletin of the Institute of the Classical Studies 24 (1977). 7–16.
Santas, G. “The Socratic Fallacy.” Journal of the History of Philosophy 10 (1972). 127–41.

c. Knowledge as Perception

Bolton, R. “Plato’s Distinction between Being and Becoming.” Review of Metaphysics 29 (1975/6). 66–95.
Burnyeat, M. F. “Protagoras and Self Refutation in Plato’s Theaetetus.” Philosophical Review 85 (1976). 172–95.
Burnyeat, M. F. “Plato on the Grammar of Perceiving.” Classical Quarterly 26 (1976). 29–51.
Burnyeat, M.F. “Idealism and Greek Philosophy: What Descartes Saw and Berkeley Missed.” Philosophical Review 90 (1982). 3–40.
Cole, A. T. “The Apology of Protagoras.” Yale Classical Studies 19 (1966). 101–18.
Cooper, J. M. “Plato on Sense Perception and Knowledge: Theaetetus 184 to 186.” Phronesis 15 (1970). 123–46.
Lee, E.N. “Hoist with His Own Petard: Ironic and Comic Elements in Plato’s Critique of Protagoras (Tht. 161–171),” in E.N. Lee and A.P.D. Mourelatos (eds.) Exegesis and Argument: Studies in Greek Philosophy Presented to Gregory. Vlastos. Assen, 1973. 225–61.
Matthen, M. “Perception, Relativism, and Truth: Reflections on Plato’s Theaetetus 152 - 160.” Dialogue 24 (1985). 33–58.
McCabe, M.M. Plato and his Predecessors: The Dramatisation of Reason. Cambridge, 2000.
Modrak, D.K. “Perception and Judgment in the Theaetetus.” Phronesis 26 (1981). 35–54.
Rowe, C.J. et al. “Knowledge, Perception, and Memory: Theaetetus 166B.” Classical Quarterly 32 (1982). 304–6.
Silverman, A. “Flux and Language in the Theaetetus.” Oxford Studies in Ancient Philosophy 18 (2000). 109–52.
Waterlow, S. “Protagoras and Inconsistency.” Archiv für Geschichte der Philosophie 59 (1977). 19–36.

d. Knowledge as True Judgment

Ackrill, J. “Plato on False Belief: Theaetetus 187–200.” Monist 50 (1966). 383–402.
Burnyeat, M.F. and J. Barnes, “Socrates and the Jury: Paradoxes in Plato’s Distinction Between Knowledge and True Belief.” Aristotelian Society Supplementary Volume 54 (1980). 173-91 and 193–206.
Denyer, N. Language, Thought and Falsehood in Ancient Greek Philosophy. London, 1991.
Lewis, F.A. “Foul Play in Plato’s Aviary: Theaetetus 195Bff,” in E.N. Lee and A.P.D. Mourelatos (eds.) Exegesis and Argument: Studies in Greek Philosophy Presented to Gregory. Vlastos. Assen, 1973. 262–84.
G.B. Matthews, G.B. “A Puzzle in Plato: Theaetetus 189b–190e,” in David F. Austin (ed.) Philosophical Analysis: A Defense by Example. Dordrecht, 1988. 3–15.
Rudebusch, G. “Plato on Sense and Reference.” Mind 104 (1985). 526–37.
C.F.J. Williams, C.F.J. “Referential Opacity and False Belief in the Theaetetus.” Philosophical Quarterly 22 (1972). 289-302.

e. Knowledge as True Judgment with Logos

Annas, J. “Knowledge and Language: The Theaetetus and the Cratylus,” in Malcolm Schofield and Martha C. Nussbaum (eds.) Language and Logos: Studies in Ancient Greek Philosophy presented to G.E.L. Owen. Cambridge, 1982. 95–114.
Fine, G.J. “Knowledge and Logos in the Theaetetus.” Philosophical Review 88 (1979). 366–97.
Gallop, D. “Plato and the Alphabet.” Philosophical Review 72 (1963). 364–76.
Morrow, G.R. ”Plato and the Mathematicians: An Interpretation of Socrates’ Dream in the Theaetetus.” Philosophical Review 79 (1970). 309–33.
Ryle, G. “Letters and Syllables in Plato.” Philosophical Review 69 (1960). 431–51.

Author Information

Zina Giannopoulou
Email: zgiannop@uci.edu
University of California, Irvine
U. S. A.

Plato: The Timaeus

There is nothing easy about the Timaeus. Its length, limited dramatic discourse, and arid subject-matter make for a dense and menacing work. But make no mistake, it is a menacing work of great subtly and depth. Cosmology has traditionally received the bulk of scholarly attention. No less important, however, are the dialogue’s narrative elements, beginning with its characters. Socrates needs no introduction, yet who are Timaeus, Critias, and Hermocrates, and why does Plato give them starring roles? Also worth considering is the dialogue’s narrative structure. What begins as a snappy exchange between Socrates and Timaeus soon gives way to a pair of protracted speeches. It is not like Socrates to sit idly by while others pontificate, yet he does. Is this a sign that Socrates endorses these speeches or is there another reason for his silence? And where is Plato? He is absent from the drama, but to what extent is he philosophically present? When reading a dramatic work, one ordinarily assumes a critical distance between the author and his characters. Is the Timaeus any different? Does Plato endorse any of the ideas presented? If he does, is there any way of telling which ideas given that he never speaks for himself?

Like any Platonic dialogue, the Timaeus is dynamic and multifarious—a complex interplay between muthos and logos, art and argument, theatrics and theory. The purpose of this entry is not to render a definitive interpretation of the dialogue, but rather to reveal the possibilities afforded by a close reading of the text.

1. Authorship

Most scholars agree that Plato wrote somewhere between 30 and 40 dialogues. The precise number, however, is an open question owing to disputes over authorship. A case in point is First Alcibiades. Some scholars (such as Denyer) believe that it is authentic; others (such as Schleiermacher) do not. More commonly included among the Platonic dubia are the Cleitophon, Epinomis, Eryxias, Lovers, Minos, Second Alcibiades, and Theages (but reference Altman’s “Reading Order and Authenticity: The Place of Theages and Cleitophon in Platonic Pedagogy”). While doubts surround the authorship of some dialogues, this is not so with the Timaeus, and for good reason. As evidence, we have, for starters, ancient testimony. We find, for instance, in Aristotle more references to the Timaeus than to any other dialogue. It seems unlikely that Aristotle—given his familiarity with Plato’s works, having spent nearly 20 years in the Academy—would have repeatedly attributed this work to Plato if its authorship were doubtful. The Timaeus retained its place in the Platonic corpus throughout late antiquity and the Middle Ages. It was translated into Latin by Cicero (whose translation ends at 47b) and Calcidius, and it inspired commentaries by Plutarch and Proclus. At no point in its transmission was its authorship seriously contested. Confidence in the dialogue’s authenticity remains steady today. Thus, although we may not have the autograph—the original, handwritten text by the author—we have excellent reason to include the Timaeus among, and no good reason to exclude it from, those works issuing from Plato’s hand.

2. Date of Composition

No one knows exactly when Plato wrote his dialogues or their precise order of composition. Nevertheless, it has become commonplace to group them into three compositional periods: early, middle, and late. The Protagoras, for instance, is usually included among Plato’s early dialogues and, if the doxographical tradition is to be trusted, the Laws is his last. As for the Timaeus, scholars are divided. Some (for example Cherniss) include it among the late dialogues—along with the Critias, Sophist, Statesman, Philebus, and Laws—given their stylistic affinity. Others (including Owen) call attention to the Timaeus’s philosophical content—particularly its use of paradeigmata to explain predication—as evidence of an earlier dating. It is debatable, however, whether style can reliably establish a dialogue’s age. Consider, for example, the statue Laocoön and His Sons. One may ask: Is it a Greek original, a Roman original, or a Roman copy of a Greek original? Regrettably, there is little, if any, telling if style is the sole measure. A feel for style, after all, is what led Winkelmann to propose erroneously a fourth-century BCE date for the statue. Or consider another example: a mature artist who completes an unfinished work from his youth. Where does it fit in his oeuvre? Because the piece was finished late, classifying it as “early” would not be entirely fitting; but because it was started early, calling it “late” also seems mistaken. This is not to say that dating artwork is impossible, but it does suggest that knowing a work’s time of production requires knowing its method of production, which, concerning the dialogues, we know preciously little about.

Ordering the dialogues based on content is also problematic. Suppose that Plato writes three dialogues: one advancing an idea, a second expanding on that idea, and a third rejecting the more fully developed version of the idea. If we set these works side-by-side, there seems to be a progression of thought from an idea’s birth and development to its repudiation, which suggests that the dialogues were written in chronological order. Behind this thinking, however, lies an assumption: that the dialogues record Plato’s personal teachings as they emerged and evolved over time. This, admittedly, has some plausibility to it. Philosophers have been known to write dialogues for didactic purposes: Galileo’s Dialogues Concerning the Two Chief World Systems and Berkeley’s Three Dialogues between Hylas and Philonous come to mind. But the difference lies in the fact that Galileo and Berkeley, apart from dialogues, wrote treatises wherein they expressed their own thoughts in their own voices. With the exception of letters, several of which are likely spurious, Plato wrote dialogues exclusively, never once stepping out from behind his dramatis personæ. This makes attributing ideas to Plato considerably more difficult. If his purpose were to proselytize, then why did he not utilize a more direct form of discourse? It was, after all, not uncommon practice for ancient philosophers in their writings to speak for themselves. Heraclitus (Diogenes Laertius, IX. 5–6), Zeno of Elea (Plato, Parm. 127c–d) and Anaxagoras (Diogenes Laertius, II. 6; cf. Plato, Phd. 97b) all wrote books and, if the testimonia is any indication, wrote them in such a way that their voices were unmistakable. That Plato does not speak for himself suggests that his interests may have been less with dictation than with participation. Given their lively dramatic character, the dialogues act as powerful magnets, drawing us in, inviting us to listen to the conversation, to participate in the exchange, and to live the only kind of life that Socrates considered worth living. If this is what the dialogues are about—if they are more about the questions raised than about the answers given—then the Timaeus’s content will tell us little, if anything, about when it was written.

By no means do these considerations extinguish the heated debate over the Timaeus’s date of composition, but they do at least provide one with compelling reasons for thinking that rendering a decisive compositional chronology is a problem that will not soon be resolved.

There are many fine studies that may be consulted on the problems and possibilities of dating Plato’s dialogues. Excellent points of departure include Brandwood’s “Stylometry and Chronology” and Howland’s “Re-Reading Plato: The Problem of Platonic Chronology.”

3. Dramatis Personæ

a. Timaeus

Opinion has shifted over Timaeus’s historicity. The ancients (such as Cicero and Iamblichus) took him to be a real person, whereas scholars today tend to regard him as a literary invention. Be that as it may, his character, thanks to Plato’s creative genius, radiates an abundant life. Socrates introduces Timaeus as a foreigner from Locri, a town in southern Italy, praising him as a poet and sophist and as one who has managed high-ranking political offices and reached the summit in all areas of philosophy (20a). Timaeus’s philosophical credentials are reaffirmed by Critias, who honors him as an astronomer who investigates the nature of all things (27a). Philosopher, diplomat, and lyricist—Timaeus has the markings of a true polymath. These wide-ranging talents bring to mind the Republic’s philosopher-king who composes an autochthonous myth to explain human origins (414c–415c). The philosopher-statesman Timaeus will in similar fashion captivate his audience with a likely story about cosmic origins. But the philosopher-king in the Republic promulgates his story knowing it to be untrue. Does Timaeus do the same?

b. Socrates

In practically every Platonic dialogue, from beginning to end, Socrates is the guiding narrative force. Often, he lures others into discussion, leading them through dialectic to see where their thinking has gone astray. Whether he is asking questions or providing answers, Socrates is usually engaged in conversation. In the Timaeus, however, he is conspicuously silent. He invites his companions to give speeches of their own, but once they begin, he listens intently, never interrupting. There are other dialogues—the Phaedrus, Symposium, and Republic, to name a few—where Socrates demonstrates patience while listening to lengthy discourses. But Timaeus’s speech easily surpasses these in duration and ambition. Why does Socrates hold his tongue? One reason seems to be that the day before he entertained his guests with a speech (17b ff.) and now they are expected to return the favor (20b). Dressed for the occasion, he vows to “keep his peace and listen” (27a1) while he dines on his “feast of speeches” (27b7–8). Another reason for Socrates’s speech: it is not an account but a story (muthos), and thus not to be scrutinized but savored. Still, Socrates is not himself—at least, not what we come to expect. What is he up to? Or maybe one should ask: What is Plato up to in depicting Socrates as he does?

c. Critias

The identity of Critias is disputed. The name brings to mind the notorious oligarch Critias: student of Socrates, uncle of Plato, and leader of the Thirty Tyrants. But the dialogue’s dramatic date suggests that we might be dealing with someone else. By most accounts, the dialogue takes place between 429 and 408 (see Dramatic Date and Setting). At that time, Critias the oligarch (b. 460) would have been an astute man between the age of 30 and 50. The dialogue’s Critias, however, struggles to recollect basic things discussed the day before (26b) while at the same time having little difficulty recalling a story he heard “a long time ago” (26c5–6). Short-term memory loss and a robust long-term memory are qualities typically associated not with a sharp-minded, middle-aged man, but rather with someone who is elderly. Also worth noting is Critias’s remark that when he first heard the Atlantis story from his grandfather, the poems of Solon were new (21b). Even if we assume that these poems were written late in Solon’s life (d. 560), it seems strange that someone living in the mid-fifth century would think of them as new. These considerations suggest that the dialogue’s Critias is probably not the oligarch, but more likely his grandfather or someone else with the same name. If that is the case, why does Plato include a character named Critias, knowing what that name would have connoted to his Athenian audience? For 21^st century speculations on Critias’s identity, see Lampert and Planeaux “Who’s Who in Plato’s Timaeus-Critias and Why,” Welliver, Character, Plot, and Thought in Plato’s Timaeus-Critias, and Nails, The People of Plato: A Prosopography of Plato and Other Socratics.

d. Hermocrates

There is little doubt that Hermocrates is the great Syracusan diplomat and general of the Peloponnesian War, whose intelligence, courage, and experience earned him praise from Thucydides (Thuc. 6.72). At the peace conference at Gela, Hermocrates alerted the Sicilian Greeks – and at Syracuse his fellow citizens – to the imperial threat posed by Athens. Moreover, because of his effort to unify warring factions, Athens met her defeat in the Sicilian expedition. Plato’s audience would have known Hermocrates not only for his ability to induce action through speech, but also as one of the chief adversaries of imperialistic Athens. Readers should therefore note the irony when Hermocrates cajoles Critias into telling his story about ancient Athens’ effort to liberate those nations subjugated by imperialistic Atlantis (20d).

4. Dramatic Date and Setting

There is no specific mention of locale, but since Socrates receives the speeches as “guest gifts” (20c1, 27a2), it is likely that, like Timaeus and Hermocrates, Socrates is a guest at Critias’s home in Athens. As for the dialogue’s dramatic date, based on Critias’s remark that his discourse will be both payment of debt to Socrates and a tribute to the goddess on her feast-day (21a; cf. 26e), it is reasonable to think that the Timaeus takes place during one of many Athenian festivals celebrated in honor of Athena. Opinions vary as to which festival Plato has in mind. Some (such as Cornford) argue that it is either the annual (Lesser) Panathenaea or the quadrennial (Greater) Panathenaea, both of which took place in Hecatombaeon (July/August). Others (such as Taylor), who regard the events described in the Republic and Timaeus as occurring on subsequent days, argue that it must be a different Athena-centered festival (like Plynteria), since the events in the Republic take place during the Bendideia, which was celebrated in Thargelion (May/June), a full two months before the Panathenaea. Opinions regarding the year of the drama also vary: 429 (Nails), 421 (Lampert and Planeaux), 411 (Press), and 409–408 (Zuckert).

5. Narrative Structure

Apart from the characters, dramatic date, and physical setting, narrative structure is an important feature of Plato’s dialogues. Some dialogues such as the Republic, Symposium, and Phaedo are narrated. Others such as the Euthyphro, Apology, and Crito are dramatic, consisting of direct dialogue between characters without narration. Although it may seem trivial, narrative structure can have a bearing on how one reads and interprets a dialogue. Unlike a narrated dialogue, which is presented by someone who has already digested and formed an opinion about the material that he is relating to his audience, a dramatic text is free of such bias. In a narrated dialogue, however, an author can provide extra-dialogical details such as a character’s body language and tone of voice, how characters are physically oriented to one another, and a running commentary. A narrated dialogue can also have varying degrees of depth, from a narrator reporting a conversation he himself heard to a narrator reporting a conversation he heard from someone else, who might have heard it from yet another person, and so on. This depth naturally raises questions about the narrator’s credibility. This is relevant to a dialogue such as the Symposium, which Aristodemus relates to Apollodorus, who in turn relates it to his friend Glaucon, an exchange that we ourselves witness as readers. Narrative depth also plays a role in the Republic, where we find Socrates criticizing mimetic speech while practicing it as the dialogue’s narrator. As a direct drama, the Timaeus lacks narrative depth, nor is it particularly rich in dramatic discourse. Although there are dialogical passages such as the opening exchange between Socrates and Timaeus, uninterrupted speeches account for over 70 of the work’s 75 Stephanus pages. This raises a fair number of concerns, many of which pertain to Plato’s relation to the text. One may argue that by not interrupting Timaeus’s speech, Plato is giving it his assent. Why else would he allow Socrates to fade uncharacteristically into the background? It is worth noting, however, that the narrative does not end at Timaeus 92c, but continues with Critias 106a. In other words, the Timaeus and Critias are published as separate dialogues, but they form a narrative unit. Because Plato left the Critias incomplete, we have no idea how it was to end or whether, as some have speculated, Plato planned a third dialogue, the Hermocrates, to round out a trilogy. Socrates might have remained a passive observer throughout, or he might have remained temporarily silent, waiting politely for Critias to finish his speech before launching his Socratic assault. But maybe Plato left the Critias unfinished on purpose as an exercise for his audience to pick up where he left off, to bring the dialogue to a close, and to be not just passive spectators but active participants, like the characters in the dialogues, makers of philosophical discourse. Open questions abound.

6. Outline & Analysis of the Dialogue

a. Prologue, Part 1: An Invitation to Storytelling (17a–20c)

Socrates opens the dialogue with a question, although not the kind the reader expects. Rather than asking about piety, justice, or beauty—the usual Socratic fare—he enquires into the whereabouts of a missing guest. He counts those present, “One, two, three,” only to come up short: “But where is the fourth?” Timaeus attests that the guest’s absence is not intentional: “Some illness (astheneia) befell him” (17a). Nevertheless, one wonders whether Timaeus is telling the truth. Was the guest willing but unable to come, or might Timaeus be covering for someone unwilling to face Socrates? And who might this person be? Plato never reveals his identity. Theaetetus, Clitophon, and Plato himself were candidates put forward by ancient authorities (Procl. In Ti. 16–17). But a compelling case has been made in recent years for thinking that the missing guest is Alcibiades, whose absence may have had to do less with physical illness than with moral weakness (see Lampert and Planeaux). Timaeus does not say what kept the guest away, but only that it is astheneia, which could refer to either physical or moral infirmity. If moral sickness is the reason, one cannot accuse Timaeus of dishonesty. Then again, he is not completely forthcoming either, leaving ambiguous the real reason for the guest’s absence. This is not surprising given Timaeus’s own admission that he can give nothing more than an imprecise account of anything related to the physical world (29b)—a deficiency that would presumably extend to the physical or psychological condition of an absent party guest. At any rate, Timaeus, speaking for Critias and Hermocrates, assures Socrates not to worry: those who are present will repay Socrates for the gifts he so generously bestowed the day before.

Socrates’ gifts, it turns out, were speeches about the best kind of polis (17c–19a). At Timaeus’s request, Socrates rehearses his chief points. In the best polis:

1) everyone is given one occupation suited to his or her nature;

2) there is no gender discrimination: occupations are open to men and women alike;

3) the artisans occupy a class separate from the guardians, who are charged with making war on behalf of the polis;

4) the guardians, who have a spirited and philosophic nature, live communally, may not own private property, and undergo the same rigorous training regardless of gender;

5) all marriages and child-rearing are regulated by the polis; and

6) offspring of good citizens are reared as guardians while offspring of bad citizens are handed over to the polis to be raised presumably as artisans.

These points naturally bring to mind the Republic’s kallipolis, but what is included on the list is just as intriguing as what is excluded; for Socrates leaves untouched, among other things:

1) the deleterious effects of poetry on the soul (Rep. 3 and 10);

2) the search for justice and the analogy between the soul and the state (Rep. 4);

3) the distinction between knowledge and opinion and their respective objects (Rep. 5);

4) the metaphor of the sun, divided line, and allegory of the cave (Rep. 6 and 7);

5) the philosopher-king and his education in mathematics and dialectic (Rep. 7); and

6) the eventual decline and collapse of the kallipolis into tyranny (Rep. 9 and 10).

Socrates in the Timaeus paints a picture that pales in comparison to his account in the Republic, bringing to light the polis’s political foundations but disregarding the philosophical forces animating it. How strange for Socrates to assemble a political body only to leave it soulless. Equally strange is Timaeus’s reaction. Upon finishing his summary, Socrates asks whether he has omitted anything. Timaeus responds, “Not at all” (19b). Surely, this is contrary to the reader’s expectations. If, from a dramatic point of view, the Republic and Timaeus had taken place on subsequent days, Timaeus should have pointed out these omissions. What are we to make of this? One suggestion is thatTimaeus forgot parts of the discussion from the day before and answers to the best of his recollection. Or, maybe Timaeus knows Socrates left bits out, but responds as he does just to move the conversation along. Another possibility, however, is that Socrates has summarized his speech in its entirety, omitting nothing. In this case, the polis of the Timaeus is not the kallipolis of the Republic, but rather its likeness or approximation. This reading fits the rest of the drama quite well, especially when considering that the showpiece of the dialogue, Timaeus’s cosmology, is itself no more than a likely story, an approximation of the truth (29d).

Plato drives the wedge even deeper between the Republic and Timaeus by having Socrates express a desire to see his polis set in motion—like beautiful animals “moving and contending in some struggle” (19c). Contrast this with Socrates’ claim in the Republic that the kallipolis, regardless of whether it could actually come to be, would still serve as “a heavenly model for anyone who wants to see and found a polis within himself” (592b). Of course, this might be an inconsistency in Socrates’ thinking, but it might also be that he is up to his old ironic tricks. In the Republic, because Glaucon and Adeimantus were receptive to dialectic, Socrates’ traditional psychoanalytic approach of asking questions was enough to set their souls in motion. Timaeus and Critias, given their social status and alleged reputation for wisdom, would predictably be a bit more stubborn and less receptive to dialectic. For this reason, Socrates, like a behavioral psychologist, sets up a test with his speeches from the day before in order to draw from their responses insight into their natures. Just before he finishes, Socrates, as he so often does, flatters his companions, singling them out as the only living men capable of satisfying his desire (20b)—a transparent display of Socratic irony if there ever was one. Thus, the apparent inconsistency in Socrates’ thinking might be nothing more than a change in methodology. Socrates, as is so often the case, is toying with his interlocutors, using them as guinea pigs in his little experiment. One wonders whether it is for this reason that the fourth member of their party—if he is indeed Socrates’ spurned lover, Alcibiades, who had drunkenly embarrassed himself in the Symposium—failed to show.

b. Prologue, Part 2: The Story of Atlantis (20c–27b)

Hermocrates, promising to repay Socrates’ guest gifts, invites Critias to recount a story that he shared the day before. Critias first heard the story as a ten-year old from his grandfather while attending the Apaturia (21b), a three-day festival associated with hereditary groups—phratries, as they were known—which gathered to celebrate their patrilineal kinship (homopatoria) and to receive new members. A legendary border dispute between Athens and Boeotia served as the festival’s etiological backdrop—an important fact omitted by Critias. The principal figures were two combatants: the Boeotian king Xanthus (“Fair One”) and the Athenian champion Melanthus (“Dark One”). The two proved to be equals—that is, until Melanthus at one point cried out to his opponent, “You are cheating, Xanthus, for there is someone behind you!” Xanthus, distracted, whirled around and Melanthus, seizing his opportunity, dealt a fatal blow. Some versions of the story allege that Melanthus tricked Xanthus; others blame Zeus Apātenōr (“Zeus Deceiver”) or Dionysus Melanaigis (“Dionysus of the Black Goatskin”) for the ruse. All versions explain the festival’s origins with a punning etymology: the Apaturia commemorates Athen’s victory by apatē (deception). Thus, “Apaturia” would have had for Plato’s audience a dual meaning, signifying both a reception and a deception. The reader should keep this in mind when listening to Critias, for his story emulates the Apaturia: it pays respect to common origins and fraternity, yet has an element of deception insofar as it presents a distorted picture of the state that Socrates wishes to be set in motion.

Before relating his story, Critias provides some background regarding its transmission. It dates back to Solon, Critias’s distant relative, who heard it from an old priest from Sais, an Egyptian city that shared with Athens the same patron goddess (Neith/Athena, 21e). This is significant; for just as the Apaturia reunited communities with blood ties, the meeting between Solon and the Egyptian priest marks the reunion of two cultures with tutelary ties. But there is another tie worth noting, namely the intellectual kinship between Critias and the priest. From his emphasis on the story’s lineage, Critias makes known his esteem for ancient records and hearsay. The Saisian priest likewise shows his preference for ancient hearsay by criticizing Solon’s speeches about antiquities. “You are young, young in soul, all of you,” the priest tells Solon. In particular, he criticizes the Greek myth of Phaethon, describing it as a story (muthos) with no basis in empirical fact (22c–d). Socrates, of course, was critical of this type of unimaginative positivism, which in the Phaedrus he refers to as a sort of “rural wisdom” (agroika sophia, 229e). The reader may wonder whether Socrates’ companions will ever fulfill his wish. He has presented them with a lifeless state and entreated that they set it in motion, yet it seems unlikely that an appeal to the lifeless science of the Egyptians will accomplish this end. This is worth bearing in mind when listening later to Timaeus’s strange, but lively, creation story (muthos).

With the background of the story out of the way, Critias gets to the story proper, which, like the Apaturia’s etiological myth, concerns an ancient dispute. The players are Atlantis and Athens—not the Athens familiar to Solon, but rather an Athens existing some 9,000 years before. Governed by excellent laws and unsurpassed in war, Athens struggled against the imperialistic Atlantis. Although the odds were stacked against her, Athens emerged victorious, liberating nations that Atlantis had enslaved along the way (25b–c). It is worth remembering that fifth-century Athens, far from being a spirited liberator, was herself an ambitious, imperialist power. These ambitions would contribute not only to Athens’ greatness, but also to her demise. Perhaps her greatest embarrassment was the disastrous Sicilian Expedition. Shortly after deploying a massive fleet of ships and hoplites, Athens recalled the expedition’s principal proponent, Alcibiades, to stand trial for sacrilege. Rather than returning to Athens, Alcibiades fled to Sparta, where he gave his best advice on how to overcome his mother city. The Athenian war effort deteriorated rapidly. Its eventual defeat was assisted by none other than Hermocrates, who, like Melanthus, achieved victory through deception (Thuc. 7.73–4). One night, he sent associates to the Athenian camp. Pretending to be traitors, they misled the Athenians into believing that Syracusans were guarding the roads and that it would be safer to withdraw during the day. Unaware of the ruse, the Athenians lingered, giving the Syracusans time to block the escape routes and disable the Athenian ships. Days later, the expedition would end in catastrophe with thousands of retreating Athenians killed and several thousand more sold into slavery or left to die in prisons.

Permeating Critias’s speech, therefore, is the theme of deception. He not only receives the story at a festival of deception, but transmits it at a time when Athens herself would fall victim to deception. One even begins to wonder whether Critias himself should be trusted. Consider his claim that Socrates’ speech the day before “was not far off the mark from agreeing with … what Solon said” (25e). This clearly overstates the truth. Not unlike Socrates’ polis, ancient Athens was a regimented society with discrete class divisions: (1) craftsmen, (2) shepherds, hunters, and farmers, (3) warriors responsible only for executing matters of war, and (4) priests (24a–b). But here the similarities end. Socrates makes no mention of priests; and although he does separate the artisans and farmers from the warriors, he does not separate the artisans from the farmers (17c). Moreover, Critias says nothing about how ancient Athens treated its women, the moral character of its warrior class, or whether marriages and child rearing were state-regulated. Socrates’ polis and ancient Athens have much less in common than Critias suggests, which prompts the question: What is the point of Critias’s story? Why does Plato include it in the dialogue? Two reasons come to mind. One is that Plato likely intends to invoke a sense of dramatic irony. Critias ironically relates a story of Atlantis’ imperial hubris at a time in history when Athens was planning the Sicilian Expedition. To do so at the behest of Hermocrates (20d) only intensifies the irony (see Dramatis Personæ: Hermocrates). Another reason is to invite his readers to ponder how the love of glory can obstruct the pursuit of truth. Critias believes that the poleis described by Solon and Socrates are the same, but because he is so enamored with the story’s lineage, he fails to notice their differences. By inflating his reputation (doxa), Critias leaves himself vulnerable to the deceptiveness of opinion (doxa).

c. Monologue, Part 1: The Creation Story of Intellect (27c–47e)

Almost as a tease, Critias confesses that he stopped short of giving a full account of ancient Athens. If Socrates cares to hear the rest of the story, he must first listen to Timaeus, who will speak on cosmic origins and the creation of man (27a). Socrates, thrilled at his forthcoming feast of speeches, invites Timaeus to begin, requesting that he first follow custom by invoking the gods. What Timaeus does instead is peculiar. To start with, he pauses to reflect on the relevance of such an invocation, remarking that at the onset of any affair, small or great, everyone, even someone of “little prudence,” calls on some god (27c). What is to be made of this? Is it merely an incidental remark or a subtle jab at Socrates and Critias, who, having made no invocation themselves, lay bare their own imprudence? At any rate, there is an underlying irony to Timaeus’s remark: he sanctimoniously chides those who make no pious gestures, while making no pious gesture himself (27d). Instead of calling upon the gods, he calls upon ordinary men who will judge his speech (29d). Is this Plato’s way of suggesting to the reader that Timaeus is himself imprudent? Or is it that Timaeus, being a sophist, believes that there are two sets of rules: those that apply to him and those that apply to everyone else? It is difficult to say what precisely Plato intends by this, but one thing is for sure: as with Critias, the reader must guard himself against Timaeus’s potential deceptiveness.

As he begins, Timaeus lays some philosophical groundwork, discussing four issues vital to his cosmology:

1) the metaphysical distinction between Being and Becoming;

2) the principle that whatever comes to be does so owing to some cause;

3) the role played by a divine craftsman or demiurge in making the cosmos; and

4) the extent to which we can be confident that an account is true given the entities with which it is concerned.

The first of these—the Being-Becoming distinction—Timaeus introduces without hesitation or defense. There are, he says, two kinds of entities: (1) genuinely existing, un-generated and indestructible, changeless entities, which are grasped by reason together with a rational account and (2) entities that do not genuinely exist, that come to be and pass away, and that individuals form opinions about based on irrational sensation (27d–28a). Readers familiar with the Republic, Phaedo, and Symposium will recognize this as the traditional “Platonic” distinction between unchanging Forms and changing objects of everyday experience. Timaeus does not explicitly identify the first class of entities as “Forms” (ideai, eidē), but he does refer to them repeatedly as “models” or “paradigms” (paradeigmata, 28a–c, 29b, 31a, 37c, 38b–c, 39e, 48e–49a), a term that Plato uses elsewhere to denote the Forms (Euthphr. 6e, Rep. 472c, and Prm. 132c–d).

Next, Timaeus turns his attention to the cosmos, which is visible and tangible and hence something belonging to the second class of entities: those that come to be and pass away. But what caused the cosmos to be? In other dialogues, the Forms function as causes (Euthphr. 5d, 6d–e; Phd. 100b–103a, 103c–105c). In the Timaeus, the principal cause of cosmic order is the demiurge, or divine craftsman (dēmiourgos). Timaeus explains that a craftsman, when making something, bases his work on a model (paradeigma, 28a). This model, he argues, must belong to the class of unchanging things because craftsmen always intend their work to be beautiful and only an unchanging model can help craftsmen achieve this end. It is no different regarding the cosmos, which the demiurge makes by looking to “that which is grasped by reason and prudence and is in a self-same condition” (29a). As he prepares to give his account of cosmic origins, Timaeus offers a word of warning: an account concerned with changing things will always be less accurate than one concerned with unchanging things. Consider the difference between a mathematical proof and a forensic analysis: the latter, while it might be compelling, is merely probabilistic; the former, as long as one has done the calculation properly, guarantees that one has grasped the truth. Timaeus’s point is that insofar as the cosmos is itself something generated, any account pertaining to it, like a forensic analysis, can only be likely, never certain. With that in mind, he concludes, “It is fitting for us to receive the likely story (ton eikota muthon) about these things and not to search further for anything beyond it” (29d).

Socrates expresses his enthusiasm for Timaeus’s proposal, encouraging him to “perform the song (ton nomon) himself” (29d). This is an interesting choice of words. In the Republic, Socrates stresses the sovereignty of musical training, emphasizing how rhythm and harmony are able to permeate the soul and perfect it (401e). Socrates, by referring to Timaeus’s forthcoming speech as a “song,” acknowledges not only its overall significance, but also the potential impact, positive or negative, on those who are listening. Also noteworthy is Socrates’ seemingly complimentary remark, “We have received your prelude so wondrously (thaumasiōs).” The word thaumasios literally means “wonderful” or “marvelous,” which by itself seems innocuous enough, but Plato does occasionally uses it ironically (Phdr. 242a, Rep. 435c). Is this the case here? Is Socrates returning Timaeus’s earlier jab (27a), a final salvo before Timaeus begins his speech? It would certainly not be out of character for Socrates to let Timaeus know in a veiled manner, “Something is not right. I am on to you.” Plato, with his word choice, might be giving readers fair warning: something about Timaeus is not sitting well with Socrates, so his speech will be received gladly as a guest-gift should, but with the right amount of caution. It would be best for us too, as readers, to follow Socrates’ circumspect lead.

Resuming his speech, Timaeus gives a general account of how the demiurge began his work. “The god” (ho theos), as Timaeus calls him, being beautiful and intelligent, intended his creation to resemble him as much as possible (29e–30a). Onto pre-existing matter, therefore, which moved unmusically and without purpose, a rational order was imposed. Knowing the intelligent to be more beautiful than the unintelligent, the demiurge imbued the cosmic body with soul (30b). As his model, the demiurge used that living being (zōion, 30b) which embraces all living beings: “holds them within itself, just as this cosmos holds and embraces us and all the other nurslings constructed as visible” (30c–d). As for whether there is one cosmos or many, Timaeus argues against the Presocratic pluralists who posit an infinite number of kosmoi (for example, Democritus, DK 67A1). For Timaeus, because the cosmos resembles its model and its model is one in number, the cosmos too must be one in number. To create the cosmic body, the demiurge drew upon four elements—fire, air, earth and water—in equal proportion; and basing his work on a model, he created a body whole and perfect, one in number, free of old age and disease, and spherical in shape (31b, 33a–b). In addition, because the cosmic body was to be self-sufficient—in no need of anything external to it—it was made without eyes or ears, atmosphere for breathing, or organs for digestion (33c). It also lacked hands, legs, and feet; and the motion imposed on it was not directional—moving linearly in this or that direction—but rotational. The reader may rightly consider strange this so-called cosmic body, for even though it is based on a model embracing all living beings, its appearance is wholly unlike any other known living thing. But without any doubt, the strangeness does not end here.

Next comes the creation of the cosmic soul (34c–36d). This passage is notoriously difficult, as it contains a detailed account of how the demiurge fashions the substance of the soul from a mixture of pairs: (1) of the Indivisible and the Divisible and (2) of the Same and the Other. How can seemingly unmixable things like the indivisible and the divisible be mixed together? This is a puzzle that Timaeus leaves for his audience to work out. Just as puzzling is the subsequent passage on the movement of this soul according to certain mathematical ratios. Is the reader to take these passages seriously? Several ancient commentators including Aristotle, Xenocrates, and Plutarch did. Perhaps we should as well. But there is good reason to think that something else is intended, even though what that is might be somewhat obscure. For one thing, one might ask how Socrates, Critias, and Hermocrates could follow Timaeus’s incredibly complicated and arguably convoluted story. It is not as though Timaeus had visual aids—at least none of which the reader is aware. Would anyone listening to Timaeus not want some clarification? Would someone not think to ask a question or two? It is unusual for Socrates, of all persons, to not hit the pause button to engage his companion. This is not to say that Timaeus is being insincere or that he has something up his sleeve, but so much of the narrative up to this point has raised questions about trustworthiness. Perhaps there is something more devious, even diabolical, to Timaeus’s speech. Or perhaps this is being too cynical. There is much ground yet to cover.

Timaeus concludes the first part of his story by describing how the demiurge makes time (37c–38c), the planets (38c–39e), and lesser gods (39e–40b). The creation of man the demiurge delegates to these lesser gods (40d–47e, see Monologue, Part 3: The Creation Story of Man). Particularly strange is how Timaeus describes the divine revolutions of the soul. These motions, he says, are bound within a spheroform body named “head,” which is attached to a body in order to prevent it from rolling along on the ground (44d). This passage conjures up the nightmarish image of Empedoclean eyeballs rolling about on the ground in search of foreheads (DK 31B57). But it also should remind readers of the spherical humanoids featured in Aristophanes’ account of the origins of love in the Symposium. There is no questioning the ambitiousness and inventiveness of Timaeus’s story, yet its content, bordering on the absurd, makes it difficult to see it as something other than a parody. The suggestion that Timaeus is manufacturing a sort of parody becomes even more plausible in the second part of his story.

d. Monologue, Part 2: The Creation Story of Necessity (47e–69a)

The cosmos, as Timaeus’s story continues, emerges not only from an act of divine reason; it also arises from brute necessity. Because reason and necessity are cosmic co-creators, Timaeus transitions from the role played by a calculating demiurge to that of unthinking necessity. For starters, he returns to the distinction drawn earlier between Forms and sensible things, basing this metaphysical distinction now on an epistemological distinction between intellect (nous) and true opinion (doxa alēthēs). Because different epistemic states require different objects, intellect and true opinion must be drawn to different objects—Forms and sensible things, respectively (51d–e). But here he argues that there must be a third item added to the list. Children are not born from a single parent, but rather from two: a father and a mother. Thus, in addition to that which comes to be (offspring ~ sensible thing) and that from which it comes (father ~ Form), there must be something in which the created thing comes to be (mother ~ space [chōras], 52a). Note, however, how Timaeus presents his argument. He does not say that any of this is demonstrably true—that there is some intellectual compulsion to believe it. Instead, he says, “Here’s how I myself cast my vote (psēphon)” (51d). Voting is how a legislature promulgates a law or how a law court arrives at a legal decision; it is not the preferred method of arriving at scientific truth. Timaeus draws a distinction between reason and true opinion—the former immovable by persuasion, the latter alterable by persuasion—yet given that he casts a vote, how can his account be anything other than mere opinion and hence something that he, or anyone else, might be persuaded against?

What follows is yet another complicated passage—a lengthy one concerning the constitution of matter (53c–55c). This is his famous discourse on triangles. As has already been established, there are four kinds of matter—fire, air, earth, and water—and each contains particles, which, we are now told, are geometrical solids (acting as molecules) composed of elementary right triangles (acting as atoms), either isosceles or scalene. In effect, all bodies can be reduced to collections of triangles. There is little need here to spell out Timaeus’s theory in detail. Other scholars have already performed that formidable task (see, for example, Cornford, Plato’s Cosmology and Kalkavage, Plato’s Timaeus, Appendix C). Suffice it to say, what Timaeus renders, if anything, is an aesthetically pleasant picture of the physical world with all of its beautiful geometrical shapes: tetrahedrons (fire), octahedrons (air), icosahedrons (water), hexahedrons (earth), and dodecahedrons (panels for the constellations). His picture is also a lyrical one; for in a brief digression on the subject of whether the cosmos is one or many, Timaeus says, “In reasoning about all these things, someone would do so musically (emmelōs)” (55c). It is as if he considers himself to be engaged in a dramatic contest of sorts. Who can render the most compelling, the most rhapsodic, the most beautiful song? Whose story (muthos) will collect the most votes from the judges? Timaeus has already let his audience know for whom his voting stone (psēphos), if he were given one, would be cast. Others, he confesses, may cast theirs for another (55d).

As one might expect from a highly refined literary work like Timaeus’s, word play abounds. Consider, for instance, the passage where Timaeus pauses to reflect on his storytelling (59c–d). He says at first that it would not be difficult to see where his story is headed—not for anyone “who pursues the look of likely stories.” Whenever such a person puts aside or buries (katathemenos) definite accounts of the unchanging and turns to likely accounts of transient things, he permits himself a pleasure (hēdonē) and time to engage in a sort of childish play (paidian). Thus, he invites his audience to “give free rein to this very play … [and] proceed to the likelihoods next in order.” The very next sentence engages in this sort of play: water mixed with fire, which Timaeus calls “fluid” (hugron), comes from “flowing over the earth” (huper gen reon, 59d). In this way, he presents the physical derivation in terms of a linguistic one. Clearly, this is Timaeus having a bit of fun, but it is consistent with his entire speech up to this point. Not long after, he claims that fire (thermon) is hot because it minces (kermon, 62a)—yet another play on words. Timaeus’s comedic storytelling continues with his account of eating, which he describes obscurely in terms of voiding (kenōseis) and refilling (plērōsis). His subsequent accounts of tastes (64a–65b), smells (66d–67a), sounds (67a–c), and colors (67c–68d) are just as impish, often stated matter of factly without explanation regardless of how absurd they might sound to his audience. Is the reader to take these accounts seriously, or are they in fact sly Platonic parodies of the detailed, yet cold and soulless accounts popular among scientists of his day? Timaeus’s most baffling claim perhaps—at least, among his more baffling claims—is in his discussion on color mixing. Red and black, he posits, when mixed together yield green (68d). This simply does not make sense—not from a scientific point of view, at any rate. How can this be taken seriously? What precisely is Timaeus doing?

Drawing his Story of Necessity to a close, Timaeus prepares to deliver his conclusion. In doing so, he adopts a more serious tone, but there is still something strange about what he says. He begins with a metaphor: “Now that the kinds of causes have been sifted out and lie ready to hand for us, like wood for builders, out of which we must weave together the account that remains…” (69a). A reasonable response to this would be a quizzical one. Flour and grains are sifted, not wood, and Timaeus clearly knows this given what he says earlier in his story about the movement and ordering of the elements in space: “just like the particles shaken and winnowed out by sieves and other instruments used for purifying grain: the dense and heavy are swept to one site and settle, the porous and light to another” (52e). What also could he mean by weaving wood together? Such strange metaphors he uses. Timaeus continues: “Let us go back again briefly to the beginning and make our way swiftly to the same point from which we arrived there; and let us attempt to add to our story a finish and a head that’s joined to what has gone before” (69a–b). He has already returned—more literally, retreated or withdrawn (anachōrēteon, 48b)—to the beginning once, namely when he transitioned from his Story of Intellect to his Story of Necessity. Now he is proposing a second return. What is the meaning behind these reversals? Earlier in the dialogue, Timaeus refers to the retrograde motions of outer planets (36d). Are his literary reversals a way of mimicking the reversals found in nature? Storytelling, for Plato, being an art form, is a form of mimesis, after all. Timaeus is creating a story about cosmic creation. Thus, what holds for the cosmos in its coming to be should also hold for Timaeus’s cosmo-muthos, and vice versa.

e. Monologue, Part 3: The Creation Story of Man (69a–92c)

Socrates’ feast of speeches—at least the first course, served by Timaeus—is nearing its end. With the cosmos in place, Timaeus draws his story to a close by rhapsodizing on the creation of man. Earlier in his speech, he indicated that the demiurge fashioned the cosmos only up to a point; the creation of other life forms he left to other, lesser gods. Speaking to these gods, the demiurge explains that were he to create animals and plants, they would turn out as perfect as the gods themselves (41c). In that case, he would not be able to achieve his goal of realizing all levels and kinds of perfection. At first glance, this seems strange. How can a being capable of making something as enormous as the cosmos be unable to populate it with meager animals and plants? The problem, however, is not as it seems. It is not that the demiurge lacks power. On the contrary, being perfect, the demiurge always performs optimally; his actions yield only what is best. It would therefore be contrary to his nature—and, one may say, offensive to his impeccable aesthetic tastes—to make something that did not in the closest possible way resemble him in greatness and beauty. It would be tantamount to a masterful artist lowering himself to produce an amateurish painting. Creating a masterpiece is within his power; not doing so would be a shameful underachievement, unbefitting of his greatness. For this reason, the demiurge, exercising sovereignty over all things, delegates to lesser gods, who were themselves created (41b), the responsibility of creating animals and plants. Given their relative imperfection, they could do what the demiurge could not—namely, create less perfect life forms—and not disgrace themselves by doing so. By allowing them to complete what he started, the demiurge could fully realize his plan to ensure that the all (to pan) is genuinely all (hapan), full and complete, a plenitude lacking nothing (41c).

How, then, does man come to be? What is his origin and nature? Timaeus gives not one, but two accounts. The accounts do not conflict, but they do differ in length, detail, and artistry. The first appears at the end of the Story of Intellect (40d–47e). It begins with the demiurge creating the human soul from a mixture—not the same mixture from which the cosmic soul came to be, but a different one using the same ingredients blended less purely. Having combined these ingredients, the demiurge distributes bits of the mixture to the various stars (for example, lesser gods) like a farmer sowing seeds (42d). At this point, the lesser gods take over and begin fashioning the human body. Borrowing portions of the elements, the gods “went about gluing them together … with close-packed rivets invisible for their smallness” (42e–43a). It is worth noting here the difference in approach. Whereas the demiurge sows seeds, the lesser gods insert rivets. Whereas the demiurge creates with an eye to balance and beauty, the lesser gods simply get the job done by pasting things together. The demiurge uses art and agriculture to create; the gods appear to be workers on an assembly line. Note, too, how Timaeus’s account of vision reflects this same workmanlike approach. It tells how vision comes about, but not why it does beyond that it allows us to keep our soul in tune with the movements of the heavens (45b–46a, 47b). The creation of man, as related in the Story of Intellect, is much akin to the work of the lesser gods: it is practical, but not particularly meaningful. It relates the origin of man, but not his nature. In fact, it seems to serve as little more than a bridge between the Story of Intellect and the Story of Necessity. A far more robust account of man’s creation follows the Story of Necessity.

As with the account of man’s creation in the Story of Intellect, the Story of Man begins with the soul. From the start, however, the account is decidedly more lively and detailed. Timaeus opens by telling how the gods, still entrusted with the task of making man, sculpted a body around the immortal soul and housed within that body another kind of soul governed by “terrible and necessary affections” (deina kai anagkaia pathēmata): pleasure and pain, rashness and fear, anger and hope (69d). Notice that they do not rivet or glue the soul to the body, but sculpt the body around the soul. Already these lesser gods approach their job with more grace and flair than they did before. Moreover, they have enough sense to separate the two souls so that the mortal soul will not contaminate the immortal soul. They do this by placing the mortal soul within the chest and separating the chest from the head with an isthmus (namely, the neck) within which the spirited part of the soul resides. Next to be made is the heart, which communicates to other organs when an unjust deed has been committed, and after that the lungs, which cool the heart, enabling it to be more subservient to reason. The lungs, however, are not merely placed within man; they are implanted (enephuteusan, 70c). It is remarkable how the image of the gods from one story to another has changed. The Story of Intellect underplays their artistry, emphasizing instead their efficacy. The Story of Man, by contrast, draws them closer in nature and purpose to the demiurge: they are not only sculptor-like in how they shape the body around the soul, but also farmer-like in how they plant organs within the body. Also worth noting is the image of man himself. He is no longer an inert machine assembled with glue and rivets, but a dynamic organism animated by passions and emotions.

Continuing his story, Timaeus shifts his attention to the liver—one of his seemingly favorite organs. Reason and emotion have been physically separated—reason being located in the head and the appetites in the abdomen. Because the appetites cannot understand reason—evidently because they speak different languages—there was a need for a mediator to convey messages from the higher faculties to the lower (71a). This becomes the purpose of the liver. From the intellect, the liver receives images, which it projects onto its surface to frighten and restrain the appetites (72b). This is reminiscent of the Republic’s cave allegory, where prisoners passively watch as images flicker across a cave wall. Just as those images keep the prisoners pacified, the images projected by the liver keep the appetites at bay. Apart from helping the intellect control emotion, the liver also serves as the source of divination (71e, 72b). No one in his right mind, Timaeus says, has access to divine reason; yet when asleep or overcome by some inspiration, man receives divine messages, which must be reflected upon and interpreted. At no point does Timaeus condemn divination as a form of superstition or subterfuge, treating it instead with respect and sincerity—at least for those who think deeply and reason slowly about their divinations. But why does Timaeus treat divination with respect at all? Why not like the Saisian priest explain divination away naturalistically as either hallucination or huckstery? Perhaps the reason is that for Timaeus—and by extension Plato—man is not simply a patchwork of physical parts: cells, tissues, organs, and systems. Man is not a god, but he does have divine origins, a divine element within himself, and the ability to be divinely inspired. Whereas the Saisian priest ridiculed the idea of myth shedding light on the nature, Timaeus wants to preserve the link between the natural and supernatural. Far from setting man and the gods apart, Timaeus’s cosmo-muthos brings them closer together.

Much care and skill is brought to bear on the gods’ creative efforts. Consider how they make bone and flesh. It begins with marrow, which “gave the mortal kind its roots” (katerrixoun, 73b). Marrow, Timaeus tells his companions, comes from a universal seed-stuff (epephēmisen) comprised of smooth and unwarped triangles. Planted within the marrow are various kinds of souls (73c). The gods then take some of this marrow and form it into a spherical shape. This spherical field (aroura) receives the divine seed (to theion sperma) and becomes the brain (73d). Bone likewise comes to be through an intricate, creative process (73e). First, earth is sifted by the gods to be pure and smooth. Next, it is kneaded and soaked with marrow, baked in fire, dipped in water, placed back into the fire, and dipped once again in water. This is an utterly fantastic account—one that emphasizes the intelligence and imagination behind the creation of man and of his seemingly most mundane parts. Bone is created as if by a potter and flesh as if by a wax-modeler (74c). Man is not the product of necessity or blind chance; he arises from a series of deliberate actions. The gods—whether the demiurge or lesser gods—emerge as agents who care not only to complete their work, but to introduce into their products a sense of style and value. They care about what they make. Their artistic fingerprints can be found on everything from the cosmic soul to human skin, hair, and nails. But they also know how best to manipulate materials. Owing to their different shapes, the elements behave differently. Thus, by combining an artistic sensibility with a knowledge of how to engineer things given the materials at their disposal, the gods are able to imbue the cosmos and man with beauty, structural stability, and purposefulness.

To be sure, man is well-formed and beautiful, but he is also able to grow and flourish. In fact, he appears in Timaeus’s story as plant-like. In several passages, the gods act as farmers, planting organs within the human body. Marrow literally allows man, like a tree, to take root (73b). In addition, the gods equip man with an irrigation system: “[the gods] channelled through our body itself, just as they were cutting channels in gardens, so that the body might be refreshed as though from an inflowing stream” (77c–d). These channels help the “stream of nourishment” flow so that the “irrigation may be made uniform.” The gods use their agricultural knowledge frequently when creating man, who, Timaeus says, is “not an earthly but a heavenly plant” (phuton ouk eggeion alla ouranion, 90a). This naturally prompts the question: Why is so close a connection drawn between man and plants? One may think it is a joke. Anyone can tell the difference between humans and plants. Maybe Timaeus wanted to get a rise from his companions. But if it is a joke, it is not a very good one; for as most would agree, there are few things less amusing than an oft-repeated joke. A possible clue may be found just before the discussion of man’s irrigation system, where Timaeus tells a brief story about the origins of plants (70e–77c). After making man, the gods decide to create plants, unlike animals in appearance, yet having sensations and “a nature akin to man.” Plants are indeed animals, he notes, because “everything that partakes of living may justly and most correctly called an animal” (77a–b). Since plants are intended to be eaten (77c), this cannot be a solemn plea for vegetarianism. Even so, it is certainly possible that Timaeus’s message is ecological. Sometimes, because of our egocentric and homocentric concerns, we lose track of our place in the world. It would be an overstatement to suggest that Timaeus is advancing an environmentalist ethics; but his holistic view of creation, if taken seriously, does raise important questions (1) about the relationship between creator and created, that is, between planter and planted (87b), (2) about the kinship between man and nature, and (3) about how the good for man relates to the good for other living things. Rarely has Plato been considered a philosopher with ecological concerns, but perhaps a careful study of the Timaeus would help to change this opinion.

Although man is capable of flourishing, he is also subject to collapse and decay. For this reason, Timaeus pivots to the origin and nature of diseases. He uses a strange word to describe their origin, saying that they are “constructed” or “contrived” (sunistēmi, 81e). Is the implication that the gods have a hand in creating diseases? Was this to ensure the imperfection of man? Timaeus, unfortunately, leaves these questions unanswered. Instead, he launches into a discussion of diseases that specifically afflict the body. These arise from an excess, deficiency, or misplacement of elements (82a–b). In other words, there is a physical imbalance, causing a body to become unmusical (plēmmelēsēi) and out of harmony with the cosmos (82b). After bodily diseases, Timaeus turns to diseases of the soul, giving special attention to folly, which comes in two varities: stupidity and madness. Stupidity, he says, is the greatest disease, arising when a body becomes too large and the intellect too weak (88a–b). When this happens, bodily motions gain mastery, causing the soul to become dull, slow, and forgetful. But does this mean that only large people are stupid? Are small folk immune to this disease? It seems an obvious question to ask, but Timaeus does not consider it. Moving along, Timaeus traces madness to overly seeded marrow (86c–d), not to wickedness, as some do: “people hold the opinion that he’s not diseased but willingly bad. But the truth is…” (86d). Timaeus’s claim here is both Socratic and un-Socratic. It is Socratic in that it affirms that no one performs wrongful acts willingly; however, it is un-Socratic in that rather than attributing wrongdoing to ignorance, as Socrates does, Timaeus roots it in bodily disease. In fact, physical causes are responsible for madness and stupidity. As for treating disease, Timaeus prescribes physical exercise and an avoidance of medicinal drugs (89a–c). Idleness and inactivity will only make matters worse; the body must mimic the cosmos and stay in motion. In addition, a person should tune the motions in his soul by applying himself to the liberal arts and all philosophy (88c). Striking the right balance and keeping one’s mind on higher things—these, according to Timaeus, are the ingredients to a good life and healthy soul. At this point, one might wonder: Would the silent Socrates be nodding in agreement or shaking in disagreement? Perhaps he would be doing both.

This would seem like a good place for Timaeus to stop. Critias promised Socrates that Timaeus’s story would explain the origins and nature of mankind. Timaeus has clearly gone above and beyond. Not only has he explained the origins and nature of man, but he has also given his companions lessons in human anatomy and physiology and human pathology. But Timaeus is not finished yet. There is one topic left to cover: the invention of sex. One might assume that man and woman have the same origin, but that is not so. The gods created man beautiful and well-ordered, but man is prone to physical and moral decay. He is also destined to die and, as it turns out, be reincarnated. Timaeus does not say what happens to courageous and just men, but as for the cowardly and unjust, they return not as men, but as women (90e). Women are therefore derivative, being born from morally deficient men. It is hard to know what to make of this, especially in light of the fact that in Socrates’ polis—the one that Timaeus is helping to animate—men and women are social equals. The subsequent account of intercourse is likewise peculiar. The channel for releasing urine, Timaeus says, also releases marrow (that is, seed) from the brain (91b). This marrow, being imbued with soul, gives the male reproductive organ a desire for emission. As a result, male genitals have become unpersuadable and autocratic, like an irrational animal (91b–c). In other words, the love to procreate is a form of madness in which a man loses his mind—or more literally, his brain. But is this the extent of man’s erotic feelings? Eros compels physical love, but can it compel philosophy? Can it compel movement within a polis? Timaeus rounds out his speech by explaining the origins of other animals (91d–92c). Like women, they derive from deficient men: birds from light-minded men who rely overabundantly on sight in their scientific demonstrations, land animals from unphilosophical men, and fish from the stupidest men. With the cosmos now made and fully populated, Timaeus delivers his closing line, which dispenses with the puns, jokes, and tomfoolery: “having been filled up, this cosmos has come to be—a visible animal embracing visible animals, a likeness of the intelligible, a sensed god; greatest and best, most beautiful and most perfect—this one heaven being alone of its kind” (92c). So ends Timaeus’s story, but not Socrates’ feast of speeches, which continues in the Critias.

7. Concluding Remarks

What is a contemporary audience to make of Plato’s Timaeus? Is it a serious attempt at natural philosophy or a farcical parody? There is no way of settling definitively Plato’s intent in writing the dialogue. In fact, that seems to be the nature of Plato’s art in general: he always wants his readers to keep wondering, to keep asking questions, to keep returning to his texts with the hope of discovering something new and exciting. Timaeus’s speech is very much a microcosm of the world around us with its multiple layers, interlocking pieces, and abrupt movements back and forth. But it also fits in well with a recurring theme in Plato’s dialogues. Time and again, we find in the dialogues a critique of science—not just any science, but the sort of science that tends to view nature in materialistic and mechanistic terms. In the Phaedrus, for instance, Socrates describes naturalized myths as displaying “rural wisdom” (229e). Scientific naturalism is also taken to task in the Phaedo, where Socrates recounts his youthful flirtations with the natural philosophy of Anaxagoras. Reading Anaxagoras, Socrates delighted in learning details about the shape and location of the earth and various facts about the sun, the moon, and the other heavenly bodies. Socrates also shares his delight when he learned from Anaxagoras that Mind (Nous) is the ordering principle of the world. But in the end, he was left disappointed: “I thought he’d go on to take me through the best for each and the good (agathon) common to all” (98b). Anaxagoras, therefore, impressed Socrates with his explanation of how things work, but he failed to explain why they are the way that they are and why they are good. In other words, Anaxagoras’s cosmos, in Socrates’ opinion, was without value: it moved, but without any rhyme or reason. Mind controlled everything, moving things about, but why did it move things in this way instead of that? Why did it move things at all?

If there is any message to be gleaned from the Timaeus, it is that material explanations alone cannot render a clear and complete picture of the world. Recall that the dialogue begins with Socrates recounting his speech, the day before, about the best polis. Not long after, he invites his companions to set this polis in motion—like beautiful animals “moving and contending in some struggle.” By the end of the dialogue, readers are left wondering: Has Timaeus really granted Socrates’ wish? Is Socrates’ polis any more alive at the end of the dialogue than it was at the beginning? Before rushing to judgment, one must remember that the Timaeus leads directly into the fragmentary Critias, which in turn may lead into a third dialogue, the Hermocrates. It would therefore be rash to answer these questions without taking the entire, unbroken narrative into account. Even so, there does seem to be an effort by Timaeus to create a living cosmos—one with more life and vitality than what the youthful Socrates found in Anaxagoras. It is true that Timaeus’ story at times radiates absurdity and silliness. At the same time, however, it is a lively artistic creation, much like the very cosmos his story depicts. There is craftsmanship behind its creation. Moreover, the cosmos is itself a living thing with a soul. The gods, as heavenly bodies, move in accord with reason, as does the entire cosmos itself. Beauty, goodness, and life permeate the universe. This might not be a direct response to Socrates’ invitation to set his polis in motion; but it is a step in the right direction and a powerful reminder from Plato that a philosophy that sacrifices the beautiful and the good—that sacrifices spirited muthos on the cold, antiseptic altar of logos—sacrifices a vital part of reality.

8. References and Further Reading

All translations of the Timaeus in this article are by Kalkavage, Plato’s Timaeus, Newburyport, MA: Focus Publishing, 2001.

a. Standard Greek Text

Burnet, John. “Clitopho,” “Respublica,” “Timaeus,” “Critias.” Platonis Opera, Vol. IV. Oxford: Clarendon Press, 1902.

Critical edition of the ancient Greek text. Essential for scholarly work.

b. English Translations

Bury, R. G. Plato: Timaeus, Critias, Cleitophon, Menexenus, Epistles, Cambridge, Mass.: Loeb Classical Library, 1960.

Interlinear Greek-English translation. Includes an introduction and notes. Essential for scholarly work.

Cornford, F. M. Plato’s Cosmology, London: Routledge & Kegan Paul, 1937. Reprinted, Indianapolis: Hackett Publishing Co., 1997.

Good translation, although perhaps a bit dated. Includes a detailed commentary and notes.

Jowett, Benjamin. “Timaeus,” The Collected Dialogues of Plato: Including the Letters. Eds. Edith Hamilton & Huntington Cairns, Princeton, NJ: Princeton University Press, 1961.

Dated translation, but still useful. Part of an anthology of Plato’s complete works. Readily available online, for example, here, here, and here.

Kalkavage, Peter. Plato’s Timaeus. Newburyport, MA: Focus Publishing, 2001.

Superb translation. Includes an interpretative essay, glossary, and several appendices.

Lee, Desmond. Timaeus and Critias. Revised by Thomas Kjeller Johansen, 2008, London: Penguin Books, 1972.

Good translation. Includes a lengthy introduction and notes.

Waterfield, Robin. Timaeus and Critias. Oxford: Oxford University Press, 2008.

Good translation. Includes a lengthy introduction, summary, and explanatory notes by Andrew Gregory.

Zeyl, Donald J. “Timaeus,” Plato: Complete Works. Ed. John M. Cooper, Indianapolis: Hackett Publishing Company, 1997.

Good translation. Part of an anthology of Plato’s complete works with concise introductions and notes.

c. Classic Studies

Cherniss, H. F. “The Relation of the Timaeus to Plato’s Later Dialogues.” The American Journal of Philology, Vol. 78, No. 3 (1957): 225–266. Reprinted in Studies in Plato’s Metaphysics. Ed. R. E. Allen, London and New York: Routledge and Kegan Paul, 1965. Also in Selected Papers. Ed. Leonardo Tarán, Leiden: Brill, 1977.

Makes the case for placing the Timaeus in Plato’s late compositional period.

Owen, G. E. L. “The Place of the Timaeus in Plato’s Dialogues.” The Classical Quarterly NS 3 (1953): 79–95. Reprinted in Studies in Plato’s Metaphysics. Ed. R. E. Allen, London and New York: Routledge and Kegan Paul, 1965. Also in Logic, Science and Dialectic. Ed. Martha Nussbaum. Ithaca: Cornell University Press, 1986.

Makes the case for placing the Timaeus in Plato’s middle compositional period.

Taylor, A. E. A Commentary on Plato’s Timaeus. Oxford: Clarendon Press, 1928. Reprinted, New York: Garland, 1967.

Lengthy and ambitious commentary on the dialogue. An early effort to challenge the view that the dialogue presents Plato’s own thoughts on cosmology.

Vlastos, Gregory. “The Disorderly Motion in the Timaeus.” Studies in Plato’s Metaphysics. Ed. R. E. Allen, London and New York: Routledge and Kegan Paul, 1965. Reprinted in Studies in Greek Philosophy, Vol. 2, ed. D. W. Graham, Princeton: Princeton University Press, 1995.

Considers the nature of the disorderly motion discussed at Ti. 30a, 52d–53b, 69b.

Vlastos, Gregory. “Creation in the Timaeus: Is It a Fiction?” Studies in Plato’s Metaphysics. Ed. R. E. Allen, London and New York: Routledge and Kegan Paul, 1965b. Reprinted in Studies in Greek Philosophy, Vol. 2, ed. D. W. Graham, Princeton: Princeton University Press, 1995.

Follow-up to Vlastos’s essay “The Disorderly Motion in the Timaeus” in the light of Cherniss’s work.

Vlastos, Gregory. Plato’s Universe. Seattle: University of Washington Press, 1975. Reprinted by Luc Brisson, Las Vegas: Parmenides Publishing, 2005.

Offers an interpretation of the Timaeus’s cosmology within the broader context of Presocratic natural philosophy. Attributes the cosmological ideas in the dialogue to Plato himself.

d. Classical Studies

The following ancient commentaries are mainly of historical and scholarly interest. Newcomers to the dialogue will likely want to consult more recent scholarship.

Calcidius. On Plato’s Timaeus. Ed. and trans. John Magee, Cambridge: Harvard University Press, 2016.
Plutarch. “On the Generation of the Soul in the Timaeus.” Plutarch’s Moralia, Vol. 1, Pt. 1. Ed. and trans. Harold Tarrant, Cambridge: Harvard University Press, 1976.
Proclus. “Commentary on Plato’s Timaeus.” Vol. 1, Book 1: Proclus on the Socratic State and Atlantis. Ed. and trans. Harold Tarrant, Cambridge: Cambridge University Press, 2007.
Proclus. “Commentary on Plato’s Timaeus.” Vol. 2, Book 2: Proclus on the Causes of the Cosmos and its Creation. Eds. and trans. David T. Runia & Michael Share, Cambridge: Cambridge University Press, 2009.
Proclus. “Commentary on Plato’s Timaeus.” Vol. 3, Book 3, Part 1, Proclus on the World Soul. Ed. and trans. Dirk Baltzly, Cambridge: Cambridge University Press, 2010.
Proclus. “Commentary on Plato’s Timaeus.” Vol. 4, Book 3, Part 2, Proclus on the World Soul. Ed. and trans. Dirk Baltzly, Cambridge: Cambridge University Press, 2010.
Proclus. “Commentary on Plato’s Timaeus.” Vol. 5, Book 4: Proclus on Time and the Stars. Ed. and trans. Dirk Baltzly, Cambridge: Cambridge University Press, 2016.
Proclus. “Commentary on Plato’s Timaeus.” Vol. 6, Book 5: Proclus on the Gods of Generation and the Creation of Humans. Ed. and trans. Harold Tarrant, Cambridge: Cambridge University Press, 2017.

e. Other Studies of Related Interest

Altman, William H. F. “Reading Order and Authenticity: The Place of Theages and Cleitophon in Platonic Pedagogy.” The Electronic Journal of the International Plato Society, n 11, 2011: 1–50.

Argues against the orthodoxy for the authenticity of Theages and Cleitophon. Relevant to the study of Platonic authorship.

Arieti, James A. Interpreting Plato: The Dialogues as Drama. Savage, MD: Rowman & Littlefield Publishers, Inc., 1991.

Offers a literary reading of eighteen dialogues, including the Timaeus. Argues that the dialogues ought to be approaches principally as dramas, not philosophical discourses.

Brandwood, Leonard. “Stylometry and Chronology.” The Cambridge Companion to Plato. Ed. Richard Kraut, Cambridge: Cambridge University Press, 1992.

Recounts attempts made by various scholars to date Plato’s dialogues using stylometry.

Howland, Jacob. “Re-Reading Plato: The Problem of Platonic Chronology.” Phoenix, Vol. 45, No. 3 (Autumn 1991): 189–214.

Offers a powerful and compelling case against efforts by some scholars to arrange Plato’s dialogues chronologically.

Ives, Charles. Socrates’ Request and the Educational Narrative of the Timaeus. Lanham, MD: Lexington Books, 2017.

Draws attention to the connection between Timaeus’s cosmology and Socrates’ request for a speech about war.

Lampert, Lawrence and Planeaux, Christopher. “Who’s Who in Plato’s Timaeus-Critias and Why.” The Review of Metaphysics, Vol. 52, No. 1 (September 1998): 87–125.

Important examination into the characters and historical-political background of the Timaeus and Critias.

Lovejoy, Arthur O. The Great Chain of Being: A Study of the History of an Idea. Cambridge, MA: Harvard University Press, 1936.

Classic work in the history of ideas tracing the origin and evolution of three philosophical principles: plenitude, continuity, and graduation.

Mohr, Richard. One Book, The Whole Universe: Plato’s Timaeus Today. Las Vegas/Zurich/Athens: Parmenides Publishing: 2010.

Ambitious anthology covering a broad range of topics related to the Timaeus. Derived from the Timaeus Conference at University of Illinois at Urbana–Champaign, September 2007.

Nails, Debra. The People of Plato: A Prosopography of Plato and Other Socratics. Indianapolis: Hackett Publishing Company, 2002.

Meticulous study of the individuals represented in Plato’s dialogues and their relationships to one another. Essential for scholarly work.

Parke, Herbert W. Festivals of the Athenians. Ithaca, NY: Cornell University Press, 1977.

Valuable study of the religious festivals of ancient Athens. Contains a thorough discussion of the Apaturia.

Press, Gerald A. Plato: A Guide for the Perplexed. London & New York: Continuum, 2007.

Very nice introduction to Plato’s art and thought urging that the dialogues be read as both philosophical and dramatic works.

Rutherford, R. B. The Art of Plato. Cambridge: Harvard University Press, 1995.

Offers a literary interpretation of the dialogues, including the Timaeus, focusing on their formal structure, language, character development, and imagery.

Sallis, John. Chorology: On Beginning in Plato’s Timaeus. Bloomington: Indiana University Press, 1999.

Interesting study focusing on the dialogue’s strange and mysterious “space” (chōra).

Welliver, Warman. Character, Plot, and Thought in Plato’s Timaeus-Critias. Leiden: E. J. Brill, 1977.

Close and careful examination of the Timaeus’s characters and their underlying political antagonisms.

Westra, Laura and Robinson, Thomas M. The Greeks and the Environment. Lanham, MD: Rowman & Littlefield Publishers, 1997.

Anthology devoted to the examination early Greek thinking on nature and ecology. Several chapters are devoted to Plato.

Zuckert, Catherine. Plato’s Philosophers: The Coherence of the Dialogues. Chicago; University of Chicago Press, 2012.

Bold and ambitious interpretation of Plato’s dialogues based on their dramatic order.

Author Information

Frank Grabowski
Email: fgrabowski@rsu.edu
Rogers State University
U. S. A.

Platonism and Theism

This article explores the compatibility of, and relationship between, the Platonic and Theistic metaphysical visions. According to Platonism, there is a realm of necessarily existing abstract objects comprising a framework of reality beyond the material world. Platonism argues these abstract objects do not originate with creative divine activity. Traditional Theism contends that God is primarily the creator and that God is the source of existence for all realities beyond himself, including the realm of abstract objects.

A primary obstacle between these two perspectives centers upon the origin, nature and existence of abstract objects. The Platonist contends that these abstract objects exist as a part of the framework of reality and that abstract objects are, by nature, necessary, eternal and uncreated. These qualities stand as challenges for the Traditional Theist, attempting to reconcile his or her metaphysic with that of Platonism since Traditional Theism contends that God is uniquely necessary, eternal, uncaused, and is the cause of everything that exists. The question, therefore, emerges as to whether these two metaphysical visions are reconcilable and, if not, then why not, and, if so, then how might this be accomplished?

Despite the differences, some Traditional Theists have found Platonism to be a helpful framework by which to convey their conclusions regarding the nature of God and of ultimate reality. Others pursue reconciliation between Theism and Platonism through the proposal of what has been defined as a modalized Platonism, which concludes that necessarily existing abstract objects, nevertheless, have origin in the creative activity of God. Still others refuse any consideration of Theism in relationship to Platonism.

Traditional Theism

Emerging Tensions

Selected Proposals

References and Further Reading

1. The Problem

Is the platonic metaphysical vision compatible with that of Traditional Theism? Some would contend that the two are compatible, while others would argue to the contrary. Platonists argue that at least some, if not all, abstract objects are uncreated, and exist necessarily and eternally; whereas Traditional Theism asserts that God exists as the uncreated creator of all reality existing beyond himself.

But can this central conclusion of Traditional Theism be reconciled with the Platonic understanding of abstract objects as uncreated, necessarily extant, and eternal? Furthermore, if it is possible to reconcile these worldviews, how might one do so? Put differently, is there anything, other than himself, that God has not created? Or are we to understand the conclusion that God has created everything in a qualified or restricted sense? Are there things which are not to be included in the Theistic tenet of faith that God is the creator of all things? If so, what things do not result from God’s creative activity?

2. Platonism and Abstract Objects

Contemporary Platonism argues the existence of abstract objects. Abstract objects do not exist in space or time and are entirely non-physical and non-mental. Contemporary Platonism, while deriving from the teachings of Plato, is not directly reflective of the teachings of Plato. Abstract objects are non-physical entities in that they do not exist in the physical world, and they are not compositionally material. Abstract objects are non-mental, meaning that they are not minds or ideas in minds, neither are they disembodied souls or gods. Further, abstract objects are said to be causally inert. In short, Platonism contends that abstract objects exist necessarily, are eternal, and cannot be involved in cause and effect relationships with other objects.

Platonists argue the existence of abstract objects since it makes sense to believe, for instance, that numbers exist and that the only legitimate view of these things is that they are abstract objects. For Platonists, however, there are several categories of things, including physical things, mental things, spiritual things, and the problematic fourth category that includes things such as universals (the wisdom of Socrates, the redness of an apple), relationships (for example, loving, betweenness), propositions (such as 7 + 5 = 12, God is just), and mathematical objects such as numbers and sets. (Menzel, 2001, 3)

As we shall see below, the existence of abstract objects represents a significant challenge for the Christian in particular and for Traditional Theists in general since it is central to these worldviews that God is the creator of everything other than God himself. Generally, however, abstract objects are considered to be like God in that they are said to have always existed, and to always exist in future. Consequently, there is no point at which God is considered to have brought them into being. (Menzel, 2001, 1-5).

But why would the Platonist conclude that God has not created all abstract objects, or has created selected abstract objects? The response to this question moves us to a consideration of the nature of abstract objects as necessarily extant, uncreated, and eternal, and to briefly address why God’s creation of abstract objects is questionable.

a. Abstract Objects and Necessary Existence

What is meant by the phrase necessary existence? A thing is said to possess necessary existence if it would have existed no matter what or if it would have existed under any possible circumstances. A thing has necessary existence if its non-existence is impossible. For instance, if x is a necessary being, then the non-existence of x is as impossible as a round square or a liquid wine bottle. Human beings are said not to exist necessarily since we would never have existed if our parents had never met and this is a possible circumstance. (Van Inwagen, 1993, 118)

For the Platonist, God’s creation of abstract objects is questionable since they are understood to exist necessarily. As such, abstract objects cannot have not existed. Consequently, consider whether God can create something existing necessarily? Put differently, does the assertion “x exists necessarily” entail that “x is uncreated”? If this constitutes a valid assumption, the Platonic understanding of the nature of abstracts objects as necessarily extant excludes the creation of these objects by God or any other external source.

b. Abstract Objects as Uncreated

Second, for the Platonist, God’s creation of abstract objects is questionable since the creative event in Traditional Theism is understood to be a causal event and Platonism understands abstract objects as being uncreated and also as being incapable of entering into causal relations. If, therefore, abstract objects are uncreated, then it seems that God is just one more extant entity existing in the universe and God cannot be the maker of all things, both visible and invisible. (Menzel, 1986)

c. Abstract Objects as Eternal

Third, for the Platonist, God’s creation of abstract objects is questionable due to their being eternal. There is no point at which God could be said to have brought abstract objects into being and, therefore, it is difficult to think of them as creatures since they are not created. If an abstract object has no beginning in time there could not have been a time at which God first created it. (Menzel, 2001, 4-6) If abstract objects are eternal, then they possess a character which parallels God, since according to Traditional Theism God is considered to be eternal.

These platonic affirmations regarding the nature of abstract objects as eternal, necessary and uncreated pose significant challenges to any effort to merge the worldviews of Platonism and Traditional Theism. With this understanding of abstract objects, we now turn to a consideration of the definition of Traditional Theism.

3. Traditional Theism

What are the central tenets of Traditional Theism? First, Traditional Theism and Classical Theism (hereafter referred to as Traditional Theism) are regarded as synonymous. Traditional Theism is supported in the writings of authors such as Moses Maimonides (1135-1204), the Islamic author Avicenna (980-1037), and the Christian author Thomas Aquinas (1224-74). Traditional Theism constitutes what all Jews, Christians and Muslims officially endorsed for many centuries. In addition, Traditional Theists strongly endorse the aseity-sovereignty doctrine, according to which God is the uncreated Creator of all things and all things other than God depend upon God, while God depends on nothing whatsoever. (Davies, 2004, 1) Numerous philosophers have assumed that God is as defenders of Traditional Theism consider him to be, the source of all reality external to himself. From the period of St. Augustine of Hippo (354-430) to the time of G. W. Leibniz (1646-1716), philosophers carried on with the assumption that belief in God is belief in Traditional Theism. This understanding has been endorsed by many theologians, and is represented in the tenets of the Roman Catholic Church. These beliefs were also endorsed and propagated by many of the major Protestant reformers, such as the eighteenth century American Puritan, Jonathan Edwards.

It is to the definition of Traditional Theism that we turn since it is these tenets of faith that represent the primary obstacles in our effort to reconcile the Theistic and Platonic metaphysical perspectives. These include: God as creator, Creation as ex nihilo, and the assertion of divine freedom.

a. God as Creator

Traditional Theism understands God to be the creative source for his own existence, as well as for the existence of all reality existing outside of himself. First, as regards God’s being the creative source for his own existence, if something else created God, and then God created the universe, it would seem to most that this other thing was the real and ultimate source of the universe and that God is nothing more than an intermediary. (Leftow, 1990, 584) Therefore, according to Traditional Theism, there can be no regress of explanations for what exists past the explanations for God’s existence.

Second, Traditional Theism not only endorses the belief that God is responsible for his own existence, but also that God is the Creator of all extant reality beyond himself. Consequently, God is essentially what accounts for the existence of anything beyond God or God is responsible for the existence of something rather than nothing. For Traditional Theism, this notion entails not only that God is responsible for the fact that the universe began to exist, but that God’s work is also responsible for the continued existence of the cosmos. (Davies, 2004, 3)

b. Creatio ex Nihilo

Is there anything that can pre-exist the creative activity of God? Traditional Theists respond to this question with a resounding, “No.” Aquinas writes,

We must consider not only the emanation of a particular being from a particular agent, but also the emanation of all being from the universal cause, which is God; and this emanation we designate by the name of creation. Now what proceeds by particular emanation is not presupposed to that emanation; as when a man is generated, he was not before, but man is made from not-man, and white from not-white. Hence, if the emanation of the whole universal being from the first principle be considered, it is impossible that any being should be presupposed before this emanation. For nothing is the same as no being. Therefore, as the generation of a man is from the not-being which is not-man, so creation, which is the emanation of all being, is from the not-being which is nothing. (Thomas Aquinas, 1948, Ia, 45, 1.)

Traditional Theism, therefore, understands God as the one who creates ex nihilo, or from nothing. The phrase denotes not that God, in the creative act, worked with something called “nothing” but that God creates that which is external to himself without there being anything prior to his creative act with the exception of himself. The challenging implication of this tenet of Traditional Theism for the Platonic notion of abstract objects is obvious. Traditional Theists counter the Platonic notion that abstract objects are uncreated, contending that if God did not create non-substance items, such as abstract objects, creation would not truly be ex nihilo, since these entities would have accompanied God from all eternity and become aspects of God’s creation, for example, by being unsubstantiated. (Leftow, 1990, 583-84).

c. Divine Freedom

Traditional Theists also argue that God’s choices to act are always carried out in the context of divine freedom, signifying that God is not constrained by anything beyond the laws of logic and His own nature. This is regarded as true by the Traditional Theist since God has established these laws and can alter them if he chooses to do so. Further, God cannot be compelled to choose. If God makes choices in response to human action, so says the Traditional Theist, it is always in his power to prevent actions by any method he chooses.

In short, God always responds to the actions he permits. Consequently, God is always ultimately in control, even in the context of actions that we have created. Therefore, if God carried out his creative activity in the context of complete divine freedom and if God is not and cannot be compelled to act creatively by any external source, then how can God’s freedom be reconciled with the Platonic notion of abstract objects as existing necessarily, since, if abstract objects exist necessarily by God’s creative act, then God was compelled to create them by forces beyond himself. Again, the tension between the two worldviews of Traditional Theism and Platonism becomes apparent.

As this examination of the central tenets of Traditional Theism demonstrates, a challenge exists in the effort to integrate the worldviews of Traditional Theism and Platonism. In summary, Platonists contend that abstract objects are uncreated, whereas Traditional Theists argue that God created all reality; Platonists believe that abstract objects exist necessarily, whereas Traditional Theists contend that God alone is necessarily extant; Platonists propose that abstract objects are eternal, whereas Traditional Theists believe that God alone is eternal. With these contrasts in mind, we turn now to consider specific problems said to emerge from them.

4. Emerging Tensions

As has been observed in this article, the apparent conflict between Platonism and Traditional Theism emerges from the central notion of Traditional Theism, that God is the absolute creator of everything existing distinct from himself; and the central claim of contemporary Platonism, that there exists a realm of necessarily existent abstract objects that could not fail to exist. In considering the tension between abstract objects and Traditional Theism, Gould writes,

To see what the problem is, consider the following three jointly inconsistent claims: (a) there is an infinite realm of abstract objects which are (i) necessary independent beings and are thus (ii) uncreated; (b) only God exists as a necessary independent being; (c) God creates all of reality distinct from him, i.e. only God is uncreated. Statement (a) represents a common understanding of Platonism. Statements (b) and (c) follow from the common theistic claim that to qualify for the title “God,” someone must exist entirely from himself (a se), whereas everything else must be somehow dependent upon him. (Gould, 2010, 2)

A contradiction emerges in consideration of the first and third claims. Proposal (a) posits the existence of abstract objects that are necessary, independent and uncreated. Proposal (c) posits that all reality existing separately from God has its origin in divine creative activity. These two proposals would appear to be mutually exclusive. As a result a rapprochement appears to exist between Platonism and Traditional Theism. Platonism asserts that the existence of all things outside of God is rooted in divine activity. Platonism further argues that there are strong reasons for recognizing in our ontology the existence of a realm of necessarily existent abstract objects. In contradistinction, the Traditional Theist claims that the realm of necessity as well as that of contingency is within the province of divine creation. For the Traditional Theist, therefore, God is, in some fashion, responsible for the existence of all necessarily existent entities, as well as for contingent objects such as stars, planets and electrons, and so forth. (Morris and Menzel, 1986, 153)

But what are the specific problems associated with the effort to merge Platonism and Traditional Theism? Menzel clarifies,

On the [P]latonist conception, most, if not all, abstract objects are thought to exist necessarily. One can either locate these entities outside the scope of God’s creative activity or not. If the former, then it seems the believer must compromise his view of God: rather than the sovereign creator and lord of all things visible and invisible, God turns out to be just one more entity among many in a vast constellation of necessary beings existing independently of his creative power. If the latter, the believer is faced with the problem of what it could possibly mean for God to create an object that is both necessary and abstract. (Menzel, 1987, 1)

Therefore, both horns of this dilemma lead to inevitable challenges. To contend that God created abstract objects has been said to lead to a problem of coherence and a questioning of divine freedom. To contend that God did not create abstract objects has been understood to lead to a problem regarding the sovereignty of God, as well as the uniqueness of God. It is to these matters that we now turn.

a. God as the Origin of Abstract Objects

Consider the conclusion that God created abstract objects. Two objections arise from this proposal.

First, the coherence problem contends that it makes no sense to discuss the origin of things considered to exist necessarily, or that could not have failed to exist, such as abstract objects. (Leftow, 1990, 584) Supposing that at least some abstract objects exist necessarily, does the truth of this conclusion entail also that God has not created such abstract objects that exist of necessity?

Second, the freedom problem has its origin in the contention of Traditional Theism that God always acts in total freedom. However, if abstract objects exist necessarily, then God had no choice in the matter of their creation. Therefore, God is constrained by something other than himself, a conclusion leading to questions regarding the nature of God as omnipotent and possessing complete freedom. Traditional Theists are quick to affirm that God’s intentions or choices are not constrained by any entity other than God and no chain of true explanations goes beyond a divine intention or choice – or else beyond God’s having his nature and whatever beliefs he has logically before he creates, which may explain certain of God’s intentions and choices. For if nothing other than God forces God to act as he does, the real explanation of God’s actions always lies within God himself. (Leftow, 1990, 584-585)

b. Abstract Objects as Uncreated

Suppose, on the other hand, that God did not create abstract objects. Problems still emerge. First, if God did not create abstract objects, and if abstract objects are eternal, necessary and uncreated, then these realities are sovereign, as is God who also is eternal, necessary and uncreated, according to the Traditional Theist. God therefore is merely one more object in the vast array of items in the universe, which also includes abstract objects. This dilemma has been designated as the sovereignty problem. (Leftow, 1990, 584)

Further, a necessary object is said to constitute its own reason for existence. It is said to exist of and from itself. Therefore there is no need for a further explanation of the reason for the existence of the necessary object, a belief known as the doctrine of aseity. Aseity, however, has been associated uniquely with God. Therefore, if abstract objects exist a se, then God is not unique, exists alongside abstract objects and, exists as one being among many others existing by their own nature. This problem has been designated as the uniqueness problem.

In consideration of the relationship of Platonism and Traditional Theism, these problems force the Theist to revise, in some fashion, his understanding of the nature of God, reject Platonism altogether, or to seek a manner in which to reconcile the two. We now turn to a consideration of certain of the efforts made by Traditional Theists to merge or reconcile these two major metaphysical perspectives.

5. Selected Proposals

Can the worldviews of Traditional Theism and Platonism be merged in a manner that does not compromise the core tenets of these seemingly divergent metaphysical perspectives? Proposals range from those which reject altogether the notion of compatibility to those that use the Augustinian notion of abstract ideas as products of the intellectual activity of God. The present section considers five prominent proposals.

a. James Ross: A Critical Rejection of Platonism

Ross’ approach represents a rejection of the integration of Platonic and Theistic metaphysical perspectives. Ross presents a highly critical analysis of Platonism. He denies the Platonic notion of the world of eternal forms, opting instead for a thorough-going Aristotelianism, positing the existence of inherent explanatory structures throughout reality, which he understands as “forms”. According to Ross, if the independent necessary beings of Platonic Theism are other than God, both the simplicity and independence of God are compromised. Ross further posits that by attracting our attention to the Platonic abstractions, which all existing things are supposed to exemplify, we are consequently distracted from the things or objects themselves. (Ross, 1989, 3)

Ross presents a further set of objections to Platonic metaphysics. He points out that the whole set of abstract entities, which all physical objects are supposed to instantiate, are held to be eternal and changeless realities. Within a Theistic point of view, two options exist regarding these abstract entities according to Ross. First, some Theists propose that abstract entities are co-eternal with God because they are in fact one with God, and second, abstract objects are in some other sense ideas in the mind of God and therefore co-eternal with him.

Ross objects that the first possibility is incompatible with an attribute traditionally ascribed to God, that is, God’s simplicity. Ross further objects that the second contention compromises the Traditional Theists’ understanding of God as the source of all extant realities beyond himself. Third, Ross counters that the divine creation seems not to involve much creativity or choice if it consists completely of God instantiating beings that had already existed for all of eternity, thereby compromising God’s freedom. Further, the whole sense of creatio ex nihilo is, therefore, eliminated if we are to conceive of God as not making things up but only granting physical existence to that which already shared abstract existence co-eternally with him. (Ross, 1989, 3-5)

Ross concludes that there is an inherent incompatibility of Platonism and Traditional Theism since the incorporation of the Platonic worldview, which entails the existence of abstract objects that exist eternally, necessarily, and are uncaused, forces the Traditional Theist to compromise in some fashion his understanding of the nature of God, thereby leading the Theist to a departure from what is regarded as an orthodox understanding of the nature of God.

b. Nicholas Wolterstorff: A Restrictive Idea of Creation

Nicholas Wolterstorff finds a mediating position between the Platonic and Theistic worldviews. He does so, however, by adopting a non-Traditional Theistic perspective, which according to some is an unavoidable consequence of endorsing Platonism. Wolterstorff proposes that necessarily existing abstract objects are in fact not dependent upon God. (Wolterstorff, 1970) and he promotes the view that some properties, specifically those exemplified by God, are to be excluded from God’s creative activity. (Gould, 2010, 134) Wolterstorff goes so far as to propose that God in his nature has properties that he did not bring about. (Wolterstorff, 1970, 292) He writes:

[Consider] the fact that propositions have the property of being either true or false. This property is not a property of God. . . . For the propositions “God exists” and “God is able to create” exemplify being true or false wholly apart from any creative activity on God’s part; in fact, creative ability on his part presupposes that these propositions are true, and thus presupposes that there exists such a property as being either true of false. (Wolterstorff, 1970, 292; Gould, 2010, 135)

As such, Wolterstorff presents what may be termed a restrictive understanding of the creative activity of God. (Wolterstorff, 1970, 292). Wolterstorff, a Christian, argues that the biblical writers simply did not endorse a wide scope reading of the doctrine of creation. He posits that it cannot legitimately be entertained that the biblical writers actually had universals in view when speaking of God’s being the Creator of all things. In addition, he points out that the creator/creature distinction is invoked in Scripture for religious and not theoretical or metaphysical reasons.

Again we see in Wolterstorff’s approach what those who reject Traditional Theism altogether understand to be an inevitable result of endorsing Platonism. Wolterstorff, due to his endorsing of Platonism, is said therefore to have compromised the understanding of Traditional Theism in that God ceases to be the creator of various dimensions of his own identity, as well as of objects existing beyond himself.

c. Morris and Menzel: Theistic Activism

Christopher Menzel and Thomas Morris acknowledge a tension between Theism and Platonism, but seek to reconcile the divergent metaphysical perspectives utilizing the concept of Theistic Activism. Morris and Menzel ask whether God can not only be responsible for the creation of all contingent reality, but also if it can be intelligently and coherently concluded that God can also be creatively responsible for necessary existence and necessary truth. Morris and Menzel proceed to demonstrate what they term as the extraordinary compatibility of core elements of the Platonic and Theistic metaphysical visions. (Morris and Menzel, 1986, 361). Menzel writes,

The model that will be adopted . . . is simply an updated and refined version of Augustine’s doctrine of divine ideas, a view I will call theistic activism, or just activism, for short. Very briefly, the idea is this. On this model, abstract objects are taken to be contents of a certain kind of divine intellective activity in which God is essentially engaged; roughly, they are God’s thoughts, concepts, and perhaps certain other products of God’s mental life. This divine activity is. . . causally efficacious: the abstract objects that exist at any given moment, as products of God’s mental life, exist because God is thinking them; which is just to say that he creates them. (Menzel, 1986)

The authors, therefore, attempt to provide a Theistic ontology which places God at the center and which views everything else as exemplifying a relation of creaturely dependence on God. The authors agree that Platonism, in general, has been viewed historically as incompatible with Western Theism, but they propose that this perceived incompatibility is not insurmountable, and that the notion of Theistic Activism can overcome this apparent incompatibility. Menzel and Morris have two consequent objectives. First, they strive to eliminate the apparent inconsistency between Platonism and Theism. Second, the authors strive to preserve the Platonic notions of abstract objects, such as properties as necessary beings, as eternal, and as uncreated.

Morris and Menzel resolve the tension between abstract objects existing in simultaneity with God, concluding that God, in some fashion, must be creatively responsible for abstract objects. The authors therefore advance Theistic Activism, suggesting that the origination for the framework of reality that includes abstract objects has its source in the divine intellectual activity.

First, they argue that a Theistic Activist will hold God creatively responsible for the entire modal economy, for what is possible as well as what is necessary, and even for what is impossible. As stated above, the authors resort to the Augustinian divine ideas tradition, which concludes that the Platonic framework of reality arises out of the creatively efficacious intellective activity of God. The authors contend that the entire Platonic realm is, therefore, to be understood as deriving from God (Morris and Menzel, 1986, 356).

Second, Morris and Menzel proceed to propose a continuous model of creation, according to which God is always playing a direct causal role in the existence of his creatures and his creative activity is essential to a creatures being at all times, throughout its spacio-temporal existence. This is true regardless of whether God initially causes the created entity to exist. This conclusion is essential to the proposal of Morris and Menzel in that it provides a framework in which it can coherently be argued that God creates absolutely all objects, be they necessary or contingent. (Menzel, 1982, 2)

Third, for the Theistic Activist, God is understood to necessarily create the framework of reality. Morris and Menzel acknowledge the potentially problematic nature of this contention with regard to the activity of God as a free creator. As a resolution to the dilemma posed by the notions of God necessarily creating and God’s freedom, the authors argue that divine freedom must be understood in a radically different fashion from human freedom. Divine freedom is shaped by God’s moral nature. Therefore, God could not have done morally otherwise than was conducted in the act of creation.

Fourth, Morris and Menzel also address the problem of God’s own nature in relationship to this creative activity. The authors give consideration to the question of whether the varied dimensions of God’s own nature are part of the creative framework. The authors have two responses. They reject the proposal of some that God is to be understood as pure being and therefore devoid of determinate attributes such as omnipotence or omniscience. Morris and Menzel opt for the solution that God has a nature and that God creates his own nature. (Morris, 1989)

The writers conclude:

On the view of absolute creation, God is indeed a determinate, existent individual, but one whose status is clearly not just that of one more item in the inventory of reality. He is rather the source of absolutely everything there is: to use Tillich’s own characterization, he is in the deepest sense possible the ground of all-being. (Morris and Menzel, 1986, 360)

d. Bergman and Brower: Truthmaker Theory

Bergman and Brower conclude that Platonism is inconsistent with the central thesis of Traditional Theism, the aseity-dependence doctrine, which holds that God is an absolutely independent being who exists entirely from himself or a se. This central thesis of Traditional Theism led both philosophers and theologians of the Middle Ages to endorse the doctrine of divine simplicity by which God is understood to be an absolutely simple being, completely devoid of any metaphysical complexity. Further, according to the doctrine, God lacks the complexity associated with material or temporal composition, as well as the minimal form of complexity associated with the exemplification of properties.

The inconsistency is most apparent with regard to the tension between Platonism and divine simplicity. Platonism requires all true predications to be explained in terms of properties. Divine simplicity requires God to be identical with each of the things that can be predicated of him. If both are true, then God is identical with each of his properties and is therefore himself a property. This conclusion stands in contrast with the Traditional Theists understanding of God as a person and the conclusion that persons cannot be exemplified. Therefore Bergman and Brower advance that Platonism is inconsistent with the aseity-dependence doctrine itself. They further argue that the rejection of divine simplicity fails to remove this tension. In their conclusion, contemporary philosophers of religion have lost sight of a significant tension existing between Traditional Theism and Platonism, concluding that the two are perfectly compatible.

Bergman and Brower describe Platonism as characterized by two components. They remind that Platonism entails the view that a unified account of predication can be provided in terms of properties or exemplifiables. They also point out that Platonism entails the view that exemplifiables are best conceived of as abstract objects. Bergman and Brower indicate that Traditional Theism has typically addressed the second of these views and they propose that the distinctive aspect of their own argument targets the first. For Bergman and Brower this distinction is all important since it is often concluded that the inconsistency of Platonism and Traditional Theism is avoided merely by rejecting the Platonic view of properties in favor of another, such as the Augustinian view that properties are ideas in the mind of God. They write,

Traditional Theists who are Platonists, therefore, cannot avoid the inconsistency merely by dropping the Platonic conception of properties and replacing it with another – whether it be an Aristotelian conception (according to which there are no unexemplified universals), some form of immanent realism (according to which universals are concrete constituents of things that exemplify them), a nominalistic theory of tropes (according to which properties are concrete individuals), or even the Augustinian account (according to which all exemplifiables are divine concepts). (Bergman and Brower, 2006, 3-4)

However, Bergman and Brower contend that the inconsistency between the two metaphysical perspectives remains as long as the Traditional Theist continues to endorse the second of the two components of Platonism cited above. They further argue that the inconsistency can be resolved in only one of two ways. Either one is compelled to reject Traditional Theism and, therefore, become either a non-Theist or a non-Traditional Theist, or one is compelled to reject any unified account of predication in terms of exemplifiables. Those who desire to maintain the perspective of Traditional Theism are naturally inclined to adopt a unified account of predication and it is at this point that Bergman and Brower propose the alternative of Truthmaker Theory. (Bergman and Brower, 2006, 4)

But what is intended with the designation Truthmaker? The authors point out that the designation is not to be understood in causal terms or literally in terms of a “maker”, but on the contrary it is to be understood in terms of what they regard as a broadly logical entailment. Bergman and Brower begin their defense of Truthmaker Theory with a defense of the Truthmaker Theory of predication. Twenty-first century philosophers typically speak of Truthmakers as entailing the truth of certain statements or as predication by which is intended the truths expressed by them. For instance:

TM: If an entity E is a Truthmaker for a predication P, then “E exists” entails the truth expressed by P.

As a result, Socrates may be regarded as the Truthmaker for the statement “Socrates is human,” and God may be regarded as the Truthmaker for the statement, “God is divine.” If Traditional Theists desire to explain the truth of this predication in terms of something other than properties or exemplifiables, they can do so in terms of Truthmakers since, given that “God is divine” is a case of essential predication and that God necessitates its truth, God is, therefore, a plausible candidate for its Truthmaker. (Bergman and Bower, 2006, 25-27)

Not only do Bergman and Brower defend a Truthmaker Theory of predication, but they also attempt to demonstrate that Truthmaker Theory yields an understanding of the doctrine of divine simplicity that rescues the doctrine from the standard contemporary objection leveled against it, its alleged lack of coherence. Therefore, from the fact that God is simple, the medievals infer that God lacks any accidental or contingent properties and therefore that all true predications of the form “God is F” are cases of essential predication. Therefore, from the truth, “God is divine” it can be inferred that God is identical with his nature or divinity, which conclusion redeems the doctrine of divine simplicity. From the truth “God is good,” it can be inferred that he is identical with his goodness, the essence of the doctrine of divine simplicity. This is true for every other predication of this nature. Further, it can be concluded that just as God is identical with each of these qualities, so also each of these qualities is identical with each of the others, a further component of the doctrine of divine simplicity.

e. Plantinga: Christian Platonism

Alvin Plantinga has been described as a Platonist par–excellence. (Gould, 2010, 108) If Platonism is defined as the metaphysical perspective that there are innumerably many necessarily existing abstract entities, then Plantinga’s Does God Have A Nature? represents a thorough defense of Christian Platonism. (Freddoso, 145-53) Plantinga acknowledges that most Christians believe that God is the uncreated creator of all things and all things depend on him, and he depends upon nothing at all. The created universe presents no problem for this doctrine. God’s creation is dependent on him in a variety of ways and God is in no way dependent upon it. However, what does present a problem for this doctrine is the entire realm of Platonic universals, properties, kinds, propositions, numbers, sets, states of affairs and possible worlds. These things are everlasting, having no beginning or end. Abstract objects are also said to exist necessarily. Their non-existence is impossible. But how then are these abstract objects related to God? Plantinga frames the problem:

According to Augustine, God created everything distinct from him; did he then create these things? Presumably not; they have no beginnings. Are they dependent on him? But how could a thing whose non-existence is impossible . . . depend upon anything for its existence? And what about the characteristics and properties these things display? Does God just find them constituted the way they are? Must he simply put up with their being thus constituted? Are these things, their existence and their character, outside his control? (Plantinga, 1980, 3-4)

Plantinga acknowledges two conflicting perceptions regarding God and he attempts to reconcile these two perspectives. On the one hand, it is argued that God has control over all things (sovereignty) and we believe that God is uncreated or that God exists a se. Second, it is argued that certain abstract objects and necessary truths are independent of God and that certain of these, such as omniscience, omnipotence, omni-benevolence, constitute God’s nature. These two conclusions, however, are logically contradictory. How can God have sovereign control over all things and abstract objects exist independently?

Either the first or the second of these intuitions must be false. The entirety of Does God Have A Nature? is dedicated to an attempt to resolve this dilemma. Plantinga first discusses the proposal of Kant. Kant resolved the problem of these two conflicting intuitions through the denial that God has a nature, a conclusion that Plantinga rejects. Plantinga then moves to the consideration of the proposed solution of Thomas Aquinas. Aquinas argues on behalf of the doctrine of divine simplicity, which posits that God has a nature, but that God is identical with his nature. Plantinga concludes that Aquinas’ proposal is also inadequate due to the implications of the doctrine of divine simplicity, which seems to be problematic in that it leads to the denial of the personhood of God, thereby reducing him to an abstract object. Plantinga then turns to nominalism. The nominalist contends that abstract objects, such as properties, do not exist in any real sense. Abstract objects, therefore, are nothing more than designations and do not refer to any objects. Nominalism fails, in Plantinga’s opinion, since it is irrelevant to the real issue, the preservation of God’s absolute control. Plantinga then contends, in light of the failure of the previous approaches, that we may resolve to deny the truth of our intuition that abstract objects are necessary, or eternal, a conclusion which is designated as universal possibilism since the implication of the position is that everything is possible for God, a notion which Plantinga also rejects, since, in his opinion, this conclusion simply seems absurd.

However, for Plantinga the bifurcation between the Theistic notion of God as the uncreated creator of all that exists outside of himself and the Platonic notion of the existence of abstract objects, which exist necessarily and eternally, is not insurmountable. Plantinga endorses a form of Platonic realism. He espouses a conception of properties according to which these abstract objects are a specific type of abstract entity, namely, universals. Plantinga, proposes the following solution to the dilemma,

Augustine saw in Plato a vir sapientissimus et eruditissimus (Contra Academicos III, 17); yet he felt obliged to transform Plato’s theory of ideas in such a way that these abstract objects become . . . part of God, perhaps identical with his intellect. It is easy to see why Augustine took such a course, and easy to see why most later medieval thinkers adopted similar views. For the alternative seems to limit God in an important way; the existence and necessity of these things distinct from him seems incompatible with his sovereignty. (Plantinga, 1980, 5)

Plantinga, therefore, concludes that there may be some sense of dependence between God and abstract objects, that these abstract objects depend on God asymmetrically, and that they are the result of God’s intellective activity.

From the preceding overview we see that there exists a tension between the central notion of Traditional Theism, that God exists as the uncreated creator and that all objects existing beyond God have the source of their being in the creative activity of God, and the central notion of Platonism, that there exists a realm of abstract objects which are uncreated, and exist necessarily and eternally. Furthermore, we have seen that there exists a variety of proposals ranging from those that reject altogether the notion that these two distinctive worldviews are reconcilable, to those that would argue on behalf of their compatibility. (Freddosso, 1983)

6. References and Further Reading

a. Books

Aquinas, T. (1948). Summa Theologiae, trans. Fathers of the English Dominican Province. U.S.A: Christian Classics.
Brown, C. (1968). Philosophy and the Christian Faith. Illinois: Intervarsity Press.

Provides an examination of the historical interaction of philosophical thought and Christian theology.

Campbell, K. (1990). Abstract Particulars. Basil Blackwell Ltd.

Provides an in-depth analysis of Abstract Particulars.

Davies, B. (2004) An Introduction to the Philosophy of Religion (3^rd ed.). New York: Oxford University Press.

An excellent introduction to the basic issues in Philosophy of Religion.

Gerson, L. P. (1990). Plotinus: The Arguments of the Philosophers. New York: Routledge.

Provides an analysis of the development of Platonic philosophy and its incorporation into Christian Theology.

Morris, T. (1989) Anselmian Explorations: Essays in Philosophical Theology. Notre Dame: University of Notre Dame Press.
Plantinga, A. (1980). Does God Have a Nature? Milwaukee, Wisconsin: Marquette University Press.

Discusses the relationship of God to abstract objects.

Plantinga, A. (2000). Warranted Christian Belief. New York: Oxford University Press.

Explores the intellectual validity of Christian faith.

Van Inwagen, P. (1993) Metaphysics. Westview Press.

An in-depth exploration of the dimensions of metaphysics.

Wolterstorff, N. (1970). On Universals: An Essay in Ontology. University of Chicago.

Explores the nature of Platonic thought, the tenets of Traditional Theism.

b. Articles

Bergman, M., Brower, J. E. (2006). “A Theistic Argument against Platonism.” Oxford Studies in Metaphysics, 2, 357-386.

Discusses the logical inconsistency between Theism and Platonism by virtue of the aseity dependence doctrine.

Brower, J. E. “Making Sense of Divine Simplicity.” Unpublished.

Presents an in-depth analysis of the nature of divine simplicity.

Freddoso, A. (1983). “Review of Plantinga’s ‘Does God Have a Nature?’.” Christian Scholars Review, 12, 78-83.

An excellent and helpful review of Plantinga’s most significant work.

Gould, P. (2010). “A Defense of Platonic Theism: Dissertation.” Purdue University West.

A defense of Platonic Theism, which seeks to remain faithful to the Theistic tradition.

Leftow, B. (1990). “Is God an Abstract Object?.” Nous, 24, 581-598.

Strives to demonstrate that the Identity Thesis follows from a basic Theistic belief.

Menzel, C. (2001). “God and Mathematical Objects.” Bradley, J., Howell, R. (Eds.). Mathematics in a Postmodern Age: A Christian Perspective. Eerdman’s.
Menzel, C. (1987). “Theism, Platonism, and the Metaphysics of Mathematics.” Faith and Philosophy, 4(4), 1-22.
Morris, T., Menzel, C. (1986). “Absolute Creation.” American philosophical quarterly, 23, 353-362.

Seeks to reconcile the divergent metaphysical perspectives utilizing the concept of Theistic Activism

Plantinga, A. (1982). “How to be an Anti-Realist.” Proceedings and Addresses of the American Philosophical Association, 56 (1), 47-70.

An insightful and helpful discussion of Plantinga’s rejection of contemporary anti-realism and unbridled realism.

Ross, J. (1989). “The Crash of Modal Metaphysics.” Review of Metaphysics, 43, 251-79.

Addresses Quantified Modal Logic as at one time promising for metaphysics.

Ross, J. (1983). Creation II. “In The Existence and Nature of God.” A. J. Freddoso, (Ed). Notre Dame: University of Notre Dame Press.
Van Inwagen, P. (2009). “God and Other Uncreated Things.” Timpe, K. (Ed). Metaphysics and God: Essays in Honor of Eleonore Stump, 3-20.

Addresses the question regarding whether there is anything other than himself that God has not created.

Van Inwagen, P. (1988). “A Theory of Properties.” Oxford Studies in Metaphysics, 1, 107-138.

Explores the rationality of belief in abstract objects in general and properties in particular.

Author Information

Eddy Carder
Email: efcarder@pvamu.edu
Prairie View A & M University
U. S. A.

Mathematical Platonism

Mathematical platonism is any metaphysical account of mathematics that implies mathematical entities exist, that they are abstract, and that they are independent of all our rational activities. For example, a platonist might assert that the number pi exists outside of space and time and has the characteristics it does regardless of any mental or physical activities of human beings. Mathematical platonists are often called "realists," although, strictly speaking, there can be realists who are not platonists because they do not accept the platonist requirement that mathematical entities be abstract.

Mathematical platonism enjoys widespread support and is frequently considered the default metaphysical position with respect to mathematics. This is unsurprising given its extremely natural interpretation of mathematical practice. In particular, mathematical platonism takes at face-value such well known truths as that "there exist" an infinite number of prime numbers, and it provides straightforward explanations of mathematical objectivity and of the differences between mathematical and spatio-temporal entities. Thus arguments for mathematical platonism typically assert that in order for mathematical theories to be true their logical structure must refer to some mathematical entities, that many mathematical theories are indeed objectively true, and that mathematical entities are not constituents of the spatio-temporal realm.

The most common challenge to mathematical platonism argues that mathematical platonism requires an impenetrable metaphysical gap between mathematical entities and human beings. Yet an impenetrable metaphysical gap would make our ability to refer to, have knowledge of, or have justified beliefs concerning mathematical entities completely mysterious. Frege, Quine, and "full-blooded platonism" offer the three most promising responses to this challenge.

Nominalism, logicism, formalism and intuitionism are traditional opponents of mathematical platonism, but these metaphysical theories won't be discussed in detail in the present article.

What Is Mathematical Platonism?

Arguments for Platonism

The Fregean Argument for Object Platonism

The Quine-Putnam Indispensability Argument

Challenges to Platonism

Supplement: The Epistemological Challenge to Platonism

Supplement: The Referential Challenge to Platonism

References and Further Reading

1. What Is Mathematical Platonism?

Traditionally, mathematical platonism has referred to a collection of metaphysical accounts of mathematics, where a metaphysical account of mathematics is one that entails theses concerning the existence and fundamental nature of mathematical ontology. In particular, such an account of mathematics is a variety of (mathematical) platonism if and only if it entails some version of the following three Theses:

Existence: Some mathematical ontology exists.
Abstractness: Mathematical ontology is abstract.
Independence: Mathematical ontology is independent of all rational activities, that is, the activities of all rational beings.

In order to understand platonism so conceived, it will be useful to investigate what types of items count as mathematical ontology, what it is to be abstract, and what it is to be independent of all rational activities. Let us address these topics.

a. What Types of Items Count as Mathematical Ontology?

Traditionally, platonists have maintained that the items that are fundamental to mathematical ontology are objects, where an object is, roughly, any item that may fall within the range of the first-order bound variables of an appropriately formalized theory and for which identity conditions can be provided. Section 2 provides an outline of the evolution of this conception of an object. Those readers who are unfamiliar with the terminology "first-order bound variable" can consult Model-Theoretic Conceptions of Logical Consequence. Let us call platonisms that take objects to be the fundamental items of mathematical ontology object platonisms. So, object platonism is the conjunction of three theses: some mathematical objects exist, those mathematical objects are abstract, and those mathematical objects are independent of all rational activities. In the last hundred years or so, object platonisms have been defended by Gottlob Frege [1884, 1893, 1903], Crispin Wright and Bob Hale [Wright 1983], [Hale and Wright 2001], and Neil Tennant [1987, 1997].

Nearly all object platonists recognize that most mathematical objects naturally belong to collections (for example, the real numbers, the sets, the cyclical group of order 20). To borrow terminology from model theory, most mathematical objects are elements of mathematical domains. Consult Model-Theoretic Conceptions of Logical Consequence for details. It is well recognized that the objects in mathematical domains have certain properties and stand in certain relations to one another. These distinctively mathematical properties and relations are also acknowledged by object platonists to be items of mathematical ontology.

More recently, it has become popular to maintain that the items that are fundamental to mathematical ontology are structures rather than objects. Stewart Shapiro [1997, pp. 73-4], a prominent defender of this thesis, offers the following definition of a structure:

I define a system to be a collection of objects with certain relations. … A structure is the abstract form of a system, highlighting the interrelationships among the objects, and ignoring any features of them that do not affect how they relate to other objects in the system.

According to structuralists, mathematics’ subject matter is mathematical structures. Individual mathematical entities (for example, the complex number 1 + 2i) are positions or places in such structures. Controversy exists over precisely what this amounts to. Minimally, there is agreement that the places of structures exhibit a greater dependence on one another than object platonists claim exists between the objects of the mathematical domains to which they are committed. Some structuralists add that the places of structures have only structural properties—properties shared by all systems that exemplify the structure in question—and that the identity of such places is determined by their structural properties. Michael Resnik [1981, p. 530], for example, writes:

In mathematics, I claim, we do not have objects with an "internal" composition arranged in structures, we only have structures. The objects of mathematics, that is, the entities which our mathematical constants and quantifiers denote, are structureless points or positions in structures. As positions in structures, they have no identity or features outside a structure.

An excellent everyday example of a structure is a baseball defense (abstractly construed); such positions as pitcher and shortstop are the places of this structure. Although the pitcher and shortstop of any specific baseball defense (for example, of the Cleveland Indians’ baseball defense during a particular pitch of a particular game) have a complete collection of properties, if one considers these positions as places in the structure "baseball defense," the same is not true. For example, these places do not have a particular height, weight, or shoe size. Indeed, their only properties would seem to be those that reflect their relations to other places in the structure "baseball defense."

Although we might label platonisms of the structural variety structure platonisms, they are more commonly labeled ante rem (or sui generis) structuralisms. This label is borrowed from ante rem universals—universals that exist independently of their instances. Consult Universals for a discussion of ante rem universals. Ante rem structures are typically characterized as ante rem universals that, consequently, exist independently of their instances. As such, ante rem structures are abstract, and are typically taken to exist independently of all rational activities.

b. What Is It to Be an Abstract Object or Structure?

There is no straightforward way of addressing what it is to be an abstract object or structure, because "abstract" is a philosophical term of art. Although its primary uses share something in common—they all contrast abstract items (for example, mathematical entities, propositions, type-individuated linguistic characters, pieces of music, novels, etc.) with concrete, most importantly spatio-temporal, items (for example, electrons, planets, particular copies of novels and performances of pieces of music, etc.)—its precise use varies from philosopher to philosopher. Illuminating discussions of these different uses, the nature of the distinction between abstract and concrete, and the difficulties involved in drawing this distinction—for example, whether my center of gravity/mass is abstract or concrete—can be found in [Burgess and Rosen 1997, §I.A.i.a], [Dummett 1981, Chapter 14], [Hale 1987, Chapter 3] and [Lewis 1986, §1.7].

For our purposes, the best account takes abstract to be a cluster concept, that is, a concept whose application is marked by a collection of other concepts, some of which are more important to its application than others. The most important or central member of the cluster associated with abstract is:

1. non-spatio-temporality: the item does not stand to other items in a collection of relations that would make it a constituent of the spatio-temporal realm.

Non-spatio-temporality does not require an item to stand completely outside of the network of spatio-temporal relations. It is possible, for example, for a non-spatio-temporal entity to stand in spatio-temporal relations that are, non-formally, solely temporal relations—consider, for example, type-individuated games of chess, which came into existence at approximately the time at which people started to play chess. Some philosophers maintain that it is possible for non-spatio-temporal objects to stand in some spatio-temporal relations that are, non-formally, solely spatial relations. Centers of gravity/mass are a possible candidate. Yet, the dominant practice in the philosophy of mathematics literature is to take non-spatio-temporal to have an extension that only includes items that fail to stand in all spatio-temporal relations that are, non-formally, solely spatial relations.

Also fairly central to the cluster associated with abstract are, in order of centrality:

2. acausality: the item neither exerts a strict causal influence over other items nor does any other item causally influence it in the strict sense, where strict causal relations are those that obtain between, and only between, constituents of the spatio-temporal realm—for example, you can kick a football and cause it (in a strict sense) to move, but you can't kick a number.

3. eternality: where this could be interpreted as either

3a. omnitemporality: the item exists at all times, or

3b. atemporality: the item exists outside of the network of temporal relations,

4. changelessness: none of the item’s intrinsic properties change—roughly, an item’s intrinsic properties are those that it has independently of its relationships to other items, and

5. necessary existence: the item could not have failed to exist.

An item is abstract if and only if it has enough of the features in this cluster, where the features had by the item in question must include those that are most central to the cluster.

Differences in the use of "abstract" are best accounted for by observing that different philosophers seek to communicate different constellations of features from this cluster when they apply this term. All philosophers insist that an item have Feature 1 before it may be appropriately labeled "abstract." Philosophers of mathematics invariably mean to convey that mathematical entities have Feature 2 when they claim that mathematical objects or structures are abstract. Indeed, they typically mean to convey that such objects or structures have either Feature 3a or 3b, and Feature 4. Some philosophers of mathematics also mean to convey that mathematical objects or structures have Feature 5.

For cluster concepts, it is common to call those items that have all, or most, of the features in the cluster paradigm cases of the concept in question. With this terminology in place, the content of the Abstractness Thesis, as intended and interpreted by most philosophers of mathematics, is more precisely conveyed by the Abstractness⁺ Thesis: the mathematical objects or structures that exist are paradigm cases of abstract entities.

c. What Is It to Be Independent of All Rational Activities?

The most common account of the content of "X is independent of Y" is X would exist even if Y did not. Accordingly, when platonists affirm the Independence Thesis, they affirm that their favored mathematical ontology would exist even if there were no rational activities, where the rational activities in question might be mental or physical.

Typically, the Independence Thesis is meant to convey more than indicated above. The Independence Thesis is typically meant to convey, in addition, that mathematical objects or structures would have the features that they in fact have even if there were no rational activities or if there were quite different rational activities to the ones that there in fact are. We exclude these stronger conditions from the formal characterization of "X is independent of Y," because there is an interpretation of the neo-Fregean platonists Bob Hale and Crispin Wright that takes them to maintain that mathematical activities determine the ontological structure of a mathematical realm satisfying the Existence, Abstractness, and Independence Theses, that is, mathematical activities determine how such a mathematical realm is structured into objects, properties, and relations. See, for example, [MacBride 2003]. Athough this interpretation of Hale and Wright is controversial, were someone to advocate such a view, he or she would be advocating a variety of platonism.

2. Arguments for Platonism

Without doubt, it is everyday mathematical activities that motivate people to endorse platonism. Those activities are littered with assertions that, when interpreted in a straightforward way, support the Existence Thesis. For example, we are familiar with saying that there exist an infinite number of prime numbers and that there exist exactly two solutions to the equation x² – 5x + 6 = 0. Moreover, it is an axiom of standard set theories that the empty set exists.

It takes only a little consideration to realize that, if mathematical objects or structures do exist, they are unlikely to be constituents of the spatio-temporal realm. For example, where in the spatio-temporal realm might one locate the empty set, or even the number four—as opposed to collections with four elements? How much does the empty set or the real number p weigh? There appear to be no good answers to these questions. Indeed, to even ask them appears to be to engage in a category mistake. This suggests that the core content of the Abstractness Thesis--that mathematical objects or structures are not constituents of the spatio-temporal realm--is correct.

The standard route to the acceptance of the Independence Thesis utilizes the objectivity of mathematics. It is difficult to deny that “there exist infinitely many prime numbers” and “2 + 2 = 4” are objective truths. Platonists argue—or, more frequently, simply assume—that the best explanation of this objectivity is that mathematical theories have a subject matter that is quite independent of rational beings and their activities. The Independence Thesis is a standard way of articulating the relevant type of independence.

So, it is easy to establish the prima facie plausibility of platonism. Yet it took the genius of Gottlob Frege [1884] to transparently and systematically bring together considerations of this type in favor of platonism’s plausibility. In the very same manuscript, Frege also articulated the most influential argument for platonism. Let us examine this argument.

a. The Fregean Argument for Object Platonism

i. Frege’s Philosophical Project

Frege’s argument for platonism [1884, 1893, 1903] was offered in conjunction with his defense of arithmetic logicism—roughly, the thesis that all arithmetic truths are derivable from general logical laws and definitions. In order to carry out a defense of arithmetic logicism, Frege developed his Begriffsschift [1879]—a formal language designed to be an ideal tool for representing the logical structure of what Frege called thoughts. Contemporary philosophers would call them "propositions," and they are what Frege took to be the primary bearers of truth. The technical details of Frege’s begriffsschift need not concern us; the interested reader can consult the articles on Gottlob Frege and Frege and Language. We need only note that Frege took the logical structure of thoughts to be modeled on the mathematical distinction between a function and an argument.

On the basis of this function-argument understanding of logical structure, Frege incorporated two categories of linguistic expression into his begriffsschift: those that are saturated and those that are not. In contemporary parlance, we call the former singular terms (or proper names in a broad sense) and the latter predicates or quantifier expressions, depending on the types of linguistic expressions that may saturate them. For Frege, the distinction between these two categories of linguistic expression directly reflected a metaphysical distinction within thoughts, which he took to have saturated and unsaturated components. He labeled the saturated components of thoughts "objects" and the unsaturated components "concepts." In so doing, Frege took himself to be making precise the notions of object and concept already embedded in the inferential structure of natural languages.

ii. Frege’s Argument

Formulated succinctly, Frege’s argument for arithmetic-object platonism proceeds as follows:

i. Singular terms referring to natural numbers appear in true simple statements.

ii. It is possible for simple statements with singular terms as components to be true only if the objects to which those singular terms refer exist.

Therefore,

iii. the natural numbers exist.

iv. If the natural numbers exist, they are abstract objects that are independent of all rational activities.

Therefore,

v. the natural numbers are existent abstract objects that are independent of all rational activities, that is, arithmetic-object platonism is true.

In order to more fully understand Frege’s argument, let us make four observations: (a) Frege took natural numbers to be objects, because natural number terms are singular terms, (b) Frege took natural numbers to exist because singular terms referring to them appear in true simple statements—in particular, true identity statements, (c) Frege took natural numbers to be independent of all rational activities, because some thoughts containing them are objective, and (d) Frege took natural numbers to be abstract because they are neither mental nor physical. Observations (a) and (b) are important because they are the heart of Frege’s argument for the Existence Thesis, which, at least if one judges by the proportion of his Grundlagen [1884] that was devoted to establishing it, was of central concern to Frege. Observations (c) and (d) are important because they identify the mechanisms that Frege used to defend the Abstractness and Independence Theses. For further details, consult [Frege 1884, §26 and §61].

Frege’s argument for the thesis that some simple numerical identities are objectively true relies heavily on the fact that such identities allow for the application of natural numbers in representing and reasoning about reality, especially the non-mathematical parts of reality. It is applicability in this sense that Frege took to be the primary reason for judging arithmetic to be a body of objective truths rather than a mere game involving the manipulation of symbols. The interested reader should consult [Frege 1903, §91]. A more detailed formulation of Frege’s argument for arithmetic-object platonism, which incorporates the above observations, can be found below in section 5.

The central core of Frege’s argument for arithmetic-object platonism continues to be taken to be plausible, if not correct, by most contemporary philosophers. Yet its reliance on the category "singular term" presents a problem for extending it to a general argument for object platonism. The difficulty with relying on this category can be recognized once one considers extending Frege’s argument to cover mathematical domains that have more members than do the natural numbers (for example, the real numbers, complex numbers, or sets). Although there is a sense in which many natural languages do contain singular terms that refer to all natural numbers—such natural languages embed a procedure for generating a singular term to refer to any given natural number—the same cannot be said for real numbers, complex numbers, and sets. The sheer size of these domains excludes the possibility that there could be a natural language that includes a singular term for each of their members. There are an uncountable number of members in each such domain. Yet no language with an uncountable number of singular terms could plausibly be taken to be a natural language, at least not if what one means by a natural language is a language that could be spoken by rational beings with the same kinds of cognitive capacities that human beings have.

So, if Frege’s argument, or something like it, is to be used to establish a more wide ranging object platonism, then that argument is either going to have to exploit some category other than singular term or it is going to have to invoke this category differently than how Frege did. Some neo-Fregean platonists such as [Hale and Wright 2001] adopt the second strategy. Central to their approach is the category of possible singular term. [MacBride 2003] contains an excellent summary of their strategy. Yet the more widely adopted strategy has been to give up on singular terms all together and instead take objects to be those items that may fall within the range of first-order bound variables and for which identity conditions can be provided. Much of the impetus for this more popular strategy came from Willard Van Orman Quine. See [1948] for a discussion of the primary clause and [1981, p. 102] for a discussion of the secondary clause. It is worth noting, however, that a similar constraint to the secondary clause can be found in Frege’s writings. See discussions of the so-called Caesar problem in, for example, [Hale and Wright 2001, Chapter 14] and [MacBride 2005, 2006].

b. The Quine-Putnam Indispensability Argument

Consideration of the Quinean strategy of taking objects to be those items that may fall within the range of first-order bound variables naturally leads us to a contemporary version of Frege’s argument for the Existence Thesis. This Quine-Putnam indispensability argument (QPIA) can be found scattered throughout Quine’s corpus. See, for example, [1951, 1963, 1981]. Yet nowhere is it developed in systematic detail. Indeed, the argument is given its first methodical treatment in Hilary Putnam’s Philosophy of Logic [1971]. To date, the most extensive sympathetic development of the QPIA is provided by Mark Colyvan [2001]. Those interested in a shorter sympathetic development of this argument should read [Resnik 2005].

The core of the QPIA is the following:

i. We should acknowledge the existence of—or, as Quine and Putnam would prefer to put it, be ontologically committed to—all those entities that are indispensable to our best scientific theories.

ii. Mathematical objects or structures are indispensable to our best scientific theories.

Therefore,

iii. We should acknowledge the existence of—be ontologically committed to—mathematical objects or structures.

Note that this argument’s conclusion is akin to the Existence Thesis. Thus, to use it as an argument for platonism, one needs to combine it with considerations that establish the Abstractness and Independence Theses.

So, what is it for a particular, perhaps single-membered, collection of entities to be indispensable to a given scientific theory? Roughly, it is for those entities to be ineliminable from the theory in question without significantly detracting from the scientific attractiveness of that theory. This characterization of indispensability suffices for noting that, prima facie, mathematical theories are indispensable to many scientific theories, for, prima facie, it is impossible to formulate many such theories—never mind formulate those theories in a scientifically attractive way—without using mathematics.

However, indispensability thesis has been challenged. The most influential challenge was made by Hartry Field [1980]. Informative discussions of the literature relating to this challenge can be found in [Colyvan 2001, Chapter 4] and [Balaguer 1998, Chapter 6].

In order to provide a more precise characterization of indispensability, we will need to investigate the doctrines that Quine and Putnam use to motivate and justify the first premise of the QPIA: naturalism and confirmational holism. Naturalism is the abandonment of the goal of developing a first philosophy. According to naturalism, science is an inquiry into reality that, while fallible and corrigible, is not answerable to any supra-scientific tribunal. Thus, naturalism is the recognition that it is within science itself, and not in some prior philosophy, that reality is to be identified and described. Confirmational holism is the doctrine that theories are confirmed or infirmed as wholes, for, as Quine observes, it is not the case that “each statement, taken in isolation from its fellows, can admit of confirmation or infirmation …, statements … face the tribunal of sense experience not individually but only as a corporate body” [1951, p. 38].

It is easy to see the relationship between naturalism, confirmation holism, and the first premise of the QPIA. Suppose a collection of entities is indispensable to one of our best scientific theories. Then, by confirmational holism, whatever support we have for the truth of that scientific theory is support for the truth of the part of that theory to which the collection of entities in question is indispensable. Further, by naturalism, that part of the theory serves as a guide to reality. Consequently, should the truth of that part of the theory commit us to the existence of the collection of entities in question, we should indeed be committed to the existence of those entities, that is, we should be ontologically committed to those entities.

In light of this, what is needed is a mechanism for assessing whether the truth of some theory or part of some theory commits us to the existence of a particular collection of entities. In response to this need, Quine offers his criterion of ontological commitment: theories, as collections of sentences, are committed to those entities over which the first-order bound variables of the sentences contained within them must range in order for those sentences to be true.

Although Quine’s criterion is relatively simple, it is important that one appropriately grasp its application. One cannot simply read ontological commitments from the surface grammar of ordinary language. For, as Quine [1981, p. 9] explains,

[T]he common man’s ontology is vague and untidy … a fenced ontology is just not implicit in ordinary language. The idea of a boundary between being and nonbeing is a philosophical idea, an idea of technical science in the broad sense.

Rather, what is required is that one first regiment the language in question, that is, cast that language in what Quine calls "canonical notation." Thus,

[W]e can draw explicit ontological lines when desired. We can regiment our notation. … Then it is that we can say the objects assumed are the values of the variables. … Various turns of phrase in ordinary language that seem to invoke novel sorts of objects may disappear under such regimentation. At other points new ontic commitments may emerge. There is room for choice, and one chooses with a view to simplicity in one’s overall system of the world. [Quine 1981, pp. 9-10]

To illustrate, the everyday sentence “I saw a possible job for you” would appear to be ontologically committed to possible jobs. Yet this commitment is seen to be spurious once one appropriately regiments this sentence as “I saw a job advertised that might be suitable for you.”

We now have all of the components needed to understand what it is for a particular collection of entities to be indispensable to a scientific theory. A collection of entities is indispensable to a scientific theory if and only if, when that theory is optimally formulated in canonical notation, the entities in question fall within the range of the first-order bound variables of that theory. Here, optimality of formulation should be assessed by the standards that govern the formulation of scientific theories in general (for example, simplicity, fruitfulness, conservativeness, and so forth).

Now that we understand indispensability, it is worth noting the similarity between the QPIA and Frege’s argument for the Existence Thesis. We observed above that Frege’s argument has two key components: recognition of the applicability of numbers in representing and reasoning about the world as support for the contention that arithmetic statements are true, and a logico-inferential analysis of arithmetic statements that identified natural number terms as singular terms. The QPIA encapsulates directly parallel features: ineliminable applicability to our best scientific theories (that is, indispensability) and Quine’s criterion of ontological commitment. While the language and framework of the QPIA are different from those of Frege’s argument, these arguments are, at their core, identical.

One important difference between these arguments is worth noting, however. Frege’s argument is for the existence of objects; his analysis of natural languages only allows for the categories "object" and "concept." Quine’s criterion of ontological commitment recommends commitment to any entity that falls within the range of the first-order bound variables of any theory that one endorses. While all such entities might be objects, some might be positions or places in structures. As such, the QPIA can be used to defend ante rem structuralism.

3. Challenges to Platonism

a. Non-Platonistic Mathematical Existence

Since the late twentieth century, an increasing number of philosophers of mathematics in the platonic tradition have followed the practice of labeling their accounts of mathematics as "realist" or "realism" rather than "platonist" or "platonism." Roughly, these philosophers take an account of mathematics to be a variety of (mathematical) realism if and only if it entails three theses: some mathematical ontology exists, that mathematical ontology has objective features, and that mathematical ontology is, contains, or provides the semantic values of the components of mathematical theories. Typically, contemporary platonists endorse all three theses, yet there are realists who are not platonists. Normally, this is because these individuals do not endorse the Abstractness Thesis. In addition to non-platonist realists, there are also philosophers of mathematics who accept the Existence Thesis but reject the Independence Thesis. Section 6 below discusses accounts of mathematics that endorse the Existence Thesis, or something very similar, yet reject either the Abstractness Thesis or the Independence Thesis.

b. The Epistemological and Referential Challenges to Platonism

Let us consider the two most common challenges to platonism: the epistemological challenge and the referential challenge. Sections 7 and 8 below contain more detailed, systematic discussions of these challenges.

Proponents of these challenges take endorsement of the Existence, Abstractness and Independence Theses to amount to endorsement of a particular metaphysical account of the relationship between the spatio-temporal and mathematical realms. Specifically, according to this account, there is an impenetrable metaphysical gap between these realms. This gap is constituted by a lack of causal interaction between these realms, which, in turn, is a consequence of mathematical entities being abstract (see [Burgess and Rosen 1997, §I.A.2.a]). Proponents of the epistemological challenge observe that, prima facie, such an impenetrable metaphysical gap would make human beings’ ability to form justified mathematical beliefs and obtain mathematical knowledge completely mysterious. Proponents of the referential challenge, on the other hand, observe that, prima facie, such an impenetrable metaphysical gap would make human beings’ ability to refer to mathematical entities completely mysterious. It is natural to suppose that human beings do have justified mathematical beliefs and mathematical knowledge, for example, that 2 + 2 = 4, and do refer to mathematical entities, for example, when we assert “2 is a prime number.” Moreover, it is natural to suppose that the obtaining of these facts is not completely mysterious. The epistemological and referential challenges are challenges to show that the truth of platonism is compatible with the unmysterious obtaining of these facts.

This raises two questions. Why do proponents of the epistemological challenge maintain that an impenetrable metaphysical gap between the mathematical and spatio-temporal realms would make human beings’ ability to form justified mathematical beliefs and obtain mathematical knowledge completely mysterious? (For readability, we shall drop the qualifier "prima facie" in the remainder of this discussion.) And, why do proponents of the referential challenge insist that such an impenetrable metaphysical gap would make human beings’ ability to refer to mathematical entities completely mysterious?

To answer the first question, consider an imaginary scenario. You are in London, England while the State of the Union address is being given. You are particularly interested in what the U.S. President has to say in this address. So, you look for a place where you can watch the address on television. Unfortunately, the State of the Union address is only being televised on a specialized channel that nobody seems to be watching. You ask a Londoner where you might go to watch the address. She responds, “I’m not sure, but if you stay here with me, I’ll let you know word for word what the President says as he says it.” You look at her confused. You can find no evidence of devices in the vicinity (for example, television sets, mobile phones, or computers) that could explain her ability to do what she claims she will be able to. You respond, “I don’t see any TVs, radios, computers, or the like. How are you going to know what the President is saying?”

That such a response to this Londoner’s claim would be appropriate is obvious. Further, its aptness supports the contention that you can only legitimately claim knowledge of, or justified beliefs concerning, a complex state of affairs if there is some explanation available for the existence of the type of relationship that would need to exist between you and the complex state of affairs in question in order for you to have the said knowledge or justified beliefs. Indeed, it suggests something further: the only kind of acceptable explanation available for knowledge of, or justified beliefs concerning, a complex state of affairs is one that appeals directly or indirectly to a causal connection between the knower or justified believer and the complex state of affairs in question. You questioned the Londoner precisely because you could see no devices that could put her in causal contact with the President, and the only kind of explanation that you could imagine for her having the knowledge (or justified beliefs) that she was claiming she would have would involve her being in this type of contact with the President.

An impenetrable metaphysical gap between the mathematical and spatio-temporal realms of the type that proponents of the epistemological challenge insist exists if platonism is true would exclude the possibility of causal interaction between human beings, who are inhabitants of the spatio-temporal realm, and mathematical entities, which are inhabitants of the mathematical realm. Consequently, such a gap would exclude the possibility of there being an appropriate explanation of human beings having justified mathematical beliefs and mathematical knowledge. So, the truth of platonism, as conceived by proponents of the epistemological challenge, would make all instances of human beings having justified mathematical beliefs or mathematical knowledge completely mysterious.

Next, consider why proponents of the referential challenge maintain that an impenetrable metaphysical gap between the spatio-temporal and mathematical realms would make human beings’ ability to refer to mathematical entities completely mysterious. Once again, this can be seen by considering an imaginary scenario. Imagine that you meet someone for the first time and realize that you went to the same university at around the same time years ago. You begin to reminisce about your university experiences, and she tells you a story about John Smith, an old friend of hers who was a philosophy major, but who now teaches at a small liberal arts college in Ohio, was married about 6 years ago to a woman named Mary, and has three children. You, too, were friends with a John Smith when you were at the University. You recall that he was a philosophy major, intended to go to graduate school, and that a year or so ago a mutual friend told you that he is now married to a woman named Mary and has three children. You incorrectly draw the conclusion that you shared a friend with this woman while at the University. As a matter of fact, there were two John Smiths who were philosophy majors at the appropriate time, and these individuals' lives have shared similar paths. You were friends with one of these individuals, John Smith_1,while she was friends with the other, John Smith₂.

Your new acquaintance proceeds to inform you that John and Mary Smith got divorced recently. You form a false belief about your old friend and his wife. What makes her statement and corresponding belief true is that, in it, "John Smith" refers to John Smith₂, "Mary Smith" refers to Mary Smith_2,John Smith₂’s former wife, and John Smith₂ and Mary Smith₂ stand to a recent time in the triadic relation "x got divorced from y at time t." Your belief is false, however, because, in it, "John Smith" refers to John Smith₁, "Mary Smith" refers to Mary Smith_1,John Smith₁’s wife, and John Smith₁ and Mary Smith₁ fail to stand to a recent time in the triadic relation "x got divorced from y at time t."

Now, consider why John Smith₁ and Mary Smith₁ are the referents of your use of "John and Mary Smith" while John Smith₂ and Mary Smith₂ are the referents of your new acquaintance’s use of this phrase. It is because she causally interacted with John Smith₂ while at the University, while you causally interacted with John Smith₁. In other words, your respective causal interactions are responsible for your respective uses of the phrase "John and Mary Smith" having different referents.

Reflecting on this case, you might conclude that there must be a specific type of causal relationship between a person and an item if that person is to determinately refer to that item. For example, this case might convince you that, in order for you to use the singular term "two" to refer to the number two, there would need to be a causal relationship between you and the number two. Of course, an impenetrable metaphysical gap between the spatio-temporal realm and the mathematical realm would make such a causal relationship impossible. Consequently, such an impenetrable metaphysical gap would make human beings’ ability to refer to mathematical entities completely mysterious.

4. Full-Blooded Platonism

Of the many responses to the epistemological and referential challenges, the three most promising are (i) Frege’s, as developed in the contemporary neo-Fregean literature, (ii) Quine’s, as developed by defenders of the QPIA, and (iii) a response that is commonly referred to as full-blooded or plenitudinous platonism (FBP). This third response has been most fully articulated by Mark Balaguer [1998] and Stewart Shapiro [1997].

The fundamental idea behind FBP is that it is possible for human beings to have systematically and non-accidentally true beliefs about a platonic mathematical realm—a mathematical realm satisfying the Existence, Abstractness, and Independence Theses—without that realm in any way influencing us or us influencing it. This, in turn, is supposed to be made possible by FBP combining two theses: (a) Schematic Reference: the reference relation between mathematical theories and the mathematical realm is purely schematic, or at least close to purely schematic and (b) Plenitude: the mathematical realm is VERY large. It contains entities that are related to one another in all of the possible ways that entities can be related to one another.

What it is for a reference relation to be purely schematic will be explored later. For now, these theses are best understood in light of FBP’s account of mathematical truth, which, intuitively, relies on two further Theses: (1) Mathematical theories embed collections of constraints on what the ontological structure of a given "part" of the mathematical realm must be in order for the said part to be an appropriate truth-maker for the theory in question. (2) The existence of any such appropriate part of the mathematical realm is sufficient to make the said theory true of that part of that realm. For example, it is well-known that arithmetic characterizes an ω-sequence, a countable-infinite collection of objects that has a distinguished initial object and a successor relation that satisfies the induction principle. Thus, illustrating Thesis 1, any part of the mathematical realm that serves as an appropriate truth-maker for arithmetic must be an ω-sequence. Intuitively, one might think that not just any ω-sequence will do, rather one needs a very specific ω-sequence, that is, the natural numbers. Yet, proponents of FBP deny this intuition. According to them, illustrating Thesis 2, any ω-sequence is an appropriate truth-maker for arithmetic; arithmetic is a body of truths that concerns any ω-sequence in the mathematical realm.

Those familiar with the model theoretic notion of "truth in a model" will recognize the similarities between it and FBP’s conception of truth. (Those who are not can consult Model-Theoretic Conceptions Logical Consequence, where "truth in a model" is called "truth in a structure.") These similarities are not accidental; FBP’s conception of truth is intentionally modeled on this model-theoretic notion. The outstanding feature of model-theoretic consequence is that, in constructing a model for evaluating a semantic sequent (a formal argument), one doesn’t care which specific objects one takes as the domain of discourse of that model, which specific objects or collections of objects one takes as the extension of any predicates that appear in the sequent, or which specific objects one takes as the referents of any singular terms that appear in the sequent. All that matters is that those choices meet the constraints placed on them by the sequent in question. So, for example, if you want to construct a model to show that 'Fa & Ga' does not follow from ‘Fa’ and ‘Gb’, you could take the domain of your model to be the set of natural numbers, assign extensions to the two predicates by requiring Ext(F) = {x: x is even} and Ext(G) = {x: x is odd}, and assign denotations Ref(a) = 2, and Ref(b) = 3. Alternatively, you could take the domain of your model to be {Hillary Clinton, Bill Clinton}, Ext(F) = {Hillary Clinton}, Ext(G) = {Bill Clinton}, Ref(a) = Hillary Clinton, and Ref(b) = Bill Clinton. A reference relation is schematic if and only if, when employing it, there is the same type of freedom concerning which items are the referents of quantifiers, predicates, and singular terms as there is when constructing a model. In model theory, the reference relation is purely schematic. This reference relation is employed largely as-is in Shapiro’s structuralist version of FBP, whereas Balaguer’s version of FBP places a few more constraints on this reference relation. Yet neither Shapiro’s nor Balaguer’s constraints undermine the schematic nature of the reference relation they employ in characterizing their respective FBPs.

By endorsing Thesis 2, proponents of FBP endorse the Schematic Reference Thesis. Moreover, Thesis 2 and the Schematic Reference Thesis distinguish the requirements on mathematical reference (and, consequently, truth) from the requirements on reference to (and, consequently, truth concerning) spatio-temporal entities. As illustrated in section 3 above, the logico-inferential components of beliefs and statements about spatio-temporal entities have specific, unique spatio-temporal entities or collections of spatio-temporal entities as their referents. Thus, the reference relationship between spatio-temporal entities and spatio-temporal beliefs and statements is non-schematic.

FBP’s conception of reference appears to provide it with the resources to undermine the legitimacy of the referential challenge. According to proponents of FBP, in offering their challenge, proponents of the referential challenge illegitimately generalized a feature of the reference relationship between spatio-temporal beliefs and statements, and spatio-temporal entities, that is, its non-schematic character.

So, the Schematic Reference Thesis is at the heart of FBP’s response to the referential challenge. By contrast, the Plenitude Thesis is at the heart of FBP’s response to the epistemological challenge. To see this, consider an arbitrary mathematical theory that places an obtainable collection of constraints on any truth-maker for that theory. If the Plenitude Thesis is true, we can be assured that there is a part of the mathematical realm that will serve as an appropriate truth-maker for this theory because the truth of the Plenitude Thesis amounts to the mathematical realm containing some part that is ontologically structured in precisely the way required by the constraints embedded in the particular mathematical theory in question. So, the Plenitude Thesis ensures that there will be some part of the mathematical realm that will serve as an appropriate truth-maker for any mathematical theory that places an obtainable collection of constraints on its truth-maker(s). Balaguer uses the term "consistent" to pick out those mathematical theories that place obtainable constraints on their truth-maker(s). However, what Balaguer means by this is not, or at least should not be, deductively consistent. The appropriate notion is closer to Shapiro’s [1997] notion of coherent, which is a primitive modeled on set-theoretic satisfiability. Yet, however one states the above truth, it has direct consequences for the epistemological challenge. As Balaguer [1998, pp. 48–9] explains:

If FBP is correct, then all consistent purely mathematical theories truly describe some collection of abstract mathematical objects. Thus, to acquire knowledge of mathematical objects, all we need to do is acquire knowledge that some purely mathematical theory is consistent [.…] But knowledge of the consistency of a mathematical theory … does not require any sort of contact with, or access to, the objects that the theory is about. Thus, the [epistemological challenge has] been answered: We can acquire knowledge of abstract mathematical objects without the aid of any sort of contact with such objects.

5. Supplement: Frege’s Argument for Arithmetic-Object Platonism

Frege’s argument for arithmetic-object platonism proceeds in the following way:

i. The primary logico-inferential role of natural number terms (for example, “one” and “seven”) is reflected in numerical identity statements such as “The number of states in the United States of America is fifty.”

ii. The linguistic expressions on each side of identity statements are singular terms.

Therefore, from (i) and (ii),

iii. In their primary logico-inferential role, natural number terms are singular terms.

Therefore, from (iii) and from Frege’s logico-inferential analysis of the category "object,"

iv. the items referred to by natural number terms (that is, the natural numbers) are members of the logico-inferential category object.

v. Many numerical identity statements (for example, the one mentioned in (i) are true.

vi. An identity statement can be true only if the object referred to by the singular terms on either side of that identity statement exists.

Therefore, from (v) and (vi),

vii. the objects to which natural number terms refer (that is, the natural numbers) exist.

viii. Many arithmetic identities are objective.

ix. The existent components of objective thoughts are independent of all rational activities.

Therefore, from (viii) and (ix),

x. the natural numbers are independent of all rational activities.

xi. Thoughts with mental objects as components are not objective.

Therefore, from (viii) and (xi),

xii. the natural numbers are not mental objects.

xiii. The left hand sides of numerical identity statements of the form given in (i) show that natural numbers are associated with concepts in a specific way.

xiv. No physical objects are associated with concepts in the way that natural numbers are.

Therefore, from (xiii) and (xiv),

xv. The natural numbers are not physical objects.

xvi. Objects that are neither mental nor physical are abstract.

Therefore, from (xi), (xv), and (xvi),

xvii. the natural numbers are abstract objects.

Therefore, from (vii), (x), and (xvii),

xviii. arithmetic object platonism is true.

Return to section 2 where this section is references.

6. Supplement: Realism, Anti-Nominalism, and Metaphysical Constructivism

a. Realism

Since the late twentieth century, an increasing number of philosophers of mathematics who endorse the Existence Thesis, or something very similar, have followed the practice of labeling their accounts of mathematics "realist" or "realism" rather than "platonist" or "platonism," where, roughly, an account of mathematics is a variety of (mathematical) realism if and only if it entails three theses: some mathematical ontology exists, that mathematical ontology has objective features, and that mathematical ontology is, contains, or provides the semantic values of the logico-inferential components of mathematical theories. The influences that motivated individual philosophers to adopt this practice are diverse. In the broadest of terms, however, this practice is the result of the dominance of certain strands of analytic philosophy in the philosophy of mathematics.

In order to see how one important strand contributed to the practice of labeling accounts of mathematics "realist" rather than "platonist," let us explore Quinean frameworks. These are frameworks that embed the doctrines of naturalism and confirmational holism in a little more detail. Two features of such frameworks warrant particular mention.

First, within Quinean frameworks, mathematical knowledge is on a par with empirical knowledge; both mathematical statements and statements about the spatio-temporal realm are confirmed and infirmed by empirical investigation. As such, within Quinean frameworks, neither type of statement is knowable a priori, at least in the traditional sense. Yet nearly all prominent Western thinkers have considered mathematical truths to be knowable a priori. Indeed, according to standard histories of Western thought, this way of thinking about mathematical knowledge dates back at least as far as Plato. So, to reject it is to reject something fundamental to Plato’s thoughts about mathematics. Consequently, accounts of mathematics offered within Quinean frameworks almost invariably reject something fundamental to Plato’s thoughts about mathematics. In light of this, and the historical connotations of the label "platonism," it is not difficult to see why one might want to use an alternate label for such accounts that accept the Existence Thesis (or something very similar).

The second feature of Quinean frameworks that warrants particular mention in regard to the practice of using "realism" rather than "platonism" to label accounts of mathematics is that, within such frameworks, mathematical entities are typically treated and thought about in the same way as the theoretical entities of non-mathematical natural science. In some Quinean frameworks, mathematical entities are simply taken to be theoretical entities. This has led some to worry about other traditional theses concerning mathematics. For example, mathematical entities have traditionally been considered necessary existents, and mathematical truths have been considered to be necessary, while the constituents of the spatio-temporal realm—among them, theoretical entities such as electrons—have been considered to be contingent existents, and truths concerning them have been considered to be contingent. Mark Colyvan [2001] uses his discussion of the QPIA—in particular, the abovementioned similarities between mathematical and theoretical entities—to motivate skepticism about the necessity of mathematical truths and the necessary existence of mathematical entities. Michael Resnik [1997] goes one step further and argues that, within his Quinean framework, the distinction between the abstract and the concrete cannot be drawn in a meaningful way. Of course, if this distinction cannot be drawn in a meaningful way, one cannot legitimately espouse the Abstractness Thesis. Once again, it looks as though we have good reasons for not using the label "platonism" for the kinds of accounts of mathematics offered within Quinean frameworks that accept the Existence Thesis (or something very similar).

b. Anti-Nominalism

Most of the Quinean considerations relevant to the practice of labeling metaphysical accounts of mathematics "realist" rather than "platonist" center on problems with the Abstractness Thesis. In particular, those who purposefully characterize themselves as realists rather than platonists frequently want to deny some important feature or features in the cluster associated with abstract. Frequently, such individuals do not question the Independence Thesis. John Burgess’ qualms about metaphysical accounts of mathematics are broader than this. He takes the primary lesson of Quine’s naturalism to be that investigations into "the ultimate nature of reality" are misguided, for we cannot reach the “God’s eye perspective” that they assume. The only perspective that we (as finite beings situated in the spatio-temporal world, using the best methods available to us, that is, the methods of common sense supplemented by scientific investigation) can obtain is a fallible, limited one that has little to offer concerning the ultimate nature of reality.

Burgess takes it to be clear that both pre-theoretic common sense and science are ontologically committed to mathematical entities. He argues that those who deny this, that is, nominalists, do so because they misguidedly believe that we can obtain a God’s eye perspective and have knowledge concerning the ultimate nature of reality. In a series of manuscripts responding to nominalists—see, for example, [Burgess 1983, 2004] and [Burgess and Rosen 1997, 2005]—Burgess has defended anti-nominalism. Anti-nominalism is, simply, the rejection of nominalism. As such, anti-nominalists endorse ontological commitment to mathematical entities, but refuse to engage in speculation about the metaphysical nature of mathematical entities that goes beyond what can be supported by common sense and science. Burgess is explicit that neither common sense nor science provide support for endorsing the Abstractness Thesis when understood as a thesis about the ultimate nature of reality. Further, given that, at least on one construal, the Independence Thesis is just as much a thesis about the ultimate nature of reality as is the Abstractness Thesis, we may assume that Burgess and his fellow anti-nominalists will be unhappy about endorsing it. Anti-nominalism, then, is another account of mathematics that accepts the Existence Thesis (or something very similar), but which cannot be appropriately labeled "platonism."

c. Metaphysical Constructivism

The final collection of metaphysical accounts of mathematics worth mentioning because of their relationship to, but distinctness from, platonism are those that accept the Existence Thesis—and, in some cases, the Abstractness Thesis—but reject the Independence Thesis. At least three classes of accounts fall into this category. The first accounts are those that take mathematical entities to be constructed mental entities. At some points in his corpus, Alfred Heyting suggests that he takes mathematical entities to have this nature—see, for example, [Heyting 1931]. The second accounts are those that take mathematical entities to be the products of mental or linguistic human activities. Some passages in Paul Ernest’s Social Constructivism ss a Philosophy of Mathematics [1998] suggest that he holds this view of mathematical entities. The third accounts are those that take mathematical entities to be social-institutional entities like the United States Supreme Court or Greenpeace. Rueben Hersh [1997] and Julian Cole [2008, 2009] endorse this type of social-institutional account of mathematics. Although all of these accounts are related to platonism in that they take mathematical entities to exist or they endorse ontological commitment to mathematical entities, none can be appropriately labeled "platonism."

Return to section 3 where this section is referenced.

7. Supplement: The Epistemological Challenge to Platonism

Contemporary versions of the epistemological challenge ,sometimes under the label "the epistemological argument against platonism," can typically be traced back to Paul Benacerraf’s paper "Mathematical Truth" [1973]. In fairness to Frege, however, it should be noted that human beings’ epistemic access to the kind of mathematical realm that platonists take to exist was a central concern in his work. Benacerraf’s paper has inspired much discussion. An overview of which appears in [Balaguer 1998, Chapter 2]. Interestingly, very little of this extensive literature has served to develop the challenge itself in any great detail. Probably the most detailed articulation of some version of the challenge itself can be found in two papers collected in [Field 1989]. The presentation of the challenge provided here is inspired by Hartry Field’s formulation, yet is a little more detailed than his formulation.

The epistemological challenge begins with the observation that an important motivation for platonism is the widely held belief that human beings have mathematical knowledge. One might maintain that it is precisely because we take human beings to have mathematical knowledge that we take mathematical theories to be true. In turn, their truth motivates platonists to take their apparent ontological commitments seriously. Consequently, while all metaphysical accounts of mathematics need to address the prima facie phenomenon of human mathematical knowledge, this task is particularly pressing for platonist accounts, for a failure to account for human beings’ ability to have mathematical knowledge would significantly diminish the attractiveness of any such account. Yet it is precisely this that (typical) proponents of the epistemological challenge doubt the platonists’ ability to account for human beings having mathematical knowledge.

a. The Motivating Picture Underwriting the Epistemological Challenge

In order to understand the doubts of proponents of the epistemological challenge, one must first understand the conception or picture of platonism that motivates them. Note that, in virtue of their endorsement of the Existence, Abstractness, and Independence Theses, platonists take the mathematical realm to be quite distinct from the spatio-temporal realm. The doubts underwriting the epistemological challenge derive their impetus from a particular picture of the metaphysical relationship between these distinct realms. According to this picture, there is an impenetrable metaphysical gap between the mathematical and spatio-temporal realms. This gap is constituted by the lack of causal interaction between these two realms, which, in turn, is a consequence of mathematical entities being abstract—see [Burgess and Rosen 1997, §I.A.2.a] for further details. Moreover, according to this picture, the metaphysical gap between the mathematical and spatio-temporal realms ensures that features of the mathematical realm are independent of features of the spatio-temporal realm. That is, features of the spatio-temporal realm do not in any way influence or determine features of the mathematical realm and vice versa. At the same time, the gap between the mathematical and spatio-temporal realms is more than merely an interactive gap; it is also a gap relating to the types of properties characteristic of the constituents of these two realms. Platonists take mathematical entities to be not only acausal but also non-spatio-temporal, eternal, changeless, and (frequently) necessary existents. Typically, constituents of the spatio-temporal world lack all of these properties.

It is far from clear that the understanding of the metaphysical relationship between the mathematical and spatio-temporal realms outlined in the previous paragraph is shared by self-proclaimed platonists. Yet this conception of that relationship is the one that proponents of the epistemological challenge ascribe to platonists. For the purposes of our discussion of this challenge, let us put to one side all concerns about the legitimacy of this conception of platonism, which, from now on, we shall simply call the motivating picture. The remainder of this section assumes that the motivating picture provides an appropriate conception of platonism and it labels as "platonic" the constituents of realms that are metaphysically isolated from and wholly different from the spatio-temporal realm in the way that the mathematical realm is depicted to be by the motivating picture.

b. The Fundamental Question: The Core of the Epistemological Challenge

Let us make some observations relevant to the doubts that underwrite the epistemological challenge. First, according to the motivating picture, the mathematical realm is that to which pure mathematical beliefs and statements are responsible for their truth or falsity. Such beliefs are about this realm and so are true when, and only when, they are appropriately related to this realm. Second, according to all plausible contemporary accounts of human beings, human beliefs in general, and, hence, human mathematical beliefs in particular, are instantiated in human brains, which are constituents of the spatio-temporal realm. Third, it has been widely acknowledged since ancient times that beliefs or statements that are true purely by accident do not constitute knowledge. Thus, in order for a mathematical belief or statement to be an instance of mathematical knowledge, it must be more than simply true; it must be non-accidentally true.

Let us take a mathematical theory to be a non-trivial, systematic collection of mathematical beliefs. Informally, it is the collection of mathematical beliefs endorsed by that theory. In light of the above observations, in order for a mathematical theory to embed mathematical knowledge, there must be something systematic about the way in which the beliefs in that theory are non-accidentally true.

Thus, according to the motivating picture, in order for a mathematical theory to embed mathematical knowledge, a distinctive, non-accidental and systematic relationship must obtain between two distinct and metaphysically isolated realms. That relationship is that the mathematical realm must make true, in a non-accidental and systematic way, the mathematical beliefs endorsed by the theory in question, which are instantiated in the spatio-temporal realm.

In response to this observation, it is reasonable to ask platonists, "What explanation can be provided of this distinctive, non-accidental and systematic relationship obtaining between the mathematical realm and the spatio-temporal realm?" As Field explains, “there is nothing wrong with supposing that some facts about mathematical entities are just brute facts, but to accept that facts about the relationship between mathematical entities and human beings are brute and inexplicable is another matter entirely” [1989, p. 232]. The above question—which this section will call the fundamental question—is the heart of the epistemological challenge to platonism.

c. The fundamental Question: Some Further Details

Let us make some observations that motivate the fundamental question. First, all human theoretical knowledge requires a distinctive type of non-accidental, systematic relationship to obtain. Second, for at least the vast majority of spatio-temporal theories, the obtaining of this non-accidental, systematic relationship is underwritten by causal interaction between the subject matter of the theory in question and human brains. Third, there is no causal interaction between the constituents of platonic realms and human brains. Fourth, the lack of causal interaction between platonic realms and human brains makes it apparently mysterious that the constituents of such realms could be among the relata of a non-accidental, systematic relationship of the type required for human, theoretical knowledge.

So, the epistemological challenge is motivated by the acausality of mathematical entities. Yet Field’s formulation of the challenge includes considerations that go beyond the acausality of mathematical entities. Our discussion of the motivating picture made it clear that, in virtue of its abstract nature, a platonic mathematical realm is wholly different from the spatio-temporal realm. These differences ensure that not only causal explanations, but also other explanations grounded in features of the spatio-temporal realm, are unavailable to platonists in answering the fundamental question. This fact is non-trivial, for explanations grounded in features of the spatio-temporal realm other than causation do appear in natural science. For examples, see [Batterman 2001]. So, a platonist wanting to answer the fundamental question must highlight a mechanism that is not underwritten by any of the typical features of the spatio-temporal realm.

Now, precisely what type of explanation is being sought by those asking the fundamental question? Proponents of the epistemological challenge insist that the motivating picture makes it mysterious that a certain type of relationship could obtain. Those asking the fundamental question are simply looking for an answer that would dispel their strong sense of mystery with respect to the obtaining of this relationship. A plausible discussion of a mechanism that, like causation, is open to investigation, and thus has the potential for making the obtaining of this relationship less than mysterious, should satisfy them. Further, the discussion in question need not provide all of the details of the said explanation. Indeed, if one considers an analogous question with regard to spatio-temporal knowledge, one sees that the simple recognition of some type of causal interaction between the entities in question and human brains is sufficient to dispel the (hypothetical) sense of mystery in question in this case.

Next ask, "Is the fundamental question legitimate?" That is, should platonists feel the need to answer it? It is reasonable to maintain that they should. Explanations should be available for many types of relationships, including the distinctive, non-accidental and systematic relationship required in order for someone to have knowledge of a complex state of affairs. It is this justified belief that legitimizes the fundamental question. One instance of it is the belief that some type of explanation should be, in principle, available for the obtaining of the specific, non-accidental and systematic relationship required for human mathematical knowledge if this is knowledge of an existent mathematical realm. It is illegitimate to provide a metaphysical account of mathematics that rules out the possibility of such an explanation being available, because it would be contrary to this justified belief. The fundamental question is a challenge to platonists to show that they have not made this illegitimate move.

Return to section 3 where this section is referenced.

8. Supplement: The Referential Challenge to Platonism

In the last century or so, the philosophy of mathematics has been dominated by analytic philosophy. One of the primary insights guiding analytic philosophy is that language serves as a guide to the ontological structure of reality. One consequence of this insight is that analytic philosophers have a tendency to assimilate ontology to those items that are the semantic values of true beliefs or statements, that is, the items in virtue of which true beliefs or statements are true. This assimilation played an important role in both of the arguments for platonism developed in section 2. The relevant language-world relations are embedded in Frege’s logico-inferential analysis of the categories of object and concept and in Quine’s criterion of ontological commitment. This assimilation is at the heart of the referential challenge (to platonism).

a. Introducing the Referential Challenge

Before developing the referential challenge, let us think carefully about the following claim: “Pure mathematical beliefs and statements are about the mathematical realm, and so are true when, and only when, they are appropriately related to this realm.” What precisely is it for a belief or statement to be about something? And, what is the appropriate relationship that must obtain in order for whatever a belief or statement is about to make that belief or statement true? It is natural to suppose that the logico-inferential components of beliefs and statements have semantic values. Beliefs and statements are “about” these semantic values. Beliefs and statements are true when, and only when, these semantic values are related in the way that those beliefs and statements maintain that they are. The formal mathematical theory that theorizes about this appropriate relation is model theory. Moreover, on the basis of the above, it is reasonable to suppose that the semantic values of the logico-inferential components of beliefs and statements are, roughly, set or determined by means of causal interaction between human beings and those semantic values.

Applying these observations to the claim “pure mathematical beliefs and statements are about the mathematical realm, and so are true when, and only when, they are appropriately related to this realm,” we find that it maintains that constituents of a mathematical realm are the semantic values of the logico-inferential components of pure mathematical beliefs and statements. Further, such beliefs and statements are true when, and only when, the appropriate semantic values are related to one another in the way that the said beliefs and statements maintain that they are related—more formally, the way demanded by the model-theoretic notion of truth in a model.

So far, our observations have been easily applicable to the mathematical case. Yet they highlight a problem. How are the appropriate semantic values of the logico-inferential components of pure mathematical beliefs and statements set or determined? If platonists are correct about the metaphysics of the mathematical realm, then no constituent of that realm causally interacts with any human being. Yet it is precisely causal interaction between human beings and the semantic values of beliefs and statements about the spatio-temporal world that is responsible for setting or determining the semantic values of such beliefs and statements. The referential challenge is a challenge to platonists to explain how constituents of a platonic mathematical realm could be set or fixed as the semantic values of human beliefs and statements.

b. Reference and Permutations

Two specific types of observations have been particularly important in conveying the force of the referential challenge. The first is the recognition that a variety of mathematical domains contain non-trivial automorphisms, which means that there is a non-trivial, structure-preserving, one-to-one and onto mapping from the domain to itself. A consequence of such automorphisms is that it is possible to systematically reassign the semantic values of the logico-inferential components of a theory that has such a domain as its subject matter in a way that preserves the truth values of the beliefs or statements of that theory. For example, consider the theory of the group {Z,+}, that is, the group whose elements are the integers …, -2, -1, 0, 1, 2, … and whose operation is addition. If one takes an integer n to have –n as its semantic value rather than n (that is, ‘2’ refers to -2, ‘-3’ refers to 3, and so forth), then the truth values of the statements or beliefs that constitute this theory would be unaltered. For example, “2 + 3 = 5” would be true in virtue of -2 + -3 being equal to -5. A similar situation arises for complex analysis if one takes each term of the form ‘a+bi’ to have the complex number a-bi as its semantic value rather than the complex number a+bi.

To see how this sharpens the referential challenge, suppose, perhaps per impossible, that you and your acquaintance each know a person named "John Smith." John Smith₁ and John Smith₂ are actually indistinguishable on the basis of the properties and relations that you discuss with your new acquaintance. That is, all of the consequences of all of the true statements that your new acquaintance makes about John Smith₂ are also true of John Smith₁, and all of the consequences of all of the true statements that you make about John Smith₁ are also true of John Smith₂. Under this supposition, her statements are still true in virtue of her using "John Smith" to refer to John Smith₂, and your statements are still true in virtue of you using "John Smith" to refer to John Smith₁. Using this as a guide, you might claim that ‘2 + 3 = 5’ should be true in virtue of ‘2’ referring to 2, ‘3’ referring to 3, and ‘5’ referring to 5 rather than in virtue of ‘2’ referring to the number -2, ‘3’ referring to the number -3, and ‘5’ referring to the number -5 as would be allowed by the automorphism mentioned above. One way to put this intuition is that 2, 3, and 5, are the intended semantic values of ‘2’, ‘3’, and ‘5’ and, intuitively, beliefs and statements should be true in virtue of the intended semantic values of their components being appropriately related to one another, not in virtue of other items (for example, -2, -3, and, -5) being so related. Yet, in the absence of any causal interaction between the integers and human beings, what explanation can be provided of ‘2’, ‘3’, and ‘5’ having their intended semantic values rather than some other collection of semantic values that preserves the truth values of arithmetic statements?

c. Reference and the Löwenheim-Skolem Theorem

The sharpening of the referential challenge discussed in the previous section is an informal, mathematical version of Hilary Putnam’s permutation argument. See, for example, [Putnam 1981]. A related model-theoretic sharpening of the referential challenge, also due to Putnam [1983], exploits an important result from mathematical logic: the Löwenheim-Skolem theorem. According to the Löwenheim-Skolem theorem, any first-order theory that has a model has a model whose domain is countable, where a model can be understood, roughly, as a specification of semantic values for the components of the theory. To understand the importance of this result, consider first-order complex analysis and its prima facie intended subject matter, that is, the domain of complex numbers. Prima facie, the intended semantic value of a complex number term of the form ‘a+bi’ is the complex number a+bi. Now, the domain of complex numbers is uncountable. So, according to the Löwenheim-Skolem theorem, it is possible to assign semantic values to terms of the form ‘a+bi’ in a way that preserves the truth values of the beliefs or statements of complex analysis, and which is such that the assigned semantic values are drawn from a countable domain whose ontological structure is quite unlike that of the domain of complex numbers. Indeed, not only the truth of first-order complex analysis, but the truth of all first-order mathematics can be sustained by assigning semantic values drawn from a countable domain to the logico-inferential components of first-order mathematical theories. Since most of mathematics is formulated (or formulable) in a first-order way, we are left with the question, "How, in the absence of causal interaction between human beings and the mathematical realm, can a platonist explain a mathematical term having its intended semantic value rather than an alternate value afforded by the Löwenheim-Skolem theorem?"

Strictly speaking, a platonist could bite a bullet here and simply maintain that there is only one platonic mathematical domain, a countable one, and that this domain is the actual, if not intended, subject matter of most mathematics. Yet this is not a bullet that most platonists want to bite, for they typically want the Existence Thesis to cover not only a countable mathematical domain, but all of the mathematical domains typically theorized about by mathematicians and, frequently, numerous other domains about which human mathematicians have not, as yet, developed theories. As soon as the scope of the Existence Thesis is so extended, the sharpening of the referential challenge underwritten by the Löwenheim-Skolem theorem has force.

Return to section 3 where this section is referenced.

9. References and Further Reading

a. Suggestions for Further Reading

Balaguer, Mark 1998. Platonism and Anti-Platonism in Mathematics, New York, NY: Oxford University Press.

The first part of this book provides a relatively gentle introduction to full-blooded platonism. It also includes a nice discussion of the literature surrounding the epistemological challenge.

Balaguer, Mark 2008. Mathematical Platonism, in Proof and Other Dilemmas: Mathematics and Philosophy, ed. Bonnie Gold and Roger Simons, Washington, DC: Mathematics Association of America: 179–204.

This article provides a non-technical introduction to mathematical platonism. It is an excellent source of references relating to the topics addressed in this article.

Benacerraf, Paul 1973. Mathematical Truth, Journal of Philosophy 70: 661–79.

This paper contains a discussion of the dilemma that motivated contemporary interest in the epistemological challenge to platonism. It is relatively easy to read.

Burgess, John and Gideon Rosen 1997. A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics, New York, NY: Oxford University Press.

The majority of this book is devoted to a technical discussion of a variety of strategies for nominalizing mathematics. Yet §1A and §3C contain valuable insights relating to platonism. These sections also provide an interesting discussion of anti-nominalism.

Colyvan, Mark 2001. The Indispensability of Mathematics, New York, NY: Oxford University Press.

This book offers an excellent, systematic exploration of the Quine-Putnam Indispensability Argument and some of the most important challenges that have been leveled against it. It also discusses a variety of motivations for being a non-platonist realist rather than a platonist.

Field, Hartry 1980. Science Without Numbers, Princeton, NJ: Princeton University Press.

This book contains Field’s classic challenge to the Quine-Putnam Indispensability Argument. Much of it is rather technical.

Frege, Gottlob 1884. Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl, translated by John Langshaw Austin as The Foundations of Mathematics: A logico-mathematical enquiry into the concept of number, revised 2^nd edition 1974, New York, NY: Basil Blackwell.

This manuscript is Frege’s original, non-technical, development of his platonist logicism.

Hale, Bob and Crispin Wright 2001. The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, New York, NY: Oxford University Press.

This book collects together many of the most important articles from Hale’s and Wright’s defense of neo-Fregean platonism. Its articles vary in difficulty.

MacBride, Fraser 2003. Speaking with Shadows: A Study of Neo-Logicism, British Journal for the Philosophy of Science 54: 103–163.

This article provides an excellent summary of Hale’s and Wright’s neo-Fregean logicism. It is relatively easy to read.

Putnam, Hilary 1971. Philosophy of Logic, New York, NY: Harper Torch Books.

This manuscript contains Putnam’s systematic development of the Quine-Putnam Indispensability Argument.

Resnik, Michael 1997. Mathematics as a Science of Patterns, New York, NY: Oxford University Press.

This book contains Resnik’s development and defense of a non-platonist, realist structuralism. It contains an interesting discussion of some of the problems with drawing the abstract/concrete distinction.

Shapiro, Stewart 1997. Philosophy of Mathematics: Structure and Ontology, New York, NY: Oxford University Press.

This book contains Shapiro’s development and defense of a platonist structuralism. It also offers answers to the epistemological and referential challenges.

Shapiro, Stewart 2005. The Oxford Handbook of Philosophy of Mathematics and Logic, New York, NY: Oxford University Press.

This handbook contains excellent articles addressing a variety of topics in the philosophy of mathematics. Many of these articles touch on themes relevant to platonism.

b. Other References

Batterman, Robert 2001. The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence, New York, NY: Oxford University Press.
Burgess, John 1983. Why I Am Not a Nominalist, Notre Dame Journal of Formal Logic 24: 41–53
Burgess, John 2004. Mathematics and Bleak House, Philosophia Mathematica 12: 18–36.
Burgess, John and Gideon Rosen 2005. Nominalism Reconsidered, in The Oxford Handbook of Philosophy of Mathematics and Logic, ed. Stewart Shapiro, New York, NY: Oxford University Press: 515–35.
Cole, Julian 2008. Mathematical Domains: Social Constructs? in Proof and Other Dilemmas: Mathematics and Philosophy, ed. Bonnie Gold and Roger Simons, Washington, DC: Mathematics Association of America: 109–28.
Cole, Julian 2009. Creativity, Freedom, and Authority: A New Perspective on the Metaphysics of Mathematics, Australasian Journal of Philosophy 87: 589–608.
Dummett, Michael 1981. Frege: Philosophy of Language, 2^nd edition, Cambridge, MA: Harvard University Press.
Ernest, Paul 1998. Social Constructivism as a Philosophy of Mathematics, Albany, NY: State University of New York Press.
Field, Hartry 1989. Realism, Mathematics, and Modality, New York, NY: Basil Blackwell.
Frege, Gottlob 1879. Begriffsschift, eine der arithmetschen nachgebildete Formelsprache des reinen Denkens, Halle a. Saale: Verlag von Louis Nebert.
Frege, Gottlob 1893. Grundgesetze der Arithmetik, Band 1, Jena, Germany: Verlag von Hermann Pohle.
Frege, Gottlob 1903. Grundgesetze der Arithmetik, Band 2, Jena, Germany: Verlag von Hermann Pohle.
Hale, Bob 1987. Abstract Objects, New York, NY: Basil Blackwell.
Hersh, Rueben 1997. What Is Mathematics, Really? New York, NY: Oxford University Press.
Heyting, Alfred 1931. Die intuitionistische Grundlegung der Mathematik, Erkenntnis 2: 106–115, translated in Paul Benacerraf and Hilary Putnam, Philosophy of Mathematics: Selected Readings, 2^nd edition, 1983: 52–61.
Lewis, David 1986. On the Plurality of Worlds, New York, NY: Oxford University Press.
MacBride, Fraser 2005. The Julio Czsar Problem, Dialectica 59: 223–36.
MacBride, Fraser 2006. More problematic than ever: The Julius Caesar objection, in Identity and Modality: New Essays in Metaphysics, ed. Fraser MacBride, New York, NY: Oxford University Press: 174–203.
Putnam, Hilary 1981. Reason, Truth, and History, New York, NY: Cambridge University Press.
Putnam, Hilary 1983. Realism and Reason, New York, NY: Cambridge University Press.
Quine, Willard Van Orman 1948. On what there is, Review of Metaphysics 2: 21–38.
Quine, Willard Van Orman 1951. Two dogmas of empiricism, Philosophical Review 60: 20–43, reprinted in From a Logical Point of View, 2^nd edition 1980, New York, NY: Cambridge University Press: 20–46.
Quine, Willard Van Orman 1963. Set Theory and Its Logic, Cambridge, MA: Harvard University Press.
Quine, Willard Van Orman 1981. Theories and Things, Cambridge, MA: Harvard University Press.
Resnik, Michael 1981. Mathematics as a science of patterns: Ontology and reference, Noûs 15: 529–50.
Resnik, Michael 2005. Quine and the Web of Belief, in The Oxford Handbook of Philosophy of Mathematics and Logic, ed. Stewart Shapiro, New York, NY: Oxford University Press: 412–36.
Shapiro, Stewart 1991. Foundations Without Foundationalism: A Case for Second Order Logic, New York, NY: Oxford University Press.
Shapiro, Stewart 1993. Modality and ontology, Mind 102: 455–481.
Tennant, Neil 1987. Anti-Realism and Logic, New York, NY: Oxford University Press.
Tennant, Neil 1997. On the Necessary Existence of Numbers, Noûs 31: 307–36.
Wright, Crispin 1983. Frege’s Conception of Numbers as Objects, volume 2 of Scots Philosophical Monograph, Aberdeen, Scotland: Aberdeen University Press.

Author Information

Julian C. Cole
Email: colejc@buffalostate.edu
Buffalo State College
U. S. A.

quarta-feira, 5 de dezembro de 2018

PLATÃO (c. 427 - 347 a.C) - Parte II

Plato: Phaedo

Table of Contents

1. The Place of the Phaedo within Plato’s works

2. Drama and Doctrine

3. Outline of the Dialogue

a. The Philosopher and Death (59c-69e)

b. Three Arguments for the Soul’s Immortality (69e-84b)

i. The Cyclical Argument (70c-72e)

ii. The Argument from Recollection (72e-78b)

iii. The Affinity Argument (78b-84b)

c. Objections from Simmias and Cebes, and Socrates’ Response (84c-107b)

i. The Objections (85c-88c)

ii. Interlude on Misology (89b-91c)

iii. Response to Simmias (91e-95a)

iv. Response to Cebes (95a-107b)

1. Socrates’ Intellectual History (96a-102a)

2. The Final Argument (102b-107b)

d. The Myth about the Afterlife (107c-115a)

e. Socrates’ Death (115a-118a)

4. References and Further Reading

a. General Commentaries

b. The Philosopher and Death (59c-69e)

c. Three Arguments for the Soul’s Immortality (69e-84b)

d. Objections from Simmias and Cebes, and Socrates’ Response (84c-107b)

e. The Myth about the Afterlife (107c-115a)

f. Socrates’ Death (115a-118a)

Author Information

Plato: Political Philosophy

Table of Contents

1. Life - from Politics to Philosophy

2. The Threefold Task of Political Philosophy

3. The Quest for Justice in The Republic

4. The Best Political Order

5. The Government of Philosopher Rulers

6. Politics and the Soul

7. Plato’s Achievement

Author Information

Plato: The Republic

Table of Contents

1. Synopsis of the Republic

a. Book I

b. Book II

c. Book III

d. Book IV

e. Book V

f. Book VI

g. Book VII

h. Book VIII

i. Book IX

j. Book X

2. Ethics or Political Philosophy?

3. The Analogy of the City and the Soul

4. Plato’s Defense of Justice

5. References and Further Reading

a. Standard Greek Text

b. English Translations

c. General Discussions of the Republic

d. Discussions on Plato’s Ethics and Political Philosophy

e. Discussions on the City/Soul Analogy.

f. Discussions of Plato’s Defense of Justice in the Republic

g. Discussions of Political Measures Introduced in the Just City

i. Discussions of the Role of Women in the Just City

ii. Discussions of Poetry in the Just City

iii. Discussions on the Soul in the Republic

iv. Discussions on Plato’s Moral Psychology in the Republic

Author Information

Plato: Theaetetus

Table of Contents

1. The Characters of Plato’s Theaetetus

2. Date of Composition

3. Outline of the Dialogue

a. Knowledge as Arts and Sciences (146c – 151d)

b. Knowledge as Perception (151d – 186e)

c. Knowledge as True Judgment (187a – 201c)

d. Knowledge as True Judgment with Logos (201c – 210d)

4. References and Further Reading

a. General Commentaries

b. Knowledge as Arts and Sciences