There are lots of divisions among Plato scholars, but two of the biggest are these.

Some think that Plato's dialogues proceed from a single view throughout: that there is no question of a development in Plato's thought. Their opposite numbers think that there is development to be seen in the dialogues. The first view is sometimes referred to as “unitarian,” and the second could be labeled “developmental.”

Then again, some scholars see in the dialogues dramatic creations, and so the technique they favor in understanding them is literary analysis. Their opposite numbers see in the dialogues a lot of abstract argumentation, and so their favored technique is that of logical analysis. The first of these two approaches we may call “literary,” and the second “analytic.”

This latter opposition would be unreal if either position were understood as exclusive of the other: obviously the dialogues contain both drama and argument. The question of which approach to take is, then, one of emphasis. But there are extremes, and the extremes are in opposition.

This book is a defense of a developmental view with an analytic emphasis.

It is confined to the dialogues commonly regarded as early plus the Phaedo and Symposium, and to what in those latter dialogues pertains to a certain metaphysical theory, commonly referred to as the “Theory of Forms.”

Socrates, Aristotle says, was the first to fix attention on definitions, and the Socrates of the Socratic dialogues does that. But he does not simply say: let's define (say) piety. He doesn't have the word “define”: this is discussed in § 2.1.

Nor does he simply look for definitions as an abstract intellectual enterprise. He expects definitions to solve certain problems. So we must look at the problems (§ 2.2), and at the reason Socrates thinks definitions are required for solving them (§ 2.3).

PRELIMINARY: ON THE VOCABULARY FOR “DEFINING”

The Socratic dialogues do not consistently employ terms for “define” or “definition.” Aristotle has a technical terminology here, but this is after the arteries have hardened considerably. Some of his words appear in the Socratic dialogues. His favored noun, ʿορισμός, does not appear anywhere in Plato, but an alternative, ὅρος, does, as does the associated verb ʿορίζειν. All these words have to do originally with (spatial) boundaries, and the transition to technical philosophical terminology is only just under way in the Socratic dialogues. Of the six occurrences of ὅρος in these dialogues, that in the first book of the Republic is the one for which the translation “definition” is the most comfortable. There Socrates, having raised the question (331c1–3) “whether we are to say that this itself, justice, is, without qualification, truthfulness and giving back what one has taken from someone,” gives a counterexample, and says (331d2–3): “So this is not {a} definition of justice, saying the truth and giving back what one has taken.

The Socrates of Plato's Socratic dialogues was in quest of definitions because he thought they were required for living right: he supposed that in order to know whether certain actions were courageous, or pious, or admirable, one must know what the courageous, the pious, and the admirable are.

We laid out a theory of definition for Socrates: not necessarily his or Plato's own theory, but one based on the refutations of definitions in Plato's Socratic dialogues. The theory had three main components: the Substitutivity Requirement, the Paradigm Requirement, and the Explanatory Requirement.

The Explanatory Requirement, at first blush, simply demanded that one be able to use the definition for the pious in explaining why one called a given action (or person) “pious”: it was a matter of explaining content. But there turned out to be more to it than that: it was required that what one introduces and defines as the pious be itself indelibly pious. That connected the Explanatory Requirement with the Paradigm Requirement. And both were connected with the Substitutivity Requirement, construed as the demand that what is defined as the pious give necessary and sufficient conditions for something's being pious.

That theory has now turned into the Theory of Forms. Substitutivity is obvious enough: the things that partake of the Form, The Pious, have to be all and only the actions and people that are pious. The Paradigm Requirement is now the claim that the separate Form, The Pious, is through and through pious.

Socrates expects satisfactory definitions to do some sort of explanatory job. At the most elementary level, this job is that of what I shall call “explaining content.” I'll start by explaining the content of that phrase, and then, after yet another look at Euthyphro 6de, turn to one passage in which a definition is failed because it does not explain content: Euthyphro 9d–11b.

EXPLAINING CONTENT

Consider the following dialogue schema:

1. Q1: What's that?

2. A1: It's an F.

3. Q2: Why is it an F?

4. A2: Because it is H, and F=df the H.

At a minimum, Socrates expects someone with a proper definition for courage, piety, or whatever, to be able to use it in the way A does here.

Consider Q2. It is vague: it may have different forces in different contexts.

It might be that Q is not a native speaker of English, A knows this, and uses “G” to define “F” on this occasion because he knows that the words that compose “G” are English words known to Q. He might define “F” quite differently for another speaker. If Socrates were only requiring this much of definitions, it would just be a question of explaining the content of a term in a way that would make the use of the term comprehensible to a given audience.

Plainly Socrates wants more: he expects the correct definition to explain the content of the term on every occasion in which explanation is demanded.

To say that x is F because of the F or Fness is elliptical or incomplete: the relationship between x and the F by virtue of which x is F remains unspecified. The Socratic dialogues we are examining are quite unselfconscious about that relationship, by contrast with Phaedo 100cd, where we shall find Socrates using a variety of terms for the relationship between a Form and the things here below that partake of it and expressing a studious indifference about which is the right one. Back where we are, he also uses a variety of terms for the relationship between the F and the things that are F. He does not say much about this variety of terms (but see §§ 8.2.3 and 8.2.4.1). He frequently speaks of the relationship as one of presence: temperance is-present-to someone or something (παρει̃ναί τινι); common variants have the virtue or character being-added-to (προσγίγνεσθαι) or being in (εἶναι ʾεν or ʾενεῖναι) that which has it, or of someone or something as partaking of or getting a share of (μετέχειν) that virtue or character.

Does this mean that Socrates has in these dialogues a theory of forms according to which they are immanent in things? Well, he talks of forms, and he talks as if they were present in things. But does he have a theory, or is he just talking that way?

In every dialogue apart from the Parmenides in which the Theory of Forms puts in an appearance, the main topic is something else. In the Phaedo it is immortality: the Forms are used in three arguments for the immortality of the soul. But they make a separate entrance before that.

64C: AN EXISTENTIAL ADMISSION

Socrates defends his readiness to die beginning with the question (64c2) “do we think there is such a thing as death?” (ἡγούμεθά τι τὸν θάνατον εἰ̃ναι;). He immediately says what death is (c4–5): “the release of the soul from the body” or the “coming-to-be in separation” of soul and body (c5–8). He now argues that the philosopher, whom he portrays as ascetic, is engaging in separating his soul from his body (64c–69e).

Socrates' question at 64c2 concerns an existential claim to which Simmias' assent commits him. It is, once again, a topic-fixer: Simmias is only conceding that people sometimes die; he is not committed by his concession to the Theory of Forms. It is a clear implication of 105d9, d13–14, etc., that there is a Form for death. But it is only in retrospect that we can say: in 64c, Simmias had already acknowledged the existence of the Form, Death; that is like saying that someone who has acknowledged the existence of the number 13 has committed himself to the existence of a prime number, or to the existence of a positive root of the equation “845 + 1183x ⊟ 96x2 = 0.”

The Paradigm Requirement and the Explanatory Requirement are ultimately fused, and that fusion brings in some extra baggage. The anemic interpretation of the Explanatory Requirement may be all that is needed for the use to which it is put in the Euthyphro, but that is not true of all the passages in which we encounter it.

In the early dialogues, Socrates occasionally imports a presupposition about what can explain something's being F to the effect that what makes things F must itself be F; it makes things F by transmitting its Fness to them. This is the beginning of a theory of causality. Let us call any theory that employs this presupposition a “Transmission Theory” of Causality. The cause, whatever it is, is a “transmitting cause” of other things' being F.

The Theory of Forms is going to incorporate a Transmission Theory of Causality: the Form, the F, will make things F by transmitting its own being F to those things. The Theory of Forms is not unique in this: Aristotle will also advocate a Transmission Theory of Causality, especially in the domain of biology (ἄνθρωπος ἄνθρωπον γεννᾷ: it takes a human being to generate a human being), without Plato's Theory of Forms (Aristotle does, of course, have a theory of forms). So accepting a Transmission Theory does not commit one to Plato's Theory of Forms.

In Aristotle, we may distinguish between two grades of Transmission Theory: a Strong one and a Weak one.

Sometimes Socrates introduces a topic for discussion or definition by asking whether his interlocutor agrees that there is a topic there to discuss: e.g., “is there such a thing as justice?” (Protagoras 330c1–2, Hippias Major 287c4–5). Later, these existential admissions will be seen as admissions of the existence of forms.

Precisely because they carry that weight in the doctrinal dialogues, unitarians have seen them as importing that theory into the Socratic dialogues, whereas I see them as merely ways of isolating the subject to be discussed.

EXISTENCE, UNITY, CAUSALITY, AND PLATONISM

Suppose you and I are standing beside the pool watching the swimmers and discussing swimming strokes. Suppose the following dialogue takes place:

Suppose we are overheard by two more people, who whisper to each other as follows:

These two people strike me as mad. No less mad are the other two people who overhear us from the other side, and say:

Socrates' requests for definitions get no answers that pass his tests, and there are a lot of attempts. The Theory of Forms comes of investing the existence assumptions just considered with metaphysical significance, using a generalization of a pattern of argument that originates as an argument against definitions Socrates rejects. The generalized pattern is the Argument from Relativity (§ 1.2).

We are going to get at this by constructing a theory of definition for Socrates.

A SOCRATIC THEORY OF DEFINITION: PRELIMINARY

The theory is not supposed to be Socrates' (or Plato's) own. Rather, it is derived in the following way. When Socrates rejects definitions he uses certain arguments against them. We ask: what would an answer have to be like in order not to fall to that argument? We identify the assumption, and ask what general claim it might most naturally be taken to instantiate. The assumptions in question are not ones that require reference to any special entities that figure as the objects of these definitions.

This procedure will result in three main conditions of adequacy for a definition:

1. the Substitutivity Requirement: its definiens must be substitutable salva veritate for its definiendum;

2. the Paradigm Requirement: its definiens must give a paradigm or standard by comparison with which cases of its definiendum may be determined;

and

1. the Explanatory Requirement: its definiens must explain the application of its definiendum.

This and the next few chapters lay out these requirements and tie them to Socrates.

In the spring of 1966, Gregory Vlastos invited me (among others) to submit a paper for consideration for an issue of the Monist he was editing. I did. Gregory did not accept the paper, but generously (as was his way always) provided me with detailed comments. One of those comments was: “To do this, you'd have to write a book.” Here it is.

Along the way I have incurred an enormous number of intellectual debts. There is no possibility of my thanking all of those who have helped; for one thing, I would have to include all the students in seminars who have asked penetrating questions and made perceptive comments. So I'll confine myself to the oldest debt, that owed to Gregory Vlastos, and the most recent ones.

Michael Ruse sat through the better part of a seminar I gave on the book in 2002–2003, was obstreperous (often helpfully), and got me to submit the manuscript to Cambridge University Press. I won't say that without his prodding the book would never have got out, but I won't deny it either.

Hilary Gaskin, of Cambridge University Press, also pushed me to submit it. She has been unfailingly encouraging throughout the entire process.

She had it sent on to two referees, who gave me further reason to push on. One of them, Eric Brown, gave me very extensive comments indeed.

The Argument from Relativity, AR, is not applied to the beautiful in the Phaedo. It stands behind the argument of 74a–c, since Socrates thinks AR can be applied to any of a range of terms including the beautiful (76d8, 78d3). The Argument from Relativity does not appear in the Symposium, but plainly stands behind Diotima's description of the beautiful in 210e–211a.

DIOTIMA'S IMMORTALITY

According to Diotima, a human being can only find immortality by leaving behind “another new one such as it itself was” (208a7–b4). Some, according to her, do this bodily, by begetting human offspring (208e); others do it in soul (208e–209a): they are pregnant with “wisdom {φρόνησις} and excellence in general” (209a3–4), and when they come of age, they desire to beget these things (209ab). They seek out beautiful bodies, but prefer the combination of these with beautiful souls as well (209b); with such people they beget poems, as did Homer and Hesiod (209d1–3), and laws, as did Lycurgus and Solon (d4–e2): these win fame for “begetting every sort of excellence” (γεννήσαντες παντοίαν ʾɑρετήν, e2–3).

This much, she says, even Socrates might be able to grasp (209e5–210a1); she doubts whether he is up to the “final and highest mysteries for the sake of which these exist in the first place,” but she is prepared to have a shot at getting them across (210a1–4).

In Phaedo 86e–88b, Cebes objects that none of the previous arguments for immortality has ruled out the possibility of the soul's wearing out: it might exist before we come-to-be, outlast a number of incarnations, and yet perish in the end. What needs to be shown is “that {the} soul is altogether deathless and imperishable” (88b5–6).

Socrates gets around to this objection in 95a–d, and coming-to-be, perishing, and their causes become the center of his attention. He introduces a theory about these matters, which turns out to be the Theory of Forms again. We are not here primarily concerned with the immortality of the soul. But, just as Socrates and Simmias earlier (76d7–77a5) agreed that the existence of the Forms and the preexistence of the soul somehow went together, so here Socrates is going to be telling us (100b7–9) that the existence of the Forms carries immortality with it. This claim, like the earlier one, can only be understood as highly elliptical.

Socrates does not propound his theory straight off. He first discusses some “mechanistic” (as I'll call them) theories he once held (95e–97b). He rejects all of them, and then (97b–99d) introduces a different sort of theory that we may call “teleological”; this, he seems to say, is the only sort of theory that could ever be really adequate, but he has so far been unable to formulate a satisfactory one. I discuss teleological theories in § 13.1.