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.

In the Phaedo even more than in the Meno, it is important to bear in mind that what we are calling “recollection” is actually a three-termed affair: it is a matter of x's being reminded by y of z; the term occupying the “y” position acquires importance in the Phaedo.

72–73: RECOLLECTION AGAIN

Socrates concludes the Cyclical Argument by saying that there really is such a thing as coming-to-life-again (ʾɑναβιώσκεσθαι): the living come-to-be from the dead and the souls of the dead continue to exist (72d8–10). The next argument is to have the same conclusion.

It is Cebes who sets it going by adverting to the Doctrine of Recollection, which, he says (72e2–3), Socrates has often propounded. The Theory of Forms is also presented as something often propounded by Socrates. But in the case of the Forms, we can see how the Theory is a natural extension of what Socrates had been saying in the Socratic dialogues, whereas Recollection is a drastic innovation.

As Cebes states it, it is that “learning for us is nothing but being-reminded {ʾανάμνησις}” (72e3–4). So learning isn't that for others. In the next clause (e4–5), he says that what we now recollect we must have learned at some prior time, and he adds (73a1–2) that this must have been before the soul was “in human form” (τᾷ ʾανθρωπίνῳ εἴδει).

The Meno begins as a Socratic definition dialogue whose topic is “excellence” (ʾɑρετή). At 80d, Meno causes the dialogue to abort by asking Socrates how he can expect to find out what excellence is when he doesn't have even a clue to start with. Socrates' response and the rest of the dialogue bring in several new things.

First, Socrates propounds the Doctrine of Recollection:

1. (DR) What we call learning is not really that, but recollecting something we knew beforehand.

Next, Socrates is prepared to discuss, using a certain method, whether excellence is teachable even in the absence of a definition. This requires renunciation of the Intellectualist Assumption, although the dialogue opens with a firm restatement of that assumption.

The method Socrates goes on to describe is often referred to as the “Method of Hypothesis.” It bears some resemblance to the method of Geometrical Analysis, on which it is based.

Finally, Socrates retreats from the claim that knowledge is a prerequisite for excellence: he suggests that true belief might be enough. This change from the stance of the Socratic dialogues is not of central concern in this book, and I shall have only a little to say about it.

Section 9.1 below discusses a background problem for the Intellectualist Assumption. Section 9.2 briefly discusses definition in the mini-Socratic dialogue. Section 9.3 deals with Meno's question at 80d, and § 9.4 with Socrates' response, the Doctrine of Recollection. Section 9.5 takes up the Method of Hypothesis.

Greek and Roman dialectic and rhetoric taught that the art of being reasonable and persuading people toward reasonable conclusions required an understanding of the relationship between what we know from within ourselves and what we learn from others. The former was our strongest knowledge—a boy mathematician could wield such knowledge with great force. The latter was weaker—wisdom and the experiences of long life were required for its best use. The former was individual, the latter was corporate. The former was solipsistic, the latter, forensic. For Aristotle and the classical liberal arts tradition that later developed, the disciplines of dialectic and rhetoric were responsible for teaching this relationship. Aristotle ingeniously created an intellectual device that served this and other purposes. He called it topics.

Topics was a schematic structure to be used mentally for analyzing, storing, and retrieving information. Organized in a triangular structure, the student entered it at the narrow top and descended through the structure adding to the breadth and depth base of the triangle as needed. Aristotelians for two thousand years explored this malleable structure, and at times let it dominate all of logic and epistemology, but more often hedged it in beside other Aristotelian categorization strategies. Sometimes it was described as a storehouse of all knowledge in which a student could be surrounded library-like with every bit of information in spacial relation to its related bits. Topics could help a person analyze and categorize knowledge. It could also help an orator preparing a persuasive argument gather diverse bits of evidence to support a larger point. At minimum it was supposed to help a person’s memory. The fundamental organizing principle of topics was epistemological, with the kinds of knowledge separated first according to their sources. At the entrance to the storehouse, the first division of everything to the left or to the right was a distinction between technical and nontechnical sources of knowledge. To the left was all the knowledge that was worked up personally within oneself. To the right was all the knowledge gained from outside sources, from authorities. The whole system of topics was driven by distinguishing information gained from within oneself and from various testifiers and authorities.

ARISTOTLE AND THE CREATION OF TOPICS

Diogenes Laertius wrote that Aristotle said that Zeno of Elea was the inventor of dialectic.

Renaissance teachers of logic loved Cicero and Augustine more than Abelard and Peter of Spain. They preferred the eclectic and practical values of the Romans over the medieval tendency to high formalism. The humanists of Renaissance Europe appreciated the earthy optimism evident in the following from Cicero:

Committed to teaching the practical wisdom of evaluating all kinds of arguments, Renaissance textbooks revived discussion of testimony and authority in two ways. The first was classical with an emphasis on the Ciceronian. Rudolphus Agricola and Petrus Ramus were the two most influential figures in this tradition. The second was classical but also eclectically Augustinian. The latter followed the way Augustine drew epistemology, psychology, and theology into a dialectic that served Christianity. Philipp Melanchthon was the most influential figure in this tradition. The art of handling testimony and authority was promoted in both traditions.

AGRICOLA AND RAMUS REVIVE CLASSICAL TOPICS

Rudolphus Agricola Phrisius (1444–1485) wrote the first major Renaissance logic textbook: De Inventione Dialectica. Circulating in manuscript after the 1470s and first published in Louvain in 1515, it gained enormous influence in the 1520s and ’30s. By 1569, Petrus Ramus wrote that “thanks to Agricola the true study of genuine logic had first been established in Germany and thence, by way of its disciples and emulators, had spread through the whole world.” Lisa Jardine, even though noting that the published version of the book was probably a result of “collaborative editing” and its fame an aspect of a pedagogic myth created by Erasmus, describes De Inventione Dialectica as the logic textbook “most widely specified, bought, and used in schools and universities throughout Protestant Europe, between the early decades of the sixteenth century and the mid seventeenth century.” Jardine warns against placing too much weight on De Inventione Dialectica as the source of the new Renaissance emphasis on classical dialectic; but we are not too concerned here with the sources of ideas. Textbooks are rarely such sources.