This survey of metaphysics covers the historical or classical aspects of the subject as well as those currently in the post-Wittgensteinian limelight--principally materialism, platonism, essentialism, and anti-realism. Benardete sees contemporary metaphysical preoccupations as more or less thinly disguised revisitings of those of the past, and explains how metaphysics and mathematical logic are interrelated and how metaphysical studies can illuminate both scinece and the humanities.

Re-activating the philosophical quest for real definitions, I dare propose that its fulfillment is most convincingly represented, close to home, where one probably least expects it, notably in the first half of Section 36 of Word and Object, in the pages of Quine. Aristotle must inevitably remain our guide even as we insist on respecting Quine's anti-essentialism, and I must then explain how Aristotle, truncated, can be put here to use. Well, we may begin, appropriately, with a definition or with (...) what, nearly enough, smacks of being one, namely the Aristotelian slogan, definitio fit per genus proximum et differentiam specificam. Although that may be itself a real definition (of real definition), I shall not pursue this scholastic point, preferring to concentrate on my principal task which I take to be to vindicate the feasibility of formulating a real definition of some mind-independent reality. Such a vindication can scarcely succeed today unless it is recognized from the outset that we have here at hand one of those cases where the very (logical) possibility of a problematic thing can be established only by having recourse to the modal principle that actuality entails possibility. Nothing less than a concrete instance of a real definition will then suffice, and I thus expect my sceptical reader (I count on her scepticism) to be in doubt whether the scholastic bit of jargon 'real definition' picks out one of the concepts in her repertoire. (shrink)

Thomas Aquinas, in his commentary on the Metaphysics, offers a faithful rendering of the argument in the course of his almost literal paraphrase; but in the Summa Contra Gentiles, when he undertakes to give "the arguments by which Aristotle sets out to prove the existence of God," the argument from time is strangely omitted. Thomas is not peculiar in this omission. Maimonides before him evinces no recognition of the argument from time, and I am aware of no modern discussion of (...) it. The one directly relevant passage in Book Lambda is certainly exiguous enough, and it might perhaps be suggested that Aristotle himself failed to grasp the argument as independent of the argument from motion. The argument from time is indeed absent from the Physics in anything like its full force, though an abbreviated version of it is peripherally anticipated in chapter 1 of Bk. 8. There being such a meagreness of supporting documentation in the Aristotelian corpus itself, it is not altogether surprising that the key passage--Met. 1071b3-10--should be passed over as merely a highly condensed synopsis of the argument from motion. I am confident, however, that, elliptical as the passage is, it actually uncovers an argument for the prime mover quite distinct from the main argument of the Physics. (shrink)

This chapter contains sections titled: Sher's Weak Logicism Finiteness, an Infinite Sentence and Skolem Back to Strong Logicism? Benacerraf's Challenge An Anti‐realist Frege? Second‐order Logic and Sets Skolem (Again) and Megethology.

An ingenious study in the interplay between mereology and set theory, this book is launched innocuously enough with the thesis that a class just is the mereological sum or "fusion" of its sub-classes. The sub-classes of a class are parts of a class in the literal sense of the word "part," as trigonometry is literally a part of mathematics. We are thus urged to resist the suggestion that the word "part" applies first and foremost to the spatial parts of a (...) material object. The atomic parts of a class being seen to be its singleton or "unit" sub-classes, a class is now to be understood on the most basic level as a fusion of singletons but for the distressing fact that how a class might have only one member was never explained to us when we first learned that a class was supposed to be "a many combined into one.". (shrink)

On the face of it, statements like, whose truth we are readily prepared to allow, carry an "ontological commitment," in Quine's jargon, to abstract entities: Some shapes are uninstantiated. Can a nominalistic paraphrase of be provided? I take Charles Chihara to be urging a positive answer in his exciting book, with in particular meeting his precise prescription: It is possible to construct a shape predicate, in some language or other, that fails to be satisfied by anything. Not that we are (...) supposed to have in hand an effective procedure for producing any such predicate token. Rather, we are to envisage all the different shape predicate tokens that are to be found in different possible worlds. Some of them will have a null extension in those worlds. But that is not what asks of us. Think first of some shape predicate type of which there are no tokens in the actual world. Now consider a possible world in which there are tokens of that type. Finally, we are to think of those tokens as having a zero extension in our world. (shrink)