This fine book addresses the most controversial issue in Plato’s metaphysics: Are Plato’s Forms literally and universally self-predicable? The Form of Beauty is the clearest case of literal self-predication. When Plato asserts that it is beautiful (Symp.Phdo. 100c), most scholars are hard pressed to deny that he means that the Form itself is a beautiful thing. Other Forms are more problematic. Does Plato also think that the Form of triangularity has three sides, that the Form of largeness is a large object, that the Form of fire is hot, that the Form of animal is alive, that the Form of evil is evil, and so forth and so on? Malcolm defends the view that in the middle dialogues all Forms are literally self-predicable.
There are other types of self-predication besides literal self-predication. Malcolm calls any statement of the form ‘The F (itself) is F’ or ‘F-ness (itself) is F’ a self-predication (p. 1). There are various ways of interpreting such a statement depending upon whether its copula is taken to express identity or attribution and whether its subject is taken to refer to the property F-ness or to the instances of the property. Only those self-predications that ‘are understood to be asserting that the general property, F-ness, is itself an F thing’ are ‘literal’ self-predications, or what Malcolm calls ‘self-exemplifications’ (p. 1).
There are two distinctions central to Malcolm’s analysis, the first being that between a paradigm and a universal. Consider the use of a patch of color to define a particular color, say, ‘sepia’. When so used, the patch of color, the thing having the sepia color, is a paradigm instance of sepia whereas the color for which the thing serves as a paradigm case is a universal (pp. 70-72). Or consider a metal bar that is used as the standard yard. Malcolm wishes to distinguish its length, a universal, from the bar itself, a paradigm instance of the universal (pp. 159-63).
A second distinction of importance is that among three types of self-exemplification: per se, per accidens, and paradigmatic. (This last label is my own, not Malcolm’s.) The distinction between per se and paradigmatic self-exemplification corresponds to the distinction between a universal and a paradigm instance of a universal. Universals, as Malcolm understands them, do not usually exemplify themselves. Although a paradigm instance of redness is red, the color redness is not colored. In those rare cases where a universal does exemplify itself, the exemplification is per se if the universal exemplifies itself in virtue of its own nature rather than incidentally. Thus unity, considered solely as a universal, is one in its own nature, or per se (p. 22); the (Form of the) Different is different from the different (sense particulars) per accidens (since every Form is different from its sense particulars) (p. 15); and the standard yard (the bar, not the length) is a yard long paradigmatically (see pp. 70-72).
The most original part of Malcolm’s book is his account of self-predication in the earlier dialogues. Malcolm holds that the Forms of the earlier dialogues, in contrast to the transcendent paradigmatic Forms of the middle dialogues (p. 184), are ‘general (immanent) characteristics or universals’ (p. 36). Thus any interesting case of self-exemplification in the earlier dialogues will have to be per se rather than paradigmatic. And, indeed, Malcolm argues that the three explicit instances of self-predication in the earlier dialogues—’Beauty is beautiful’ (Hippias Major 292e), ‘Justice is just’, and ‘Holiness is holy’ (Protagoras 330c-e)—are all per se self-exemplifications. The Form of Beauty is the easiest case: ‘Just as unity is one per se, so Beauty may be conceived of as being in its own nature beautiful…’ (p. 22). By this account both Helen and her beauty are beautiful. Malcolm advances a short argument for Holiness being holy per se. ‘[W]hatever is beloved by (all) the gods (Euthyphro 7e) because of its very essence’ is holy; the gods love all of the cardinal virtues including Holiness; therefore, Holiness is holy per se (p. 37). As Malcolm confesses, the case for Justice being just per se is the most speculative of the three (p. 38). Malcolm begins with a characterization of justice: ‘It is just that things remain within their proper bound or limit and just things are things that do so’ (ibid.). In terms of the formula of the Republic (433a-434c; 441d-444a), it is just for things to attend to their own business. But, Malcolm continues, each general nature, or Form, is what it is, keeps to the limits of its own nature and function, and attends to its own business, its business being to determine its class of instances (ibid.). Justice is a general nature, or Form. Hence Justice (along with every other Form) is just per se. As Malcolm concedes, this conclusion is distressingly general since, according to it, such general natures as Injustice and Ugliness turn out to be just (p. 39). That the Form of Injustice is just may be paradoxical; but, as long as the Form is solely a universal and not also a paradigm instance of injustice, there seems to be no contradiction involved.
One advantage that Malcolm claims for his interpretation is that it accounts for Plato’s actual procedure in unifying the five cardinal virtues in the Protagoras. Malcolm’s interpretation, unlike its competitors, explains why Plato unifies Justice and Holiness, but not the other virtues, by means of self-predication and interpredicability. The reason is that none of the other virtues can be attributed to itself: Wisdom is not wise; Courage is not courageous; and Temperance is not temperate (pp. 40-43).
I have two reservations about Malcolm’s interpretation of the Protagoras. First of all, the arguments that Malcolm constructs to show that holiness is holy per se and justice is just per se are completely speculative. There is not a hint of either argument in the Protagoras. Not only must Malcolm stretch to find the major premiss of each argument in another dialogue, but he also has to stretch the Platonic account of justice to make it cover the realm of Forms as well as the sensible world. Secondly, the advantage of his interpretation is purchased at the price of attributing a questionable metaphysical principle to Plato. The arguments unifying holiness and justice, on Malcolm’s interpretation, rest on the following principle of unification: If two properties belong to themselves and to each other (if, as Malcolm puts it, ‘they are both subject to self-predication and they are mutually interpredicable’ [p. 40]), then they are the same or similar. But, as Malcolm himself admits (p. 43 and n. 43), this principle appears to be invalid. For the formal properties of Plato’s Forms belong to themselves and to each other. Intelligibility is both intelligible and eternal whereas Eternity is both eternal and intelligible. So by the principle of unification, every formal property of the Forms is the same as, or similar to, every other. Moreover, on Malcolm’s interpretation of Platonic justice, every formal property of the Forms is the same as, or similar to, Justice. Malcolm questions ‘the efficacy of such far-fetched Forms [as Intelligibility and Eternity] as a counter-instance within the framework of the Protagoras‘ (p. 188). But this is to ignore the fact that the principle of unification is Malcolm’s own invention. Why foist an invalid principle on Plato?
Malcolm, following Aristotle, contends that a middle-dialogue Form is a union (or intended union) of a universal and a paradigm instance. But he also holds that the Third Man Argument (TMA) of the Parmenides (132a-b) reveals this union to be illicit.
Malcolm takes the TMA to rest on a single principle buttressed by two ‘assumptions’ (where the distinction between a ‘principle’ and an ‘assumption’ seems to be the distinction between an ‘explicit’ and a ‘tacit’ premiss):
- The One-over-Many Principle: If many things are all F, there must be a single Form in virtue of which they are all F.
- ‘The Self-Exemplification Assumption (SEA): The Form, which is the general nature or universal, is also an instance of itself’ (p. 48).
- ‘The Non-Identity Assumption (NIA): The Form, as the general nature common to the members of a class, cannot be identical with any of these members’ (ibid.).
NIA expresses the fact that a Form is a universal; SEA, that it is a paradigm case (p. 3). But, as Malcolm points out, NIA and SEA are inconsistent; for by NIA a Form is not an instance of itself while by SEA it is (ibid.). Thus a Form cannot be both auniversal and a paradigm case (p. 190). I shall return to the TMA and its ramifications presently.
Malcolm considers three views concerning Forms as paradigm instances. The first, labeled ‘Thesis A’, attempts to disarm the TMA by denying that the Form of F-ness is itself an F thing. There are four versions of Thesis A. A(i), which is associated with Reginald Allen, claims that the copula in the self-predication ‘The F is F’ expresses identity and that the second ‘F’ functions as a proper name (‘F-ness’) (pp. 4, 65-69). A(ii), suggested by some (perhaps misunderstood) comments of Wittgenstein, holds that the Form of F-ness is the paradigm case of F but, as the basis of any description of an object as an F thing, cannot be itself described as an F thing (pp. 4, 69-73). A(iii), associated particularly with Alexander Nehemas, differs from A(i) in taking the second ‘F’ in ‘The F is F’ to function as a definite description (‘the essence of F’ or ‘what it is to be F’) rather than as a proper name (pp. 4, 73-88). A(iv), the view of Gregory Vlastos, claims that the copula expresses attribution but that the subject of the attribution is not the Form of F-ness but the things that participate in the Form (Pauline predication) (pp. 4, 88-90). Malcolm thinks that A(ii) rests on the false proposition that a paradigm instance of F-ness cannot be described as an F thing. His primary (though not his only) objection to the three other versions is that they cannot give an adequate account of Plato’s idea that a Form is a model of which sense particulars are copies (Model/Copy) (pp. 4-5).
Malcolm believes that two views, labeled ‘Thesis B’ and ‘Thesis C’, give a better account of Platonic doctrine than Thesis A, though under both Plato’s Forms fall prey to the TMA. According to Thesis B the Form of F-ness is an F thing, but it is an F thing in a different sense from the many empirical Fs that resemble it: the F-ness of the Form is non-univocal with that of its copies (pp. 5, 64, 92). According to thesis C, on the other hand, the Form of F-ness is an F thing univocally with the empirical Fs that participate in it (pp. 5, 64, 106).
To understand Thesis B it is necessary to understand Malcolm’s distinction between the non-univocal and the equivocal. Two items may be F non-univocally without being F equivocally. Thus the bark of a dog and the bark of a tree are bark equivocally whereas birch-bark and a photo of birch-bark are bark non-univocally but not equivocally (pp. 177, 200). Why Malcolm prefers the misleading word ‘non-univocally’ or the accurate but awkward phrase ‘non-univocally but not equivocally’ to the traditional term ‘analogously’ is unclear.
Thesis B focuses on Model/Copy, the idea that creates difficulty for Thesis A (p. 92), and takes literally the raft of examples in Plato that compare the relation of particular to Form to the relation of a picture, shadow, or reflection to its origina l (p. 5). Malcolm lists three difficulties with Thesis B. First, if the Form of F-ness and the many empirical Fs are non-univocally F, the characteristic that the many empirical Fs share among themselves—namely, that of being an image of F-ness—will be different from that directly exemplified by the Form of F-ness (pp. 101-102). Secondly, a picture or a mirror image and its original are often F univocally rather than non-univocally: the mirror image of a patch of red can be red in the same sense as the patch itself (p. 102). Thirdly and finally, there are passages in the middle dialogues, such as Symp. 211ab where the Form of Beauty is said to be more beautiful than a beautiful soul, that can be fitted to the doctrine of non-univocality only with great strain (pp. 102-103).
Thesis C, the doctrine of univocality, championed by the earlier Vlastos and G.E.L. Owen among others, maintains that the Form of F-ness is superlatively F whereas the sense particulars that participate in it are deficiently F (pp. 106-107). Thesis C, as Malcolm presents it, has two complementary aspects. Either (i) the Form of F-ness is perfectly F whereas the sense particulars that participate in it are only approximately F or (ii) the Form is absolutely F whereas its participants are only relatively F. Malcolm brings (ii) as well as (i) into the formulation of Thesis C in order to deal with the problem of enumeration where the approximation account breaks down (pp. 121-22). An empirical circle is only approximately circular; but my fingers are exactly, not approximately, ten in number. Malcolm handles such problem cases by switching from (i) to (ii). My fingers, though not approximately ten, are relatively ten since they can be viewed, not only as ten, but also as five pairs or as two matched sets or as one complete set.
Malcolm expresses a slight preference for Thesis C over Thesis B on the ground that Thesis C gives a better account of Plato’s doctrine of Degrees of Reality. His case for Thesis C relies upon a distinction between an authenticating use of ‘real’ where real things are contrasted with fakes or imitations and an evaluative use where a real F is contrasted with things that are not ‘always or unambiguously or to the fullest degree’ F (pp. 122-23). Thesis B uses ‘real’ to authenticate; Thesis C, to evaluate. By thesis B the sensible copies of the Form of F-ness are Fs only with the qualification ‘false’ or ‘imitation’. By Thesis C they are straightforwardly F, and it is the F-ness of the Form that is qualified (by ‘perfectly’ or ‘absolutely’). Malcolm points out that an examination of the text reveals that Plato’s language fits Thesis C (Rep. 477a). For Plato it is the copy of the Form of F-ness, not the Form itself, that is straightforwardly F. Plato does not maintain that my finger is a fake finger.
Though Malcolm downplays it, Thesis C, as a philosophical view, faces a problem that is the complement of one faced by Thesis B. One objection to Thesis B, it will be recalled, is that a picture or an image and its original sometimes share a property univocally. The complementary objection to Thesis C is that not every Form can share its paradigmatic features with its empirical participants univocally. Since Plato’s Forms are inanimate, the Form of Horse and Bucephalus cannot both be horses univocally. This difficulty arises whenever the formal attributes of a Form (eternity, intelligibility, unity, and so forth) conflict with the attributes that the Form is a paradigm instance of. Malcolm suggests that the Aristotelian distinction between the attributes that a Form possesses qua Form and those it possesses qua the particular Form it is (Top. 137b3-13) is sufficient in itself to allay this difficulty (p. 89). The suggestion seems to be that the alleged contradiction between the formal and paradigmatic attributes of the Form of Horse disappears because the Form is a horse qua paradigm instance of a horse though it is not a horse qua Form. But will this work? Imagine an earthly Platonism in which Forms are made of cast iron. In such a Platonism there will be a problem of creating Forms of liquidity, flesh, and bravery. Can this problem really be solved by distinguishing different aspects of a Form and noting that the Form of flesh, say, is cast iron qua Form but flesh qua paradigm instance of flesh? Furthermore, the distinction between the formal and paradigmatic attributes of a Form is an Aristotelian, not a Platonic, distinction. As I attempted to show long ago, there is evidence in both the Parmenides and the Timaeus that Plato does not draw such a distinction. So even if the distinction provided the basis for an adequate response to the philosophical difficulty facing Thesis C, it should not be exploited in the exegesis of Plato.
The basic problem with middle-dialogue Forms, in Malcolm’s view, is not an inconsistency among the attributes of certain of them but an inconsistency in the functions of all of them. Malcolm contends that a middle-dialogue Form functions both as a universal and as a paradigm case and that the TMA demonstrates the inconsistency of these two functions: ‘…it is evident that the TMA arises because the same entity is illegitimately taken to be both a universal and also its (paradigm) instance, as something in common to the particulars and as something in common with them’ (p. 52).
Malcolm has some odd things to say about the TMA. For example: ‘Although the two basic assumptions upon which the TMA rests are inconsistent, for by Non-Identity the Form is not an instance of itself and by Self-Exemplification it is, I maintain that the TMA need not be presented as an argument with inconsistent premisses, but may be seen as generating an unending regress through requiring, for each move, an additional move in order to avoid inconsistency’ (p. 3). This peculiar statement appears to confuse (or conflate) an argument and a derivation. One needs to be clear whether the TMA is an argument consisting solely of a set of premisses (both tacit and explicit) and a conclusion or whether it is a derivation of a conclusion from a set of premisses (its conclusion being that each Form is not one, but infinite, in number). Malcolm devotes most of his attention to the derivation. Thus he speaks of the ‘steps’ of the argument (pp. 48-49) and says: ‘I share with Vlastos the view that Socrates’ quandary is produced by a contradiction between the NIA and the SEA. The question at issue pertains to the manner in which this inconsistency is to be made manifest’ (p. 51). By concentrating on the derivation rather than the argument, Malcolm wanders off in the wrong direction and fails to address the main issue—whether there is any inconsistency to be made manifest.
Although Malcolm is aware of the discovery that the conclusion of the TMA can be derived from the One-Over-Many principle supplemented by a consistent set of tacit assumptions (p. 190), he does not appreciate its signific ance. Only an inconsistency entails an inconsistency. Hence, if the premisses of the TMA are consistent, they cannot demonstrate an inconsistency and a fortiori cannot demonstrate an inconsistency between the two functions of a Form. Nor can they, contrary to Malcolm (p. 49), generate a vicious rather than a vacuous regress.
One can go a step further. The main reason the TMA does not demonstrate an inconsistency between the two functions of a Form is that there is no inconsistency to be demonstrated. It is easy to show that an entity like a Form can perform the functions both of a universal and of a paradigm instance. In set theory the number five is a paradigm instance of fiveness: it is a set of five objects. (In some versions of set theory it is the set whose elements are zero, one, two, three, and four.) But the number five also functions as a universal when numbers are assigned to things, for example, when the number five is assigned to the letters in the word ‘Plato’. In the language of set theory to say that the word ‘Plato’ has five letters is to say that the set of letters composing the word is equipollent to the number five. Thus the number five, conceived as a particular set of objects, together with the notion of equipollence, performs the functions both of a paradigm instance and of a universal and, on the assumption that set theory is consistent, performs both functions consistently. Since the number five, so conceived, may well be a Platonic Form, there seems to be no inconsistency in the performance of both functions by a Platonic Form. What corresponds in the theory of Forms to equipollence in this example from set theory is of course the relation of participation. The reason there is no inconsistency in a Form’s functioning both as a paradigm case and as a universal, it can now be seen, is that, strictly speaking, the two functions are divided between the Form itself and the relation of participation. On a Platonic analysis to say that Bucephalus is a horse is to say that Bucephalus participates in the Form of Horse. In the analysans the paradigm case is referred to by the expression ‘the Form of Horse’ whereas the universal is signified by the entire predicate ‘participates in the Form of Horse’.
Although I cannot accept his claim that Plato’s ‘most critical mistake’ is the conflation of universal and paradigm object (p. 9), Malcolm has, to my mind, achieved his main goal of effectively burying Thesis A, the doctrine that the Form of F-ness is not an F thing. His critical analysis of the recent literature on self-predication and his skillful classification of the various interpretative possibilities, which provide the pathway to this goal, constitute a paradigm of Platonic scholarship.
 It is perhaps worth observing that, by Malcolm’s account of per se self-exemplification, the nature in virtue of which a given universal exemplifies itself may be either its specific or generic nature or its nature simply as a universal. Thus on Malcolm’s analysis Beauty is beautiful in virtue of its specific nature; Holiness is holy in virtue of its generic nature; and Justice is just simply in virtue of being a universal.
 ‘The Mad Craftsman of the Timaeus‘, Philosophical Review, 80 (1971), 230-35.
 For a brief history of the interpretation of the TMA from Vlastos’s seminal article to the present see S. Marc Cohen and David Keyt, ‘Analysing Plato’s Arguments: Plato and Platonism’ in Methods of Interpreting Plato and His Dialogues, edited by James C. Klagge and Nicholas D. Smith (Oxford, 1992), pp. 173-200 at 178-187.
 I am grateful to S. Marc Cohen and Cass Weller for some helpful suggestions on the penultimate version of this review.