Sanford Shieh

Saul Kripke’s “modal argument” against the description theory of proper names turns on a distinction between reference-fixing and meaning-giving. In this essay Shieh argues first that without further explanation of meaning-giving, it is unclear how this argument shows that the meanings of names cannot be given by descriptions. Second, Shieh shows that an explanation of meaning-giving sufficient to sustain the modal argument requires a notion of modal properties of meaning. This notion, in turn, yields a notion of rigidity of names that can be explained in terms of Gareth Evans’s notion of deep necessity. Shieh concludes that Kripke’s modal argument is not based simply on untutored linguistic intuitions or facts of ordinary language use but presupposes substantial metaphysical commitments.

Do considerations in the theory of meaning pose a challenge to classical logic, and in particular to the law of excluded middle? Michael Dummett suggested an affirmative answer to this question, and advocated a form of logical revisionism. In his 1981 study “Anti-Realism and Revisionism,” Crispin Wright developed a critique of Dummett’s case for logical revisionism, but in more recent work (e.g., his 1992 book _Truth and Objectivity_), Wright has advanced an argument in favour of logical revisionism. This chapter investigates the nature and limitations of anti-realist revisionism, and offers a critique of Wright’s arguments in favour of logical revisionism. It also develops an alternative proposal about how revisionism might proceed.

This chapter treats C. I. Lewis' criticism of Bertrand Russell's material implication. This chapter gives an overview of the differences between Russell's conception of logic and contemporary ones. Lewis's criticism is often taken to rest on the divergence between material implication and our intuitive conception of logical consequence. The chapter argues that a more fundamental criticism Lewis makes is internal to Russell's conception: for Russell a system of logic must not merely enable correct inferences to be made; it must state correct implications. Lewis came to hold that a primitive notion of possibility is required if the laws of logic are to capture the facts of inferential practice. But Lewis's incorporation of modality is meant to revise Principia to make its axioms properly logical. The chapter concludes the chapter by sketching some other aspects of this history, from Wittgenstein through Carnap, Quine and the full re-emergence of modal notions in analytic philosophy.

This essay analyzes a controversy between a recent, revisionary style of interpretation of Frege's conception of the relation between logic and semantics and the received interpretation that it opposes. I argue that, properly understood, the revisionary interpretation, especially that of Thomas Ricketts, differs less from such established interpretations as that of Dummett than the proponents of the former have claimed. However, the arguments underlying the revisionary interpretation have suggestive consequences for the idea of a foundation of logic.

This chapter traces Wittgenstein’s philosophical development culminating in the conception, central to Tractatus Logico-Philosophicus, of propositions as involving essentially a primitive notion of possibility. I spell out three stages of this philosophical development, starting from criticism of Russell’s multiple-relation theory of judgment, going through the conception of propositions as signifying facts in “Notes on Logic,” to struggles with what Wittgenstein calls the “Wahrheitsprobleme” in his wartime notebooks, in which he first considers appealing to the idea of picturing to understand propositions, before finally arriving at the modal view of proposition in the Tractatus. I also sketch the broader philosophical significance of the Tractarian conception of propositions, namely, Frege and Russell’s rejection of modality, and so of a venerable tradition of characterizing logic in modal terms. Against this background, Wittgenstein’s view of propositions in the Tractatus is part of a rejoinder to Frege and Russell, bringing modality back into logic.

The most puzzling and intriguing aspect of intuitionism as a philosophy of mathematics is its claim that classical deductive reasoning in mathematics is illegitimate. The two most well-known proponents of this position are L. E. J. Brouwer and Michael Dummett. Both of their criticisms of the use of classical logic in mathematics have, by and large, been taken to depend on the thesis that the principle of bivalence does not apply to mathematical statements; and the difference between these criticisms is taken to consist in their grounds for this thesis. Brouwer bases this thesis on an account of the nature of mathematics: it is an activity of mental construction essentially independent of language. Dummett, in contrast, bases the thesis on his anti-realist view of the nature of meaning. ;My first principal argument in this essay shows that the conception of anti-realism just outlined is problematic as a reading of Dummett. To begin with, Dummett explicitly rejects, not only the evidentiary restrictions of this conception, but also, more seriously, the use of specific epistemological theses in a philosophical account of meaning. Moreover, I give an alternative account of anti-realism, consisting of alternative interpretations of the manifestation requirement and of the rejection of realist truth conditions, that do not rely on an epistemology of meaning, and hence, a fortiori, not on evidential restrictions. ;My second principal argument in this essay consists of drawing a consequence of this conception of anti-realism, namely, that the failure of bivalence cannot, by itself, support a cogent criticism of classical logic. The basic reason is that, given my view of anti-realism, the claim that the legitimacy of applying classical reasoning to a class of statements depends on whether bivalence applies to that class already implies that the system of deductive reasoning applying to these statements is non-classical. Hence an argument against classical logic based on this claim is question-begging. ;Finally, I conclude by showing that Dummett's criticism of classical reasoning, as reconstructed by my third argument, fails

This chapter examines modality in the history of analytic philosophy. There were, in this history, two principal types of reductionism or eliminativism about modality, and two corresponding phases in the rejection of anti-modal stances. First, the founders of analytic philosophy, Frege, Moore, and Russell, took necessity and possibility to be reducible to more fundamental logical notions, where logic for these thinkers consists of truths about a mind- and language-independent reality extending beyond the empirical world. Against this reductionism, C. I. Lewis and Wittgenstein argued that logic itself requires modal notions. Second, Carnap advanced a pragmatically motivated account of modal terms as expressing pseudo-object properties, which appear to be properties of objects but can be construed as properties of their designations. Quine criticized this account and proposed a thoroughgoing elimination of modality. Quine’s well-known claim that quantifying into modal contexts is unintelligible without resorting to essentialism cannot be fully understood independently of Carnap’s notion of pseudo-object property. Against Quine, Ruth Marcus and Saul Kripke argued for the coherence of modal concepts and their entrenchment in ordinary language and thought, leading to the now dominant view that modal properties are mind- and language-independent features of the world.

A long tradition, going back to Aristotle, conceives of logic in terms of necessity and possibility: a deductive argument is correct if it is not possible for the conclusion to be false when the premises are true. A relatively unknown feature of the analytic tradition in philosophy is that, at its very inception, this venerable conception of the relation between logic and necessity and possibility - the concepts of modality - was put into question. The founders of analytic philosophy, Gottlob Frege and Bertrand Russell, held that these concepts are empty: there are no genuine distinctions among the necessary, the possible, and the actual. In this book, the first of two volumes, Sanford Shieh investigates the grounds of this position and its consequences for Frege's and Russell's conceptions of logic. The grounds lie in doctrines on truth, thought, and knowledge, as well as on the relation between mind and reality, that are central to the philosophies of Frege and Russell, and are of enduring philosophical interest. The upshot of this opposition to modality is that logic is fundamental, and, to be coherent, modal concepts would have to be reconstructed in logical terms. This rejection of modality in early analytic philosophy remains of contemporary significance, though the coherence of modal concepts is rarely questioned nowadays because it is generally assumed that suspicion of modality derives from logical positivism, which has not survived philosophical scrutiny. The anti-modal arguments of Frege and Russell, however, have nothing to do with positivism and remain a challenge to the contemporary acceptance of modal notions.

Responding to Russell is a constant throughout Wittgenstein's philosophizing. This Element focuses on Wittgenstein's criticisms of Russell's theories of judgment in the summer of 1913. Wittgenstein's response to these criticisms is of first-rate importance for his early philosophical development, setting the path to the conceptions of proposition and of logic in Tractatus Logico-Philosophicus. This Element also touches on further aspects of Wittgenstein's responses to Russell: the rejection of Russell's and Frege's logicisms in the Tractatus, the critique of Russell's causal-behavioristic philosophy of mind in Wittgenstein's 'middle' period, the Russellian origins of notions of privacy dialectically treated in Philosophical Investigations, and the discussion of 'surveyability' of mathematical proof in Remarks on the Foundations of Mathematics, which is, again, a response to Russellian logicism.

This paper sketches the place of Arthur Pap’s work in the complex history of modality in the analytic tradition of philosophy, contrasting it with that of the early Wittgenstein. They represent two principal paths of the philosophical history of modality that converge in the logical empiricism of the Vienna Circle. Clarifying these paths go some way towards turning aside a myth, with some sway in contemporary philosophy, which occludes a philosophically fruitful view of the philosophical-historical realities of modality in analytic philosophy.

In this paper I examine two substantial interpretations of Wittgenstein’s criticisms of Frege’s conception of logic. One is based on Frege’s rejection of psychologism and alleges that this rejection engenders a tension that is resolved in the Tractatus. The other is based on the claim that there are patterns of inference involving what are now known as propositional attitude ascriptions that Frege’s conception of logic is not equipped to handle. I show that neither of these interpretations present a compelling criticism of Frege. I then argue that Wittgenstein inherited from Frege the ideas of affirmation, denial, and the “opposite” of a thought, but came to see that these conflict with Frege’s conception of negation as a truth-function. This leads to the Grundgedanke of the Tractatus: neither negation nor any other “logical constant” is a representative in our picturing of the world.

Three clusters of philosophically significant issues arise from Frege’s discussions of definitions. First, Frege criticizes the definitions of mathematicians of his day, especially those of Weierstrass and Hilbert. Second, central to Frege’s philosophical discussion and technical execution of logicism is the so‐called Hume’s Principle, considered in The Foundations of Arithmetic . Some varieties of neo‐Fregean logicism are based on taking this principle as a contextual definition of the operator ‘the number of …’, and criticisms of such neo‐Fregean programs sometimes appeal to Frege’s objections to contextual definitions in later writings. Finally, a critical question about the definitions on which Frege’s proofs of the laws of arithmetic depend is whether the logical structures of the definientia reflect our pre‐Fregean understanding of arithmetical terms. It seems that 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 the definitions as arbitrary stipulations of the senses or references of expressions unrelated to pre‐definitional understanding. One or more of these topics may be studied in a survey course in the philosophy of mathematics or a course on Frege’s philosophy. The latter two topics are obviously central in a seminar in the philosophy of mathematics in general or more specialized seminars on logicism, or on mathematical definitions and concept formation.

This book is a study of the philosophy of arithmetic in one of the most significant periods of its history—from Frege to Carnap—prefaced by an account of Kant. Potter aims at a philosophical history, a story told from an explicit interpretative perspective. These theories of arithmetic are seen as attempts to account for its “source of content” and “source of concepts.” Potter never explains these terms; I take the former to be the thing that, when we have knowledge of it or insight into it, provides the ultimate justification for pure and applied arithmetical discourse. That is, Potter’s principal concern is both ontological and epistemological: what determines, and how do we know, the truth of the statements that express our putative arithmetical knowledge? The criterion of success of a theory of arithmetic is how well it explains arithmetic’s simultaneous necessity or apriority and empirical applicability. Potter divides the theories he discusses into four main types, determined by their accounts of the “source of content” and “concepts”: sensibility, thought, language, and the world. At the end, Potter finds that none succeeds in accounting for all of arithmetic: at best some capture the infinity of the natural numbers, but none gives the “source” of arithmetical concepts. But the “similarities … between the scopes of the various approaches” suggest a Gödelian moral for Potter’s tale: the philosophy of arithmetic must treat concepts of “thought structures or … contents,” where “reflection upon the meanings” of “propositions about these mental objects” is needed for their proofs.

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.