The “self-predication assumption” in the title of this monograph refers to a term in contemporary scholarship used to indicate a supposed characteristic of Plato’s Forms, namely, that they possess as a property that which their names name. Thus, it might be maintained that the Form of Beauty is beautiful or the Form of Largeness is large or the Form of Identity is self-identical. The problem on which Apolloni focuses is that while some case of the putative self-predication are plausible, some are not. The relevance of the self-predication of any Forms is that in Plato’s dialogue Parmenides there is an argument, the so-called Third Man Argument (TMA), that purports to show that if Forms are self-predicative then, along with the reasonable assumption that a Form must be separate from the sensibles that participate in it, a vicious infinite regress can be generated. If, for example, many large things require a Form of Largeness “over and above” them, then a new “many” consisting of the original many plus the Form itself will require a new Form “over and above” them. This regress is supposed to be vicious because the Form, stipulated as being a “one” over a “many,” will no longer be one, but will be iterated indefinitely. The evidence from the Platonic corpus regarding the question of whether or not Plato accepted self-predication is somewhat ambiguous. But more important is the question whether or not Plato is forced to accept self-predication of Forms if Forms are to be separate and to account for the properties of things that participate in them. Thus, if things are large because of the Form of Largeness, mustn’t Largeness be in some sense large?
Apolloni’s dense and well-documented study of this question in the contemporary secondary literature aims to shows that Plato has a way to avoid embracing self-predication such that it does not threaten the coherence of a theory of separate Forms. Along the way, he offers extensive treatment of the contemporary literature regarding self- predication and related matters. A graduate student wishing for an efficient means of getting up to speed on the main lines of the more than half a century of interpretation generated by Gregory Vlastos’s famous 1954 article would be well served by this book.
Apolloni’s own interpretation, set out against various high-profile alternatives at every stage, is as follows. In the so- called Recollection Argument in Plato’s Phaedo, Plato is making the crucial distinction that renders self- predication harmless. This is the distinction between the Form of Equality and “the equals” (74c1), that is, the equal sticks and stones that participate in Equality. What Apolloni wants to show is that the equality of the former and the equality of the latter are not univocally predicable of the Form and the sticks and stones. The difference is that the Form is “just equality, and they are not” (15). To maintain that the Form Equality is equal at all is indeed to be committed to self-predication, but only in the anodyne sense that “equal” describes uniquely what the Form is, that is, it names it. Actually, Apolloni switches between “is equal” and “is Equality”, evidently treating these as equivalent. He defends the latter as a predicative statement, but it seems that he does this only to reject R.E. Allen’s solution, which is to treat “the Form is F” as an identity statement (20). That the “special predicate” “is equal” when applied to the Form comes very close to an identity statement is eventually admitted by Apolloni (228-9). In fact, they are taken to be logically equivalent.
For Apolloni, the major significance of this interpretation is that it can be applied to refute the TMA. If a Form of Largeness is large, but in a unique way, then the vicious regress argument does not even get started. So, Apolloni is committed to the view that in writing Parmenides, Plato already knew how to solve the self-predication “problem”. Consequently, we must not suppose that, as Vlastos put it, that dialogue is a record of Plato’s “honest perplexity”. But this leaves us with two major interpretative issues. First, what of the rest of Parmenides’ arguments against the theory of Forms? Second, since the notoriously difficult second part of the dialogue is explicitly announced as containing an exercise necessary to answer the arguments posed in the first part, one naturally wonders what its point is.
Apolloni’s response to the first issue is to claim that the first part of the dialogue is not intended to offer a serious challenge to the theory of Forms but rather to produce a “student exercise both for young Socrates and for us” (130; cf. 197). The claim that the intended audience is “us” is too vague to be very contentious; that the “young Socrates” is also a focus of the argument is, on the other hand, quite puzzling, especially if the young Socrates is Plato himself, unless of course we take this to mean that Plato is announcing how he once was himself troubled by self-predication, though he has long since resolved the issue. But then this leaves just “us” as the target. Fair enough. But then one would have thought that all that the student needed to do to solve the problems posed by the first part of Parmenides is read Phaedo in the way that Apolloni, claims—reasonably enough in my view—is most natural.
This approach does not seem to motivate sufficiently the second part of the dialogue. Indeed, Apolloni’s response to the second issue is to argue that the entire second part of the dialogue, the “exercise” conducted by Parmenides, is intended to be “a kind of philosophical purgation” of Eleatic or “mystical” monism (202). The purgation is achieved by discovering the fallacies in Parmenides’ eristic reasoning (205). The principal evidence for this is that, as is well known, the dialogue ends ostensibly in a mass of contradictions regarding the nature of the first principle of all, the One. It is crucial for Apolloni’s thesis that these be genuine contradictory statements regarding the One and the “Others”, that is, that the “One” and the “Others” are not used equivocally throughout the exercise. This claim is dubious for at least two reasons: first, the exercise is rife with arguments and distinctions taken up by Aristotle, especially in his Physics something that one would not expect if he believed that the dialogue was a tissue of fallacies and second, that there is manifestly equivocity in, for example, the initial and second hypotheses in how they interpret “the One is”. For the first hypothesis takes a One that in no way partakes of ousia because if it did, it would be complex, and the second takes a One that does partake in ousia and is, according, complex. Someone could argue, I suppose, that “has ousia ” and “does not have ousia are intended to be contradictory attributes of the One, that is, the identical subject, but apart from the obvious fact that one would be surprised to learn that Aristotle has gleaned insights which flow from a contradiction, Plato’s Republic offers a clear example of a “One” that is “beyond ousia, namely, the Idea of the Good, and a multitude of “Ones” that actually partake of ousia, namely, the Forms. If the exercise is a reductio of Eleatic monism, one wonders why Plato takes Parmenides to be enveloped in contradictions by maintaining something that Plato himself affirms.
I believe Apolloni is right to interpret the passage in Phaedo as not entailing “bad” self-predication, though I do not think his solution is all that different from Allen’s. But I do think he is seriously misled by this reading into misreading the first part of Parmenides as not intended by Plato to be focusing on a serious threat to Forms. For the TMA and the other arguments pose a grand dilemma: either the Forms are separate from the sensible world or they are not. If the former, then they become irrelevant to explaining the samenesses and differences that we think we encounter here below. If the latter, then the regress arguments are not so easily dismissed. For the point is not that since the Form is uniquely what its name names it cannot legitimately be included in a “many” requiring a Form over and above, but that if the Form is “in” us, the “largeness in us” and the “largeness” in the Form are evidently, though different, the same in some sense, a sameness which if it is not sufficient to require a Form over and above is deeply puzzling. It is indeed absurd to maintain that the Form of Largeness is large, but it is equally absurd to maintain that the largeness in large things is large, too. This is a serious matter, and viewed in this way, it should occasion no surprise that complexity in Forms—the complexity evinced by that which has what its name names—should be a prominent part of an exercise that is intended to explore how this complexity is to be understood in order to rescue Forms.
The utility of this book is not enhanced by the publisher’s lamentable practice of printing endnotes instead of footnotes, especially given the fact that Apolloni places most of his often very lengthy discussions of opposing views in these notes. Some of these useful summaries and criticisms could well have made their way into the main body of the book and none of them should have appeared other than as footnotes.