Crispin Wright

A companion to the philosophy of language

Preface.Notes on Contributors.Part I: Meaning and Theories of Meaning:1. Meaning and Truth Conditions: From Freges Grand Design to Davidsons: David Wiggins (University of Oxford).2. Meaning, Use, Verification: John Skorupski (University of St Andrews).3. Intention and Convention: Anita Avramides (St Hildas College, University of Oxford).4. Pragmatics: Charles Travis (University of Stirling).5. A Guide to Naturalising Semantics: Charles Travis (University of Stirling).6. Meaning and Privacy: Edward Craig (University of Cambridge).7. Tacit Knowledge: Alexander Miller (University of Michigan).8. Radical Interpretation: Jane Heal (University of Cambridge).9. Propositional Attitudes: Mark Richard (Tufts University).10. Holism: Christopher Peacocke (University of Oxford).11. Metaphor: Richard Moran (Harvard University).Part II: Language, Truth and Reality:12. Realism and its Oppositions: Bob Hale (University of Glasgow).13. Theories of Truth: Ralph C. S. Walker (Magdalen College, University of Oxford).14. Analyticity: Paul Artin Boghossian (New York University).15. Rule-following, Objectivity and Meaning: Bob Hale (University of Oxford).16. The Interdeterminacy of Translation: Crispin Wright (University of St. Andrews).17. Putnams Model-theoretical Argument against Metaphysical Realism: Bob Hale and Crispin Wright (University of St. Andrews).18. Sorites: R. M. Sainsbury and Timothy Williamson (University of Edinburgh).Part III: Reference, Identity and Necessity:19. Modality: Bob Hale (University of Oxford).20. Essentialism: Graeme Forbes (Tulane University).21. Reference and Necessity: Robert Stalnaker (MIT).22. Names and Rigid Designation: Jason Stanley (Cornell University).23. Indexicals and Demonstratives: John Perry (Stanford University).24. Objects and Criteria of Identity: E. J. Lowe (University of Durham).25. Relative Identity: Harold Noonan (University of Birmingham).Glossary.Index.

Is Hume’s Principle Analytic?

One recent ‘neologicist’ claim is that what has come to be known as “Frege’s Theorem”—the result that Hume’s Principle, plus second-order logic, suffices for a proof of the Dedekind-Peano postulate—reinstates Frege’s contention that arithmetic is analytic. This claim naturally depends upon the analyticity of Hume’s Principle itself. The present paper reviews five misgivings that developed in various of George Boolos’s writings. It observes that each of them really concerns not ‘analyticity’ but either the truth of Hume’s Principle or our entitlement to accept it and reviews possible neologicist replies. A two-part Appendix explores recent developments of the fifth of Boolos’s objections—the problem of Bad Company—and outlines a proof of the principle Nq, an important part of the defense of the claim that what follows from Hume’s Principle is not merely a theory which allows of interpretation as arithmetic but arithmetic itself. 1 It was George Boolos who, following Frege’s somewhat charitable lead at Grundlagen§63, first gave the name, “Hume’s Principle,” to the constitutive principle for identity of cardinal number: that the number of Fs is the same as the number of Gs just in case there exists a one-to-one correlation between the Fs and theGs. The interest—if indeed any—of the question whether the principle is analytic is wholly consequential on what has come to be known as Frege’s Theorem: the proof, prefigured inGrundlagen§§82–83 [5] and worked out in some detail in Wright [21] 1 that second-order logic plus Hume’s Principle as sole additional axiom suffices for a derivation of second-order arithmetic—or, more cautiously, for the derivation of a theory which allows of interpretation as second-order arithmetic. (Actually I think the caution is unnecessary—more of that later.) Analyticity, whatever exactly it is, is presumably transmissible across logical consequence. If second-order consequence is indeed a species of logical consequence, the analyticity of Hume’s Principle would ensure the analyticity of arithmetic—at least, provided it really is second-order arithmetic, and not just a theory which merely allows interpretation as such, which is a second-order consequence of Hume’s Principle. What significance that finding would have would then depend, of course, on the significance of the notion of analyticity Received April 16, 1998

Dummett and Revisionism

I want in this paper to single out the idea, recurrent throughout the writings in Truth and Other Engimas (hereafter: T&OE), that to abandon the realism with which we regard so many kinds of statement will involve us in abandoning the belief that classical logic holds valid for them.2 There is no question that much of the interest which Dummett’s writings have excited is directly consequent on this notion: we are confronted by the prospect of being constrained by pure philosophical considerations to revise and modify not merely philosophical preconceptions which we hold, but substantial sections of our basic “first order” linguistic habits and practices. My concern here is thus not with the strengths or weaknesses of realism but with these putative revisionary implications of anti-realism: what, if any, outlets are open to someone who feels the force of the anti-realist arguments which Dummett has expounded, but who desires, for whatever reason, to conserve as much of our, apparently realism-inspired, linguistic practices as he can?

Focus restored: Comments on John MacFarlane

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.

Trumping assessments and the aristotelian future

In the paper we argue that truth-relativism is potentially hostage to a problem of exhibiting witnesses of its own truth. The problem for the relativist stems from acceptance of a trumping principle according to which there is a dependency between ascriptions of truth of an utterance and ascriptions of truth to other ascriptions of truth of that utterance. We argue that such a dependency indeed holds in the case of future contingents and the case of epistemic modals and that, consequently, the relativist about these domains cannot exhibit witnesses to his relativism. In the appendix we provide some results on the relation between trumping and multi-order relativism.

About “The Philosophical Significance of Gödel’s Theorem”: Some Issues

It is a very natural supposition that, for any particular consistent formal system of arithmetic, one of the pair consisting of the Godel sentence and its negation must be true. This was rejected by Wittgenstein in the notorious appendix on Godel’s Theorem in the Remarks on the Foundations of Mathematics.1 Wittgenstein there implicitly repudiated not merely any Platonist conception of mathematics, as usually conceived, but the much more deeply rooted idea that arithmetic is in the business of description of a proper subject matter of any kind. His view, it seems, was that there simply is no defensible conception of truth for the sentences of a formal arithmetic which might coherently whether or not justifiably — be thought to outrun derivability within it.

Can There Be a Rationally Compelling Argument for Anti-Realism about Ordinary ("Folk") Psychology?

One way of showing that there can be no such argument would be to provide, to the contrary, some conclusive case for realism. Another would be to show that certain areas of discourse, including ordinary psychology, are somehow off-limits for realist/anti-realist debate that the conditions for a valid such debate are somehow abrogated when the subject matter is intentional psychology. My particular concern here is to explore a case for a distinct but no less intriguing possibility: that it may actually be a consequence of (the best version of) anti-realism about ordinary psychology that it should admit of no rationally compelling support. That, I shall suggest, may well be the situation; and if it is not, it is not clear how the consequence can be avoided save by a much more radical and sweeping view than the psychological anti-realist is likely to want or to have bargained for.

Truth and Objectivity.

Inflating deflationism minimal truth, internal realism and superassertibility convergence and cognitive command appendix - the euthyphro contrast cognitive command and the theoreticity of observation realism and the best explanation of belief quietism appendix - on an argument against the coherence of minimalism about meaning.

Relativism and Classical Logic

Let me begin with a reminder of the crude but intuitive distinction from which the relativistic impulse springs. Any of the following claims would be likely to find both supporters and dissenters: That snails are delicious That cockroaches are disgusting That marital infidelity is alright provided nobody gets hurt That a Pacific sunset trumps any Impressionist canvas and perhaps That Philosophy is pointless if it is not widely intelligible That the belief that there is life elsewhere in the universe is justified That death is nothing to fear Disputes about such claims may or may not involve quite strongly held convictions and attitudes. Sometimes they may be tractable disputes: there may be some other matter about which one of the disputing parties is mistaken or ignorant, where such a mistake or ignorance can perhaps be easily remedied, with the result of a change of heart about the original claim; or there may be a type of experience of which one of the disputing parties is innocent, and such that the effect of initiation into that experience is, once again, a change of view.

Recent work on Frege

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