In this introduction we present the principal themes of the special issue and highlight the main interpretive theses of the contributions.

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. (shrink)

This collection of previously unpublished essays presents a new approach to the history of analytic philosophy--one that does not assume at the outset a general characterization of the distinguishing elements of the analytic tradition. Drawing together a venerable group of contributors, including John Rawls and Hilary Putnam, this volume explores the historical contexts in which analytic philosophers have worked, revealing multiple discontinuities and misunderstandings as well as a complex interaction between science and philosophical reflection.

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. (shrink)

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. (shrink)

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. (shrink)

In this paper I attempt to clarify a relatively little-studied aspect of Michael Dummett's argument for intuitionism: its use of the notion of ‘undecidable’ sentence. I give a new analysis of this concept in epistemic terms, with which I resolve some puzzles and questions about how it works in the anti-realist critique of classical logic.

Alongside Richard Rorty, Hilary Putnam and Jacques Derrida, Stanley Cavell is arguably one of the best-known philosophers in the world. In this state-of-the-art collection, Alice Crary explores the work of this original and interesting figure who has already been the subject of a number of books, conferences and Phd theses. A philosopher whose work encompasses a broad range of interests, such as Wittgenstein, scepticism in philosophy, the philosophy of art and film, Shakespeare, and philosophy of mind and language, Cavell has (...) also written much about Henry Thoreau and Ralph Waldo Emerson. Including contributions from Hilary Putnam, Cora Diamond, Jim Conant and Stephen Mulhall, this book is a must-have for libraries and students alike. (shrink)

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. (shrink)

Philosophers since Aristotle have traditionally held that impossibilities make up the nature of logic. Sanford Shieh investigates an important but underexplored break with this tradition: Frege and Russell questioned whether there really are such things as possibilities or necessities, and sought the foundations of logic elsewhere.

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

What is this discipline called history of philosophy? What standards are relevant to its assessment? There aren’t single, straightforward answers to these quest.

Volume 41, Issue 1, February 2020, Page 97-100.

In Relying on others [Goldberg, S. 2010a. Relying on others: An essay in epistemology. Oxford: Oxford University Press], I argued that, from the perspective of an interest in epistemic assessment, the testimonial belief-forming process should be regarded as interpersonally extended. At the same time, I explicitly rejected the extendedness model for beliefs formed through reliance on a mere mechanism, such as a clock. In this paper, I try to bolster my defense of this asymmetric treatment. I argue that a crucial (...) assumption lying behind the argument I used to establish interpersonal extendedness in testimony cases does not apply to beliefs formed through reliance on instruments. In this respect, at least, there appears to be something epistemically distinctive about relying on another epistemic agent. (shrink)

This volume collects twelve essays by Sanford C. Goldberg on the topic of social epistemology. The collection falls into two halves: the first half develops a proposal for a programme for social epistemology, its animating vision, foundational questions, and core concepts; the other half focuses on applications of this programme to particular topics. Goldberg characterizes the research programme as the exploration of the epistemic significance of other minds. This programme is dedicated to an examination of the various ways in (...) which we depend epistemically on others, and to describe the proper way to evaluate beliefs according to the sort of dependence they exhibit. It thus provides the basis for identifying and characterizing various dysfunctions of our epistemic communities. The programme is put into practice by exploring such topics as the epistemic agency exhibited in inquiry, the practices that constitute news coverage, the basis for allegations of what we or others should have known, how reliance on another's testimony contrasts with reliance on an instrument, our reliance on others as consumers of testimony, and the epistemic significance of non-epistemic social norms--moral, political, professional, or relationship-based. (shrink)

Elsewhere I and others have argued that evidence one should have had can bear on the justification of one's belief, in the form of defeating one's justification. In this paper, I am interested in knowing how evidence one should have had (on the one hand) and one's higher-order evidence (on the other) interact in determinations of the justification of belief. In doing so I aim to address two types of scenario that previous discussions have left open. In one type of (...) scenario, there is a clash between a subject's higher-order evidence and the evidence she should have had: S's higher-order evidence is misleading as to the existence or likely epistemic bearing of further evidence she should have. In the other, while there is further evidence S should have had, this evidence would only have offered additional support for S's belief that p. The picture I offer derives from two “epistemic ceiling” principles linking evidence to justification: one's justification for the belief that p can be no higher than it is on one's total evidence, nor can it be higher than what it would have been had one had all of the evidence one should have had. Together, these two principles entail what I call the doctrine of Epistemic Strict Liability: insofar as one fails to have evidence one should have had, one is epistemically answerable to that evidence whatever reasons one happened to have regarding the likely epistemic bearing of that evidence. I suggest that such a position can account for the battery of intuitions elicited in the full range of cases I will be considering. (shrink)

Many epistemologists agree that even very young children sometimes acquire knowledge through testimony. In this paper I address two challenges facing this view. The first (building on a point made in Lackey (2005)) is the defeater challenge, which is to square the hypothesis that very young children acquire testimonial knowledge with the fact that children (whose cognitive immaturity prevents them from having or appreciating reasons) cannot be said to satisfy the No-Defeaters condition on knowledge. The second is the extension challenge, (...) which is to give a motivated, extensionally-adequate account of the conditions on testimonial knowledge in early childhood. Neither challenge can be met merely by endorsing externalism about knowledge; but we can meet both by reconceiving the process that eventuates in the child’s consumption of testimony. My central thesis is that this process should be seen as implicating features of the child's social environment. The result is a novel anti-individualistic externalism about knowledge. (shrink)

Constitutions serve (at least) two central functions. One is to settle certain controversies by offering a definitive solution, such as adoption of a presidential or parliamentary system, a one-house or two-house legislature, or guaranteeing a certain term of years to judicial appointees. Not surprisingly, there is rarely litigation about such solutions, even if one finds them troublesome; instead, one can suggest amending the constitution or even replacing it. A second function is precisely to engender litigation by addressing certain issues—very often (...) involving rights—that don't lend themselves to the kinds of definitive textual solutions similar to those involving structural features of a polity. If the first constitution can be described as a “constitution of settlement,” this second constitution is a “constitution of legal conversation” inasmuch as lawyers constantly dispute the meanings to be assigned such terms as “equal protection,” “human dignity,” and the like. But how does this apply to the preambles commonly, though not always, found in constitutions? Preambles often claim to evoke what binds together the society for whom the constitution is being drafted—religion, ethnicity, histories, languages, or commitments to norms, including universalistic ones. But to what extent are such claims of unity attempts by political elites to marginalize sectors of the society that do not in fact share the attributes in question? In any event, there is nothing “innocent” about constitutional preambles, and they are well worth taking seriously whether or not they are useful to lawyers engaged in litigation. (shrink)

European Journal of Philosophy, Volume 30, Issue 2, Page 676-692, June 2022.