Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized (...) as the most powerful presentation yet of a neo-Fregean program. (shrink)

One worrying aspect of contemporary Western Society is the increasing prevalence of instances of ‘Science Denial’ in popular culture. Examples include both cases where well-attested scientific hypotheses are rejected and conversely, where scientifically discredited ideas are stubbornly retained. The paper raises the question whether the kind of argument for an anti-realist conception of empirical scientific theory considered in my contribution to the inaugural issue of this journal could in principle provide intellectual succour for these trends. The discussion proceeds through an (...) examination of the role of ‘takings for granted’ in all reflective enquiry to the conclusion that a trusting acceptance of the general credibility of informants is a precondition for the exercise of individual epistemic responsibility, and that in that context an acceptance of at least the empirical adequacy, if not the truth, realistically understood, of the teachings of scientists in general is rationally non-optional. (shrink)

This paper is a reply to George Boolos's three papers (Boolos (1987a, 1987b, 1990a)) concerned with the status of Hume's Principle. Five independent worries of Boolos concerning the status of Hume's Principle as an analytic truth are identified and discussed. Firstly, the ontogical concern about the commitments of Hume's Principle. Secondly, whether Hume's Principle is in fact consistent and whether the commitment to the universal number by adopting Hume's Principle might be problematic. Also the so-called `surplus content' worry is discussed, (...) which points out that the conceptual resources to grasp Hume's Principle vastly outstrip the conceptual resources employed in arithmetical reasoning. And lastly whether Hume's Principle is in bad company with other unsuccessful implicit definitions. In the last section, an account towards our entitlement to Hume&'s Principle is sketched. (shrink)

We now know of a number of ways of developing real analysis on a basis of abstraction principles and second-order logic. One, outlined by Shapiro in his contribution to this volume, mimics Dedekind in identifying the reals with cuts in the series of rationals under their natural order. The result is an essentially structuralist conception of the reals. An earlier approach, developed by Hale in his "Reals byion" program differs by placing additional emphasis upon what I here term Frege's Constraint, (...) that a satisfactory foundation for any branch of mathematics should somehow so explain its basic concepts that their applications are immediate. This paper is concerned with the meaning of and motivation for this constraint. Structuralism has to represent the application of a mathematical theory as always posterior to the understanding of it, turning upon the appreciation of structural affinities between the structure it concerns and a domain to which it is to be applied. There is, therefore, a case that Frege's Constraint has bite whenever there is a standing body of informal mathematical knowledge grounded in direct reflection upon sample, or schematic, applications of the concepts of the theory in question. It is argued that this condition is satisfied by simple arithmetic and geometry, but that in view of the gap between its basic concepts (of continuity and of the nature of the distinctions among the individual reals) and their empirical applications, it is doubtful that Frege's Constraint should be imposed on a neo-Fregean construction of analysis. (shrink)

Recently, there has been a significant upsurge of interest in what has come to be known as the 'Adoption Problem', first developed by Saul Kripke in 1974. The problem purports to raise a difficulty for Quine’s anti-exceptionalist conception of logic. In what follows, we first offer a statement of the problem and argue that, so understood, it depends upon natural but resistible assumptions. We then use that discussion as a springboard for developing a different adoption problem, arguing that, for a (...) significant class of basic logical principles, there is indeed a difficulty in seeing how they might be ‘freely adopted,’ thereby vindicating something close to the spirit of Kripke’s original claim. This first part of our argument will enforce a significant qualification of Quine’s claim that basic logical principles can be empirically confirmed. In the concluding sections of the paper, we turn to the question, specifically, of the empirical revisability of logic, arguing that when proper attention is paid to the role of reasoning in theory revision, it does indeed emerge that anti-exceptionalism, in full generality, is untenable. (shrink)

This volume provides a survey of contemporary philosophy of language. As well as providing a synoptic view of the key issues, figures, concepts and debates, each essay makes new and original contributions to ongoing debate.

A work using Wittgenstein's concept of philosophy to argue against the possibility of theories that seek to define art. It claims that the problems about identification and evaluation of works of art is that these problems are not theoretical, but grow out of our artistic traditions and practice.

Crispin Wright offers an original perspective on the place of “realism” in philosophical inquiry. He proposes a radically new framework for discussing the claims of the realists and the anti-realists. This framework rejects the classical “deflationary” conception of truth yet allows both disputants to respect the intuition that judgments, whose status they contest, are at least semantically fitted for truth and may often justifiably be regarded as true. In the course of his argument, Wright offers original critical (...) discussions of many central concerns of philosophers interested in realism, including the “deflationary” conception of truth, internal realist truth, scientific realism and the theoreticity of observation, and the role of moral states of affairs in explanations of moral beliefs. (shrink)

" In 'Vagueness and Alternative Logic' (Realism and Reason, Cambridge 1983, pp. 271-86, especially 285-6), Hilary Putnam puts forward a suggestion for a formal treatment of the logic of vagueness. … Putnam admits that, at the time of writing, he had not thought this idea through. What will already be apparent to the alert reader is that, in order to disclose serious difficulties for the proposal, Putnam would not have had to think far.".

Recasting important questions about truth and objectivity in new and helpful terms, his book will become a focus in the contemporary debates over realism, and ...

The rule-following debate, in its concern with the metaphysics and epistemology of linguistic meaning and mental content, goes to the heart of the most fundamental questions of contemporary philosophy of mind and language. This volume gathers together the most important contributions to the topic, including papers by Simon Blackburn, Paul Boghossian, Graeme Forbes, Warren Goldfarb, Paul Horwich, John McDowell, Colin McGinn, Ruth Millikan, Philip Pettit, George Wilson, and José Zalabardo. This debate has centred on Saul Kripke's reading of the rule-following (...) sections in Wittgenstein and his consequent posing of a "sceptical paradox" that threatens our every day notions of linguistic meaning and mental content. These essays are attempts to respond to this challenge and represent some of the most important work in contemporary theory of meaning. They examine the notion of meaning; whether it is possible to find a suitable meaning-constituting fact from our previous behaviour or mental histories; objections to, and defenses of, dispositional accounts of meaning; the plausibility of non-factualism about meaning; our attempts to develop non-reductionist accounts of meaning; and the sources of the normativity which attaches to meaning, such as the linguistic practice of the community or the dispositions of the individual. With an introductory essay and a comprehensive guide to further reading the book is an excellent resource for courses in philosophy of mind, philosophy of language, Wittgenstein, and metaphysics, as well as for all philosophers, linguists, and cognitive scientists with interests in these areas. Contributors include Simon Blackburn, Paul Boghossian, Graeme Forbes, Warren Goldfarb, Paul Horwich, John McDowell, Colin McGinn, Alexander Miller, Ruth Garrett Millikan, Philip Pettit, George. M. Wilson, Crispin Wright, and José L. Zalabardo. (shrink)

One type of argument to sceptical paradox proceeds by making a case that a certain kind of metaphysically “heavyweight or “cornerstone” proposition is beyond all possible evidence and hence may not be known or justifiably believed. Crispin Wright has argued that we can concede that our acceptance of these propositions is evidentially risky and still remain rationally entitled to those of our ordinary knowledge claims that are seemingly threatened by that concession. A problem for Wright’s proposal is (...) the so-called Leaching worry: if we are merely rationally entitled to accept the cornerstones without evidence, how can we achieve evidence-based knowledge of the multitude of quotidian propositions that we think we know, which require the cornerstones to be true? This paper presents a rigorous, novel explication of this worry within a Bayesian framework, and offers the Entitlement theorist two distinct responses. (shrink)

We focus on Timothy Williamson’s recent attack on the epistemological significance of the a priori–a posteriori distinction, and offer an explanation of why, fundamentally, it does not succeed. We begin by setting out Williamson’s core argument, and some of the background to it and move to consider two lines of conciliatory response to it—conciliatory in that neither questions the central analogy on which Williamson's argument depends. We claim, setting aside a methodological challenge to which Williamson owes an answer, that no (...) satisfactory such reconciliation is in prospect. Rather, as we then argue, —and it is on this that we base our overall negative assessment of his argument—Williamson’s core analogy is flawed by an oversight. We conclude with some brief reflections on Williamson’s ideas about the imagination as a source of knowledge. Our principal conclusion is only that Williamson’s argument fails to perform as advertised. A constructive case for confidence, to the contrary, that the intuitive contrast between a priori and a posteriori reflects something of fundamental epistemological significance is prefigured in our final section, but will not be elaborated here. (shrink)

This book is an important collection of new essays on various topics relating to realism and its rivals in metaphysics, logic, metaethics, and epistemology. The contributors include some of the leading authors in these fields and in several cases their essays constitute definitive statements of their views. In some cases authors write in response to the essays of other contributors, in other cases they proceed independently. Although not primarily historical this collection includes discussions of philosophers from the middle ages to (...) the present day, from Aquinas to Wittgenstein. No one seriously interested in questions about realism, whether as a general philosophical outlook or as a particular position within specific debates, can afford to be without this collection. (shrink)

This is a response to Paul Boghossian’s paper: What is inference?. The paper and the abstract originate from a symposium at the Pacific Division Meeting of the APA in San Diego in April 2011. John Broome was a co-commentator.

This volume, published on the fiftieth anniversary of Wittgenstein's death, brings together thirteen of Crispin Wright's most influential essays on Wittgenstein ...

In “Double Vision Two Questions about the Neo-Fregean Programme”, John MacFarlane’s raises two main questions: (1) Why is it so important to neo-Fregeans to treat expressions of the form ‘the number of Fs’ as a species of singular term? What would be lost, if anything, if they were analysed instead as a type of quantifier-phrase, as on Russell’s Theory of Definite Descriptions? and (2) Granting—at least for the sake of argument—that Hume’s Principle may be used as a means of implicitly (...) defining the number operator, what advantage, if any, does adopting this course possess over a direct stipulation of the Dedekind-Peano axioms? This paper attempts to answer them. In response to the first, we spell out the links between the recognition of numerical terms as vehicles of singular reference and the conception of numbers as possible objects of singular, or object-directed, thought, and the role of the acknowledgement of numbers as objects in the neo-Fregean attempt to justify the basic laws of arithmetic. In response to the second, we argue that the crucial issue concerns the capacity of either stipulation—of Hume’s Principle, or of the Dedekind-Peano axioms—to found knowledge of the principles involved, and that in this regard there are crucial differences which explain why the former stipulation can, but the latter cannot, play the required foundational role. (shrink)

This paper addresses three problems: the problem of formulating a coherent relativism, the Sorites paradox and a seldom noticed difficulty in the best intuitionistic case for the revision of classical logic. A response to the latter is proposed which, generalised, contributes towards the solution of the other two. The key to this response is a generalised conception of indeterminacy as a specific kind of intellectual bafflement-Quandary. Intuitionistic revisions of classical logic are merited wherever a subject matter is conceived both as (...) liable to generate Quandary and as subject to a broad form of evidential constraint. So motivated, the distinctions enshrined in intuitionistic logic provide both for a satisfying resolution of the Sorites paradox and a coherent outlet for relativistic views about, e.g., matters of taste and morals. An important corollary of the discussion is that an epistemic conception of vagueness can be prised apart from the strong metaphysical realism with which its principal supporters have associated it, and acknowledged to harbour an independent insight. (shrink)

"Dogmatism" is a term renovated by James Pryor [2000] to stand for a certain kind of neo-Moorean response to Scepticism and an associated conception of the architecture of basic perceptual warrant. Pryor runs the response only for (some kinds of) perceptual knowledge but here I will be concerned with its general structure and potential as a possible global anti-sceptical strategy. Something like it is arguably also present in recent writings of Burge 1 and Peacocke.2 If the global strategy could succeed, (...) (...) it would pre-empt any role in the diagnosis and treatment of sceptical paradoxes for the kind of notion of entitlement (rational, non-evidential warrant) I have proposed elsewhere [Wright 2004]. But my overarching contention will be that Dogmatism is, generally and locally, too problematic a stance to be helpful in that project. (shrink)