Sanford Shieh

In this paper I advance an account of the necessity of logic in Wittgenstein’s Tractatus. I reject both the “metaphysical” reading of Peter Hacker, who takes Tractarian logical necessity to consist in the mode of truth of tautologies, and the “resolute” account of Cora Diamond, who argues that all Tractarian talk of necessity is to be thrown away. I urge an alternative conception based on remarks 3.342 and 6.124. Necessity consists in what is not arbitrary, and contingency in what is up to our arbitrary choice, in the symbols we use, in how we picture or model the world. Necessity is not a mode of truth of propositions, but lies in the requirements of their intelligibility. I argue that this conception is implicit in certain “resolute” readings and in some of their critics. Both sides of the dispute are committed to certain logical features of language or thought, patterns of symbolizing constitutive of intelligibility that are not up to us to institute or alter. This conception of non-arbitrary patterns of symbolizing, I argue, is what logical syntax in the Tractatus consists in. I also argue that the well-known Tractarian view of propositions as truth-functions of elementary propositions can be understood in terms of patterns of norms governing our making sense with the affirmation and denial of propositions.

This article treats three aspects of Frege's discussions of definitions. First, I survey Frege's main criticisms of definitions in mathematics. Second, I consider Frege's apparent change of mind on the legitimacy of contextual definitions and its significance for recent neo-Fregean logicism. In the remainder of the article I discuss a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend: do the logical structures of the definientia reflect the understanding of arithmetical terms prevailing prior to Frege's analyses? Unless they do, it is unclear how Frege's proofs demonstrate the analyticity of the arithmetic in use before logicism. Yet, especially in late writings, Frege characterizes definitions as arbitrary stipulations of the senses or references of expressions unrelated to pre-definitional understanding. I conclude by examining some options for conceiving of the status of Frege's logicism in light of this apparent tension, and outline a suggestion for a philosophically fruitful way of resolving this tension.

The central premise of Michael Dummett's global argument for anti-realism is the thesis that a speaker's grasp of the meaning of a declarative, indexical-free sentence must be manifested in her uses of that sentence. This enigmatic thesis has been the subject of a great deal of discussion, and something of a consensus has emerged about its content and justification. The received view is that the manifestation thesis expresses a behaviorist and reductive theory of meaning, essentially in agreement with Quine's view of language, and motivated by worries about the epistemology of communication. In the present paper I begin by arguing that this standard interpretation of the manifestation thesis is neither particularly faithful to Dummett's writings nor philosophically compelling. I then continue by reconstructing, from Dummett's texts, an account of the manifestation thesis, and of its justification, that differ sharply from the received view. On my reading, the thesis is motivated not epistemologically, but conceptually. I argue that connections among our conceptions of meaning, assertion, and justification lead to a conclusion about the metaphysics of meaning: we cannot form a clearly coherent conception of how two speakers can attach different meanings to a sentence without at the same time differing in what they count as justifying assertions made with that sentence. I conclude with some suggestions about how Dummett's argument for global anti-realism should be understood, given my account of the manifestation thesis.

The days when Frege was more footnoted than read are now long gone; still, until very recently he has been read rather selectively. No doubt many had an inkling that there’s more to Frege than the sense/reference distinction; but few, one suspects, thought that his philosophy of mathematics was as fertile and intriguing as the present collection demonstrates. Perhaps, as Paul Benacerraf’s essay in this collection suggests, logical positivism should be held partly responsible for the neglect of this aspect of Frege’s thought, since it contributed to the following common impression of Frege’s philosophy of mathematics: Frege’s project was to reduce arithmetic to logic, in order to provide an empiricist account of mathematical knowledge; Russell’s paradox showed that this was not possible, and that the best that can be done is to reduce arithmetic to set theory; so, Frege’s logicism is demonstrably a philosophical dead end.