The Ascent from Nominalism : Some Existence Arguments in Plato's Middle Dialogues

divisibility in Physics VI. I had been assuming at that time that Aristotle's elimination of reference to the infinitely large in his account of the potential inf inite--like the elimination of the infinitely small from nineteenth century accounts of limits and continuity--gave us everything that was important in a theory of the infinite. Hilbert's paper showed me that this was not obviously so. Suddenly other certainties about Aristotle's (apparently) judicious toning down of (supposed) Platonic extremisms began to crumble. The upshot of work I had been doing earlier on Plato's 'Third Man Argument' began to look different from the way it had before. I was confronted with a possibility I had not till then so much as entertained. What if the more extreme posi­ tions of Plato on these issues were the more likely to be correct? The present work is the first instalment of the result­ ing reassessment of Plato's metaphysics, and especially of his theory of Forms. It has occupied much of my teaching and scholarly time over the past fifteen years and more. The central question wi th which I concern myself is, "How does Plato argue for the existence of his Forms (if he does )7" The idea of making this the central question is that if we know how he argues for the existence of Forms, we may get a better sense of what they are.

Analytical Table of Contents.- 1. Some Views of the Forms; a Prolegomenon for Analytical Philosophers.- Aristotle’s treatment of Plato’s Theory of Forms as a bit of metaphysical extremism, and some similar modern criticisms: Logical Form and Diagnosis.- The Platonist Request for Clarification of these Criticisms, and modern Responses appealing to theories of Logical Types and theories of the Logical Form of the Proposition.- A further, apparently unanswerable, modern riposte: Plato is committed to Universal Literal Self-Predication.- An earlier view of Plato: the Forms and Laws of Nature.- 2. A General Strategy for the Present Volume.- The two main sorts of existence arguments in the middle dialogues.- Remarks on the structure of the rest of this volume.- 3. Nominalism What.- A strategy for defeating Nominalism: anti-deflationary arguments and ontological commitment.- Anachronistic character of interpretations that have Plato believing both in Immanent Characters and in Transcendent Forms.- 4. Incorrigible Conceptual States What.- Anachronistic character of the possible charge that Plato’s anti-nominalist argument for the Forms begs the question against conceptualism p.- Incorrigible conceptual states and a priori truths.- Plato’s middle period Forms as meanings or meaning-like entities.- 5. The Frege-Quine Objections.- Psychological contexts and inferences involving existence and identity.- Moore’s argument against the ‘Naturalistic Fallacy’ not on the whole objected to as involving psychological contexts.- 6. Plato’s other main Middle Period Argument for the Existence of Forms—the Argument from the Sciences.- 7. On giving Plato a Position he ‘could have had in mind’.- Contrast of the present interpretation of passages like Phaedo 74 with Vlastos’s claim that Plato thought that Largeness was literally a large object.- Owen’s claim that Plato thought that Equality Itself was perfectly equal.- A further difficulty in attributing to Plato a position he ‘could have had in mind’: how can the Forms be ‘Paradigms’ if they are not Literally Self-Predicational?.- The Nominalist.- 1. The Recollection argument of the Phaeao, commonly thought to presuppose the existence of the Forms, actually provides an argument (against nominalist opponents) for their existence.- 2. The opponents in the Republic (the ‘lovers of sights and sounds’) and in the Parmenides (Zeno, at least if his arguments against plurality are to be conclusive) also represented as nominalists.- 3. Various difficulties for the existence argument of the Phaedo.- 4. The basic idea of the argument: that the equal we perceive we can confuse with the unequal we perceive; but the equal we conceive is, in clear cases, unconfusable with the unequal we conceive.- 5. Incorrigible conceptual states and Moore’s argument against the ‘Naturalistic Fallacy’.- 6. Forms of opposites as the opposites (themselves). How to understand the locution ‘the F-itself’.- 7. The quasi-theological predicates of the Forms. The Forms and Universal Literal Self-Predication.- 8. Peculiarities of the contrast in Republic V between Knowledge and Opinion. The notion that the objects of opinion “lie between being and not-being”.- 9. Confusing the questions ‘What is F-ness?’ and ‘What things are F?’ Deficiencies of sensible F’s as (nominalist) answers to the question ‘What is F-ness?’ The notion that Forms are “separate”.- 10. Doesn’t the description of the Form of the Beautiful in the Upward Path in Symposium 210–212 compel the self-predicative notion that sensible particular F things are always less F than the F-itself?.- 11. Examination of Symposium 210–212 shows the latter suggestion to be a consequence of confusing the questions ‘What is beauty?’ and ‘What things are beautiful?’.- 12. Plato’s argument being an anti-nominalist argument from certain sorts of psychological states to objects of those states, we must turn to look at the (from a Fregean point of view) suspicious notion of objects of thought.- Aristotle’s Dilemma.- 1. The Platonic ‘something or nothing?’ question, objects of thought, and ‘existential generalization from within psychological contexts’.- 2. ‘Intensional’ objects, ‘extensional’ objects and the inference from the existence of thoughts of Santa Claus to the existence of Santa Claus himself. Difference between a thought being directed and there being something the thought is directed towards.- 3. Intensional/extensional and the taking of equal sticks to be unequal sticks or of the Morning Star to be other than the Evening Star. ‘Substituting for identicals within psychological states’.- 4. Platonic worries about ‘logically parallel’ arguments. The suggestion in Aristotle’s discussion of the ‘Argument from Thinking’ that he is aware of the dangers of inferences in psychological contexts involving existence and identity; and a difficulty for this view—Aristotle’s endorsing of the Argument from the Sciences. (Aristotle’s Dilemma).- 5. The plausible (though in fact incorrect) suggestion that we are unable, in clear cases, to confuse equality with inequality compared with the suggestion that there are such things as intuitions of contradictoriness.- 6. The idea of a science of logic that is neutral on matters of fact and real existence. Logical Form and the Platonic Forms.- 7. How Frege violates his own inferential restrictions—in Arguments from the Sciences—and even in his own theory of psychological contexts.- Clarifications.- I. The Recollection Argument at Phaedo 72A–77A.- The way in which sensible particulars ‘fall short’ of the Forms: contrast with traditional and diagnostic interpretations.- How the recollection argument depends upon the existence of the Forms.- The possibility that Moore’s concern with conceptual incorrigibility derives from Archer-Hind and Jackson on Phaedo 74B6-C5.- Is the intrinsic implausibility of the theory of recollection from a previous life a serious defect in the Platonic theory of the soul and of its knowledge.- II. Are Forms of Opposites just Opposites? Plato’s Final Argument for the Immortality of the Soul at Phaedo 102A–107A.- III. Between Being and Non-being: Why is the Object of Knowledge Being while the Object of Opinion is “What lies between Being and Not-being”?.- A. The problem of Identity through Change.- B. Heraclitus’ problem and some doubts about the Aristotelian solution.- C. A first approximation to Plato’s view of identity through change.- D. Aristotle’s view contrasted with the views of Geach and Quine.- E. Plato’s considered view.- F. How for Plato Heracleitean flux would, but for the Forms, destroy all trans-temporal identity.- G. This-es and such-es: transtemporal identity in the Timaeus.- H. Some interim conclusions.- J. A difficulty: how can there be anything which ‘becomes’ but ‘is not’?.- K. Why does Plato restrict his ‘What is X?’ questions to Forms? How come he doesn’t ask ‘What are these sensible F particulars?’.- IV. Other Middle Period Passages with the Formula ‘The F Itself which are to be read with Caution.- A. Republic 505A2. The many surely do not think that the well-known Platonic Form of the Good is identical with pleasure: they too must be doing an ontological reduction.- How it is that Plato can deny that the good is identical with the knowledge Socrates supposes virtue to be: the good is what that knowledge is knowledge of.- B. Republic 479D3-E5. The many conventions (nomima)) that the lovers of sights and sounds identify beauty with are not universals but just the many sights and sounds-as they would have to be if the lovers of sights and sounds were nominalists.- C. Republic 515B4–517E3. The real question allegorized in the Cave passage is ‘What is justice?’, and the pervasive shadow metaphors allegorize the nominalist answer to that question. The objects of knowledge and opinion [of what justice is] are not propositions but objects like the Form of justice and (for nominalists) particular perceptible just people and events-objects from the worlds of being or becoming.- D. Cratylus 439C8-E6. The Forms, self-predication and changelessness.- E. The alleged near absence of Forms in the Theaetetus. Absence of the formula ‘The F-Itself’ not necessarily a sign that the Forms are absent.- V. Aristotle’s Lost Work On the Ideas.- The Argument from the Sciences.- The One over Many Argument.- The Argument from Thinkingp.- The Third Man Argument.- VI. Formulating the Third Man Argument.- A. Vlastos’s 1954 analysis and the later introduction of sets into more properly generalized versions of the argument.- B-E. Three principal defects in this analysis: the relation of Non-identity and Self-Predication to One over Many.- The use of sets in formulating the argument.- The failure to see that the regress is an explanatory regress.- The contradiction Vlastos finds in the premisses of the Argument.- F. Digression: how come the contradiction in the premisses of the argument did not surface till 30 years ago?.- G. Textual considerations in favor of the epistemological version of my (1967).- H. Further reflections on how Vlastos got a contradiction in the premisses of the theory of Forms: the paradoxes of logic, semantics and set theory.- J. A moral drawn from our comparison of Vlastos’s version of the Third Man with the Paradoxes.- K. Why should a self-predication assumption be involved in the consistent explanatory (and epistemological) regress we have been examining? Meaning-like entities and reflexivity without self-predication.- L. Conclusion.- VII. Aristotle on whether ‘The Universal man is [a] man’ is true in the same sense as ‘Socrates is [a] man’ is true.p.- Synonymous and paronymous predication in Aristotle’s logical works.- Categorial division trees.- Synonymous predication and being predicated in the same sense.- VIII. Plato and the Philosophers of Language.- A preview of problems to be discussed in the second instalment of the present study. Fregean theories of psychological contexts and logical form.- Conceptual incorrigibility in the Theaetetus.- Protagorean relativism and perceptual incorrigibility in the Theaetetus.- Notes.- to Introduction.- to ‘The Nominalist’.- to ‘Aristotle’s Dilemma’.- to Clarification Two.- to Clarification Three.- to Clarification Four.- to Clarification Five.- to Clarification Six.- to Clarification Seven.- to Clarification Eight.- Index of Passages Cited.- Index of Persons and Subjects.