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

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)

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)

Crispin Wright; IV*—On Putnam's Proof that We are not Brains-in-a-Vat1, Proceedings of the Aristotelian Society, Volume 92, Issue 1, 1 June 1992, Pages 67–94, h.

[Crispin Wright] Two kinds of epistemological sceptical paradox are reviewed and a shared assumption, that warrant to accept a proposition has to be the same thing as having evidence for its truth, is noted. 'Entitlement', as used here, denotes a kind of rational warrant that counter-exemplifies that identification. The paper pursues the thought that there are various kinds of entitlement and explores the possibility that the sceptical paradoxes might receive a uniform solution if entitlement can be made to reach (...) sufficiently far. Three kinds of entitlement are characterised and given prima facie support, and a fourth is canvassed. Certain foreseeable limitations of the suggested anti-sceptical strategy are noted. The discussion is grounded, overall, in a conception of the sceptical paradoxes not as directly challenging our having any warrant for large classes of our beliefs but as crises of intellectual conscience for one who wants to claim that we do. /// [ Martin Davies] Wright's account of sceptical arguments and his use of the idea of epistemic entitlement are reviewed. His notion of non-transmission of epistemic warrant is explained and a concern about his notion of entitlement is developed. An epistemological framework different from Wright's is described and several notions of entitlement are introduced. One of these, negative entitlement, is selected for more detailed comparison with Wright's notion. Thereafter, the paper shows how the two notions of entitlement have contrasting consequences for non-transmission of warrant and how they go naturally with two conceptions of the presuppositions of epistemic projects. Problems for negative entitlement are explained and solutions are proposed. (shrink)

There is now a widespread accord among philosophers that the vagueness of natural language gives rise to some particularly deep and perplexing problems and paradoxes. It was not always so. For most of the first century of analytical philosophy, vagueness was generally regarded as a marginal, slightly irritating phenomenon, —receiving some attention, to be sure, in parts of the Philosophical Investigations and in the amateur linguistics enjoyed by philosophers in Oxford in the 1950s, but best idealised away in any serious (...) theoretical treatment of meaning, understanding and valid inference. Frege, as is well known, had come to be thoroughly mistrustful of vagueness, supposing that a language fit for the purpose of articulating scientific and mathematical knowledge would have to be purified of it. Later trends in philosophical logic and semantics followed his lead, not indeed in setting about the (futile) task of expurgating vagueness from natural language but by largely restricting theoretical attention to artificial languages in whose workings vagueness was assigned no role. (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)

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.

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)

This is a short, and therefore necessarily very incomplete discussion of one of the great questions of modern philosophy. I return to a station at which an interpretative train of thought of mine came to a halt in a paper written almost 20 years ago, about Wittgenstein and Chomsky,[1] hoping to advance a little bit further down the track. The rule-following passages in the Investigations and Remarks on the Foundations of Mathematics in fact raise a number of distinct issues about (...) rules, meaning, objectivity, and reasons, whose conflation is encouraged by the standard caption, "the Rule-following Considerations".[2] So, let me begin by explaining my focus here. (shrink)

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)

Every student of English-speaking analytical metaphysics is taught that the early twentieth century philosophical debate about truth confronted the correspondence theory, supported by Russell, Moore, the early Wittgenstein and, later, J.L. Austin, with the coherence theory advocated by the British Idealists. Sometimes the pragmatist conception of truth deriving from Dewey, William James, and C.S. Peirce is regarded as a third player. And as befits a debate at the dawn of analytical philosophy, the matter in dispute is normally taken to have (...) been the proper analysis of the concept.No doubt this conception nicely explains some of the characteristic turns taken in the debate. Analysis, as traditionally conceived, has to consist in the provision of illuminating conceptual equivalences; and illumination will depend, according to the standard rules of play, on the analysans’ utilizing only concepts which, in the best case, are in some way prior to and independent of the notion being analyzed — or, if that's too much to ask, then concepts which at least permit of some form of explication which does not in turn take one straight back to that notion. (shrink)

Dummett's objections to the coherence of the strict finitist philosophy of mathematics are thus, at the present time at least, ill-taken. We have so far no definitive treatment of Sorites paradoxes; so no conclusive ground for dismissing Dummett's response — the response of simply writing off a large class of familiar, confidently handled expressions as semantically incoherent. I believe that cannot be the right response, if only because it threatens to open an unacceptable gulf between the insight into his own (...) understanding available to a philosophically reflective speaker and the conclusions available to one confined to observing the former's linguistic practice; for an observer of our linguistic practice could never justifiably arrive at the conclusion that ‘red’, ‘child’, etc., are governed by inconsistent rules. But the Sorites is not the subject of this paper. The points I hope to have made plausible are: that a generalized intuitionist position cannot be so much as formulated and that even a most local intuitionism, argued for the special case of arithmetic, is hard pressed effectively to stabilize and defend itself; that strict finitism remains the natural outcome of the anti-realism which Dummett has propounded by way of support for the intuitionist philosophy of mathematics; that it is powerfully buttressed by the ideas of the latter Wittgenstein on rule-following; and that there is no extant compelling reason to suppose that its involvement with predicates of surveyability calls its coherence into question. The correct philosophical assessment of strict finitism, and its proper mathematical exegesis, remain absolutely open, almost virgin issues. This is not a situation which philosophers of mathematics should tolerate very much longer. (shrink)

According to Gottlob Frege, his logicism died when it was discovered that the underlying theory of extensions is inconsistent. The neo-logicist attempts to found mathematics on other abstraction principles, such as the so-called Hume’s principle that two concepts have the same number if and only if they are equinumerous. This chapter discusses the state of neo-logicism, responding to various objections that have been raised against it.

For all post-1970s effort expended on the topic, the most central and important question about vagueness—what it is: what, specifically, something’s being a borderline case of a vague expression consists in—has seldom been tackled with the theoretical explicitness necessary if issues expectably downstream of it, like the nature of valid inference among vague statements, or the Sorites paradox, are to receive a properly motivated treatment. The great interest of Chapter V of The Things We Mean is that it points the (...) way towards a new kind of approach, according to which vagueness is constitutively a psychological phenomenon, grounded in the characteristic propositional attitudes of practitioners of vague discourse. It’s uncontroversial that a vague expression is one whose presence in a sentence contributes towards there being, at least in principle, situations which present borderline cases of its truth; for Schiffer, it is the status of such a situation as a borderline case that is grounded in the characteristic psychology of thinkers who appraise the sentence in that situation. (shrink)

Following Kant, Frege took the idea that there is such a thing as bona fide a priori knowledge of a large range of necessary propositions for granted. In particular he assumed that such is the character of our knowledge of basic logic and arithmetic. This view is no longer orthodoxy. The idea that pure (for Frege, logical) intellection can provide for substantial knowledge of necessary features of the world is widely regarded with suspicion. However it is fair to say that (...) most recent scepticism about it has been driven either by abstract background theoretical commitments—for instance, by a thoroughgoing empiricism, as in Mill and Quine, or by epistemological externalism1—or by the conviction that the concept of a priori justification allows of no stable, theoretically interesting characterisation.2 The present discussion focuses on the example of elementary arithmetic to develop and explore a different, relatively neglected and, it may be suggested, more fundamental kind of sceptical challenge, one prefigured in the writings on mathematics of the later Wittgenstein but independent of the discussion of following a rule to which his generally deflationary or conventionalist cast of thinking about mathematical knowledge is, after Kripkenstein,3 nowadays usually attributed. Elementary arithmetical truths are normally taken to be justifiable a priori if any truths are. They are also normally taken to be both necessary and substantial—essentially applicable to our dealings with the world and empirically predictive, yet good for counterfactual reasoning about however far-fetched and exotic scenarios. Yet, I will argue, scrutiny of the kind of methods—simple informal cognitive routines involving counting and pictures—whereby such judgements are initially apt to win our confidence serves to make it puzzling how they can justify what they are supposed to at all: how such procedures can merit either the very high levels of confidence we standardly place in the judgements they lead to, or the modal (counterfactual) significance we standardly attach to those judgements. The present discussion elaborates these apparent shortfalls (§§2–4) and reviews four proposals (§§5–8) for redressing them, arguing that each is ineffective. The sceptical challenge accordingly stands unanswered. §9 elaborates its relation to one strand in the Remarks on the Foundations of Mathematics. §10 summarises the resulting dialectical position. The upshot, I believe, is a deepened understanding of an important aspect of Wittgenstein’s later philosophy and a major intellectual challenge to those—possibly still a majority—who incline to side with Frege’s view of the epistemological status of arithmetic. (shrink)

W. V. O. Quine's contention that translation is indeterminate has been among the most widely discussed and controversial theses in modern analytical philosophy. This chapter offers some initial reflections on the content and implications of the indeterminacy thesis, and of the presuppositions that Quine makes in treating it as a stepping‐stone to semantic irrealism. It distinguishes Quine's two principal arguments for the thesis: the famous 'gavagai' argument of Word and Object, and the argument from the underdetermination of empirical theory by (...) data emphasized in 'On the reasons for the indeterminacy of translation', and lays out the essentials of the former argument. The chapter assesses the cogency of Evans's objections, and lays‐out certain basic distinctions and implications of the second and more radical argument. The translation of theoretical terms in the native scientists' language can be no more indeterminate than is the selection of an empirically adequate theory of those data. (shrink)

Chapter 4 of Being Known outlines an integrated metaphysics and epistemology for the metaphysical—absolute—notions of necessity and possibility. The leading idea is to view the modal status of a proposition as the deliverance of a set of fundamental Principles of Possibility, and our ability to recognise modal status as issuing from an implicit knowledge of these principles. Peacocke aims at a middle way between the extremes of Lewis-style realism about modality and the various—conventionalist, expressivist, Wittgensteinian—forms of non-cognitivism that were prominent (...) in the last century. An attraction of his account is its unified treatment both of a priori logical—more generally, conceptual—necessity and possibility and of a posteriori necessities of essence, identity, origin and constitution, etc. The treatment is ambitious and rich in invention and original detail, but Peacocke professes himself more wedded to the general approach than to the particular development. I shall correspondingly confine my remarks, more or less, to the general approach. (shrink)

§1 The Disjunctive Conception of Experience Descartes was surely right that while normal waking experience, dreams and hallucinations are characteristically distinguished at a purely phenomenological level, — by contrasts of spatial perspective, coherence, clarity of image, etc., — it is not essential that they be so.1 What is it like for someone who dreams that he is sitting, clothed in his dressing gown, in front of his fire can in principle be subjectively indistinguishable from what it is like to perceive (...) that one is doing so, fully conscious and awake. The same holds for multi-sense hallucination and, it is assumed, would hold of the experience of an envatted brain in the usual postulated scenario. This thought — that normal perceptual experience allows in principle of perfect phenomenological counterfeit — is, to the best of my knowledge, nowhere seriously challenged in John McDowell's writings.2 What he rejects is an idea that builds upon and would be potentially explanatory of it: the Lockean idea that, as far as the states enjoyed by the experiencing subject are concerned, there is actually no generic distinction between dream, hallucination, and wakeful perception: — that one and the same type of state of consciousness is involved in all three cases, and that which (if any) of the three a particular occurrence of the type falls under is a matter of how it is caused. On this model, the distinction between Descartes' notional fully lucid dream and the corresponding raft of perceptions of his dressing-gowned, sedentary state is like that between a certain kind of sunburn and nettle rash. For Disjunctivism, however, the Lockean — as McDowell likes to say, “Highest Common Factor” — conception of perceptual experience and its potential counterfeits is a conceptual error. There is no single type of state of consciousness present in each of dreaming, perceiving and hallucinating, whose instances fall under one or other of those characterisations purely by virtue of their aetiology.. (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)