I discuss Aristotle’s opening argument against Platonic Forms in _Metaphysics_ A.9, ‘the Razor’, which criticizes the introduction of Forms on the basis of an analogy with a hypothetical case of counting things. I argue for a new interpretation of this argument, and show that it involves two interesting objections against the introduction of Forms as formal causes: one concerns the completeness and the other the adequacy of such an explanatory project.

Kant posits the schema as a hybrid bridging the generality of pure concepts and the particularity of sensible intuitions. However, I argue that countenancing such schemata leads to a third-man regress. Siding with those who think that the mid-way posit of the Critique of Pure Reason's schematism section is untenable, my diagnosis is that Kant's transcendental inquiry goes awry because it attempts to analyse a form/matter union that is primitive. I therefore sketch a nonrepresentational stance aimed at respecting this primitivity.

Few arguments from the past have stirred up as much interest as Aristotle’s “Third man” and not so many texts have received as much attention as its account in chapter 22 of the Sophistici elenchi. And yet, several issues about both remain highly controversial, starting from the very nature of the argument at stake and the exact signification of some of its features. The essay provides a close commentary of the text, dealing with its main difficulties and suggesting an overall (...) interpretation of Aristotle’s discussion of the “Third Man” argument. (shrink)

This paper is a brief discussion of the famous 'Third Man Argument' as it appears in Plato's dialogue Parmenides . I mention, criticise and refine the most influential analytic approach to the argument; show that the actual conclusion of the argument is different from the one attributed to it by the majority of scholars; and elaborate two responses to the argument, both of which shed interesting light on the Theory of Forms.

The historian of philosophy often encounters arguments that are enthymematic: they have conclusions that follow from their explicit premises only by the addition of "tacit" or "suppressed" premises. It is a standard practice of interpretation to supply these missing premises, even where the enthymeme is "real," that is, where there is no other context in which the philosopher in question asserts the missing premises. To do so is to follow a principle of charity: other things being equal, one interpretation is (...) better than another just to the extent that the one produces a better argument than the other. We show that this principle leads to paradoxical conclusions, including the following: there is no objectively correct interpretation of any real enthymeme found in the text of a major philosopher; an interpreter will not regard a real enthymeme of a major philosopher as adequately interpreted until he has found a way of reading it that makes it into a good argument; every classical philosopher is infallible and omniscient; major philosophers never disagree. These conclusions are preposterous, but there are indications that they are in fact being reached, as we show by means of a case study of recent scholarship on Plato's Third Man Argument. To avoid the overinterpretation and anachronism that result from the unrestrained use of the principle of charity, one must employ a counterbalancing principle of parsimony: to seek the simplest explanation for the text under discussion. We study the role of the principle of parsimony by means of a mathematical case study, involving the suppressed premises in Euclid's Elements. Here the principle of parsimony plays a larger role than it does in the interpretation of philosophical texts, leading to a sharper distinction between Euclid's geometry and Euclidean geometry than we find between Plato and Platonism. We conclude by comparing two models of interpretation, which we call prospective and retrospective. Although the prospective model of interpretation leads to Platonism rather than to Plato, we argue that it still has a place in Platonic scholarship. (shrink)

Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of fictionalism also faces a (...) difficult challenge: there is evidence that Aristotle would deny the fictionalist position that mathematics is false. I argue that, in Aristotle's view, the fiction of mathematics is not to treat what does not exist as if existing but to treat mathematical objects with an ontological status they lack. This form of fictionalism is consistent with holding that mathematics is true. (shrink)

Aristotle holds that individual substances are ontologically independent from nonsubstances and universal substances but that non-substances and universal substances are ontologically dependent on substances. There is then an asymmetry between individual substances and other kinds of beings with respect to ontological dependence. Under what could plausibly be called the standard interpretation, the ontological independence ascribed to individual substances and denied of non-substances and universal substances is a capacity for independent existence. There is, however, a tension between this interpretation and the (...) asymmetry between individual substances and the other kinds of entities with respect to ontological independence. I will propose an alternative interpretation: to weaken the relevant notion of ontological independence from a capacity for independent existence to the independent possession of a certain ontological status. (shrink)

In (1991), Meinwald initiated a major change of direction in the study of Plato’s Parmenides and the Third Man Argument. On her conception of the Parmenides , Plato’s language systematically distinguishes two types or kinds of predication, namely, predications of the kind ‘x is F pros ta alla’ and ‘x is F pros heauto’. Intuitively speaking, the former is the common, everyday variety of predication, which holds when x is any object (perceptible object or Form) and F is a property (...) which x exemplifies or instantiates in the traditional sense. The latter is a special mode of predication which holds when x is a Form and F is a property which is, in some sense, part of the nature of that Form. Meinwald (1991, p. 75, footnote 18) traces the discovery of this distinction in Plato’s work to Frede (1967), who marks the distinction between pros allo and kath’ hauto predications by placing subscripts on the copula ‘is’. (shrink)