Anything worth regarding as logicism about number theory holds that its fundamental laws – in effect, the Dedekind-Peano axioms – may be known on the basis of logic and definitions alone. For Frege, the logic in question was that of the Begriffschrift – effectively, full impredicative second order logic - together with the resources for dealing with the putatively “logical objects” provided by Basic Law V of Grundgesetze. With this machinery in place, and with the course-of-values operator governed by Basic (...) Law V counting as logical, it is possible for all the definitions involved in the logicist reconstruction of arithmetic and analysis to be fully explicit, abbreviative definitions. Had Frege’s project succeeded, he would therefore have been in position – by his own lights – to regard the axioms of number theory simply as definitional abbreviations of certain theorems of his pure logic. Basic Law V, as every interested party knows, is inconsistent. But twentieth century orthodoxy would have scorned its description as a law of logic in any case, purely on the grounds of its existential fecundity. Contemporary Neo-Fregeanism in the foundations of mathematics does not, in intention at least, pick any quarrel with the idea that pure logic should be ontologically austere. It does however maintain that the existence of the natural numbers and the real numbers as classically conceived, and thereby the truth of the traditional axioms of arithmetic and analysis, may still be known a priori on the basis of logic and definitions. For the purposes of this claim, logic is once again conceived as essentially the system of Begriffschrift. But Basic Law V is superseded by a variety of abstraction principles, of which Hume's Principle is the best known example, which we are regarded as free to lay down as true by way of determination of the meaning of the non-logical vocabulary that they contain. Thus — the idea is — the Dedekind-Peano axioms, for example, may be known, a priori, to be true by virtue of their derivation in pure logic from a principle which may be regarded as stipulatively true, and whose very stipulation may be regarded as conferring content upon the sole item of non-logical vocabulary – the cardinality operator – which it contains and thereby as conferring content upon Hume's Principle itself.. (shrink)
Chapter 10 of Sosa’s important new book provides an exemplary presentation and discussion of a great dilemma for epistemologists— I’ll call it simply the Dilemma. Here is Sosa’s statement of it.
§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)
In a well-known passage in the last chapter of Frege: Philosophy of Mathematics Michael Dummett suggests that Frege’s major “mistake”—the key to the collapse of the project of Grundgesetze—consisted in “his supposing there to be a totality containing the extension of every concept defined over it; more generally [the mistake] lay in his not having the glimmering of a suspicion of the existence of indefinitely extensible concepts” (Dummett [1991, 317]). Now, claims of the form, Frege fell into paradox because……. are (...) notoriously difficult to assess even when what replaces the dots is relatively straightforward. Offerings have included, for instance, that — (A) Unrestricted quantification: Frege fell into paradox because he allowed himself to quantify over a single, all-inclusive domain of objects (Russell, Dummett). (shrink)
Metaphor enters contemporary philosophical discussion from a variety of directions. Aside from its obvious importance in poetics, rhetoric, and aesthetics, it also figures in such fields as philosophy of mind (e.g., the question of the metaphorical status of ordinary mental concepts), philosophy of science (e.g, the comparison of metaphors and explanatory models), in epistemology (e.g., analogical reasoning), and in cognitive studies (in, e.g., the theory of concept-formation). This article will concentrate on issues metaphor raises for the philosophy of language, with (...) the understanding that the issues in these various fields cannot be wholly isolated from each other. Metaphor is an issue for the philosophy of language not only for its own sake, as a linguistic phenomenon deserving of analysis and interpretation, but also for the light it sheds on non-figurative language, the domain of the literal which is the normal preoccupation of the philosopher of language. A poor reason for this preoccupation would be the assumption that purely literal language is what most language-use consists in, with metaphor and the like sharing the relative infrequency and marginal status of songs or riddles. This would not be a good reason not only because mere frequency is not a good guide to theoretical importance, but also because it is doubtful that the assumption is even true. In recent years, writers with very different concerns have pointed out that figurative language of one sort or another is a staple of the most.. (shrink)
In the Begriffschrift Frege drew no distinction—or anyway signalled no importance to the distinction—between quantifying into positions occupied by what he called eigennamen—singular terms—in a sentence and quantification into predicate position or, more generally, quantification into open sentences—into what remains of a sentence when one or more occurrences of singular terms are removed. He seems to have conceived of both alike as perfectly legitimate forms of generalisation, each properly belonging to logic. More accurately: he seems to have conceived of quantification (...) as such as an operation of pure logic, and in effect to have drawn no distinction between first-order, second-order and higherorder quantification in general. (shrink)
It is a great pleasure to have the opportunity to contribute to this volume dedicated to the critical celebration of Stephen Schiffer’s very considerable philosophical achievements. My focus will be on his recent work on vagueness.1 The broad direction of Schiffer’s researches in this area has been to give priority to what we may call the characterisation problem: the problem of saying what the vagueness of expressions of natural language consists in or, more specifically – since Schiffer takes it as (...) a given that the vagueness he is targeting consist in a propensity of vague expressions to give rise to borderline cases —the problem of saying what being a borderline case of the concept expressed by a vague expression consists in. This has not been a main preoccupation of most of the work in the field since the vagueness “boom” started in the mid 1970s. There has been a tendency to jump straight into devising semantic theories for vague languages, usually aimed at twin desiderata of saving classical logic and dissolving the various paradoxes of vagueness, with a principal focus on the standard sorites, and occasional glances at the Forced March, and others.2 Of course, such work has inevitably implicated commitment to broad conceptions of vagueness, and of borderline cases, of various kinds. The classical epistemicist approach, for example, conceives of borderline cases as instances whose correct classification in terms of the relevant concept is, for reasons it attempts to explain, unknowable. Semantic indeterminist approaches, by contrast, tend (often implicitly) to conceive of borderline cases as items to which the concept in question neither applies nor fails to apply and as coming about because our practice with the concept leaves it, in effect, merely partially defined and so ‘gappy’. A variation on this, still semantic indeterminist, regards vagueness as consisting in a phenomenon akin to divided reference, whereby a predicate, for example, may be associated with a range of extensionally distinct best candidates to be the property it refers to; borderline cases are then items which exemplify some but not all of these properties.. (shrink)
The setting of relativistic ideas about truth in the general style of semantic-theoretic apparatus pioneered by Lewis, Kaplan and others has persuaded many that they should at least be taken seriously as competition in the space of explanatory linguistic theory, a type of view which properly formulated, may offer an at least coherent — and indeed, in the view of some, a superior —account of certain salient linguistic data manifest in, for example, discourse about epistemic modals, about knowledge and about (...) matters of taste and value, and may also offer the prospect of a coherent regimentation of the Aristotelian "Open Future" (along with, perhaps, the Dummettian ’anti-real’ past.) My main purpose here to enter a reminder of certain underlying philosophical issues about relativism — about its metaphysical coherence, its metasemantic obligations, and the apparent limitations of the kind of local linguistic evidence which contemporary proponents have adduced in its favour —of which there is a risk that its apparent rehabilitation in rigorous semantic dress may encourage neglect. (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)
I have only recently come back to this debate. I left it for about ten years and more or less stopped thinking about the issues, so it’s been a great pleasure to find that others have been running on with it in the meantime and saying very creative and interesting things of, I think, considerable potential significance across wide areas of philosophy. First a bit of autobiography. I got interested in thinking about truth in a very general pluralistic way — (...) you know: maybe truth doesn’t always consist in the same kind of thing; nothing more specific than that —for two broad reasons. One was because it looked as though making some sense of different kinds of truth might help to explain why the traditional debate about truth turned out to be sterile and incomplete. Maybe the reason why the correspondence theorists, and the coherence theorists, and the pragmatists couldn’t get anywhere was because they were all overgeneralising. Of course, there were other problems with their proposals. Correspondence, for instance, notoriously had explanatory difficulties actually making out some interesting notion of correspondence, and explaining what the terms of the correspondence relation were. But the general idea of truth being determined by fit, by accuracy of some sort, doesn’t go away just because when you press, you find it’s hard to explain its parameters. It’s more resilient than that. What really seems wrong with correspondence is that it seems a tendentious way to think about mathematics, for instance, and a bad way to think about the comic: one doesn’t want to be saddled with some metaphysics of ‘out there’ comedic facts to which one's impressions about comedy may correspond just by being willing to apply ‘true’ to ordinary ascriptions of ‘funny’. The ‘out there’ view is doubtless a possible view— it’s something someone could think (and someone, in Oxford, probably does.) But it doesn’t seem that it sits well with our ordinary conceptions of truth and comedic discourse; one wants to think differently about the import of "true" in such a discourse. (shrink)
Comment on Paul Boghossian, “The nature of inference” Content Type Journal Article Pages 1-11 DOI 10.1007/s11098-012-9892-9 Authors Crispin Wright, New York University, New York, NY, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.
The pain of rejection, the sweetness of revenge Content Type Journal Article Pages 1-12 DOI 10.1007/s11098-011-9794-2 Authors Crispin Wright, Department of Philosophy, New York University, 5 Washington Place, New York, NY, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.
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)
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. (shrink)
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. (shrink)
It is common among philosophers who take an interest in the phenomenon of vagueness in natural language not merely to acknowledge higher-order vagueness but to take its existence as a basic datum— so that views that lack the resources to account for it, or that put obstacles in the way, are regarded as deficient just on that score. My main purpose in what follows is to loosen the hold of this deeply misconceived idea. Higher-order vagueness is no basic datum but (...) an illusion, fostered by misunderstandings of the nature of (ordinary, if you will ‘first-order’) vagueness itself. To see through the illusion is to take a step that is prerequisite for a correct understanding of vagueness, and for any satisfying dissolution of its attendant paradoxes. (shrink)
What is wrong with abstraction, Michael Potter and Peter Sullivan explain a further objection to the abstractionist programme in the foundations of mathematics which they first presented in their Hale on Caesar and which they believe our discussion in The Reason's Proper Study misunderstood. The aims of the present note are: To get the character of this objection into sharper focus; To explore further certain of the assumptions—primarily, about reference-fixing in mathematics, about certain putative limitations of abstractionist set theory, and (...) about the effects of impredicativity in abstraction principles—which underlie it; and To advance the debate of the issues thereby raised. Thanks for helpful comments to Roy Cook and to an anonymous referee. CiteULike Connotea Del.icio.us What's this? (shrink)
§1 To many in or on the edges of the Academy, ”Relativism” is a word with overtones of sinister iconoclasm, representing a kind of intellectual and ethical free-for-all in which the traditional investigative virtues of clarity, rigour, objectivity, consistency and the unbiased pursuit of truth are dismissed as illusory and the great scientific constructions of the last two hundred years, together with our deepest moral convictions, rated merely as ‘our way of seeing’ the world, more elaborate and organised but otherwise (...) on all fours with the cosmology and customs of primitive tribes. In his short book, Paul Boghossian aims to address, and to expose as bankrupt, the idea that there is even a coherent, let alone defensible philosophical stance about truth and knowledge that can underwrite these ‘pluralist’, or ‘postmodernist’ tendencies. But since it is crucial to his project that his style of discussion make it available to non-specialists, much of the recent more technical, less emotional debate within analytical philosophy about relativism’s renaissance as a particular form of semantic theory is passed over unmentioned. Part of my aim in what follows is to illustrate how Boghossian's discussion connects quite straightforwardly with relativism in its contemporary analytical philosophical livery—what I have elsewhere called New Age relativism1— and how some of his critical arguments may be presented in that setting. My main contentions will be, first, that when relativism about epistemic justification, and about morals, are couched in the currently canonical sort of form, they still remain in range of artillery that Boghossian positions in chapter 6 of his book; second, that there is evasive action that they can.. (shrink)
§1 It is not always true that recognizably valid reasoning from known, or otherwise epistemically warranted premises, can be enlisted to produce knowledge, or other epistemic warrant, for a conclusion. The counterexamples are cases that exhibit what I have elsewhere called warrant transmission-failure. It is nowadays widely accepted that there are indeed such counterexamples, though individual cases remain controversial. One such controversial case is the so-called McKinsey paradox. The paradox presents as a simple collision between three claims that many would (...) find attractive. (shrink)
What I am calling New Age Relativism is usually proposed as a thesis about the truth-conditions of utterances, where an utterance is an actual historic voicing or inscription of a sentence of a certain type. Roughly, it is the view that, for certain discourses, whether an utterance is true depends not just on the context of its making—when, where, to whom, by whom, in what language, and so on—and the “circumstances of evaluation”—the state of the world in relevant respects—but also (...) on an additional parameter: a context of assessment. Vary the latter and the truth-value of the utterance can vary, even though the context of its making and the associated state of the world remain fixed. (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 (though connected) (...) 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)
"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)
The central contentions of this paper are two: first, that contextualism about knowledge cannot fulfil the eirenic promise which, for those who are drawn to it, constitutes, I believe, its main attraction; secondly, that the basic diagnosis of epistemological scepticism as somehow entrapping us, by diverting attention from a surreptitious shift to a special rarefied intellectual context, rests on inattention to the details of the principal sceptical paradoxes. These contentions are consistent with knowledge-contextualism, of some stripe or other, being true. (...) What follows will not bear directly on that. (shrink)
[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)
Bob Hale & Crispin Wright (2001). Introduction. In Bob Hale & Crispin Wrigth (eds.), The Reason's Proper Study. Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University Press.
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 volume, published on the fiftieth anniversary of Wittgenstein's death, brings together thirteen of Crispin Wright's most influential essays on Wittgenstein ...
The „Paradox of the Concept Horse" arises on the assumption of the Reference Principle: that co-referential expressions should be cross-substitutable salva veritate in extensional contexts and salva congruitate in all. Accordingly no singular term can co-refer with an unsaturated expression. The paper outlines a number of desiderata for a satisfactory response to the problem and argues that recent treatments by Dummett and Wiggins fall short by their lights. It is then pointed out that a more consistent perception of the requirements (...) of the Reference Principle leads not to the Paradox but to the result that Frege had no business extending the notion of Bedeutung to unsaturated expressions in the first place. Rather the relation between, e.g., predicates and the entities that comprise the range of higher-order logical variables must be logically unlike that between singular terms and their referents; the way is therefore opened for singular terms to refer to entities of the former kind after all. The Concept Horse is a concept (and a Fregean object too.). (shrink)
Knowledge of one's own sensations, desires, intentions, thoughts, beliefs, and other attitudes is characteristically different from other kinds of knowledge: it has greater immediacy, authority, and salience. This volume offers a powerful and comprehensive look at current work on this topic, featuring closely interlinked essays by leading figures in the field that examine philosophical questions raised by the distinctive character of self-knowledge, relating it to knowledge of other minds, to rationality and agency, externalist theories of psychological content, and knowledge of (...) language. (shrink)
Lucas and Penrose have contended that, by displaying how any characterisation of arithmetical proof programmable into a machine allows of diagonalisation, generating a humanly recognisable proof which eludes that characterisation, Gödel's incompleteness theorem rules out any purely mechanical model of the human intellect. The main criticisms of this argument have been that the proof generated by diagonalisation (i) will not be humanly recognisable unless humans can grasp the specification of the object-system (Benacerraf); and (ii) counts as a proof only on (...) the (unproven) hypothesis that the object system is consistent (Putnam). The present paper argues that criticism (ii) may be met head-on by an intuitionistic proponent of the anti-mechanist argument; and that criticism (i) is simply mistaken. However the paper concludes by questioning the sufficiency of the situation for an interesting anti-mechanist conclusion. (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)
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 ...
