Logic begins but does not end with the study of truth and falsity. Within truth there are the modes of truth, ways of being true: necessary truth and contingent truth. When a proposition is true, we may ask whether it could have been false. If so, then it is contingently true. If not, then it is necessarily true; it must be true; it could not have been false. Falsity has modes as well: a false proposition that could not have been (...) true is impossible or necessarily false; one that could have been true is merely contingently false. The proposition that some humans are over seven feet tall is contingently true; the proposition that all humans over seven feet tall are over six feet tall is necessarily true; the proposition that some humans are over seven feet tall and under six feet tall is impossible, and the proposition that some humans are over nine feet tall is contingently false. Of these four modes of truth, let us focus on necessity, plus a fifth: possibility. A proposition is possible if it is or could have been true; hence propositions that are either necessarily true, contingently true, or contingently false are possible. Notions that are similar to the modes of truth in being concerned with what might have been are called modal. Dispositions are modal notions, for example the disposition of fragility. Relatedly, there are counterfactual conditionals, for example “if this glass were dropped, it would break.” And the notion of supervenience is modal.1 But let us focus here on necessity and possibility. Modal words are notoriously ambiguous (or at least context-sensitive2). I may reply to an invitation to give a talk in England by saying “I can’t come; I have to give a talk in California the day before”. This use of “can’t” is perfectly appropriate. But it would be equally appropriate for me to say that I could cancel my talk in California (although that would be rude) and give the talk in England instead. What I cannot do is give both talks.. (shrink)

The goal of this paper is to explore the significance of Montague’s paradox—that is, any arithmetical theory $T\supseteq Q$ over a language containing a predicate $P$ satisfying $P\rightarrow \varphi $ and $T\vdash \varphi \,\therefore\,T\vdash P$ is inconsistent—as a limitative result pertaining to the notions of formal, informal, and constructive provability, in their respective historical contexts. To this end, the paradox is reconstructed in a quantified extension $\mathcal {QLP}$ of Artemov’s logic of proofs. $\mathcal {QLP}$ contains both explicit modalities $t:\varphi $ (...) and also proof quantifiers $x:\varphi $. In this system, the basis for the rule NEC is decomposed into a number of distinct principles governing how various modes of reasoning about proofs and provability can be internalized within the system itself. A conceptually motivated resolution to the paradox is proposed in the form of an argument for rejecting the unrestricted rule NEC on the basis of its subsumption of an intuitively invalid principle pertaining to the interaction of proof quantifiers and the proof-theorem relation expressed by explicit modalities. (shrink)

Davidson attacks the intelligibility of conceptual relativism, i.e. of truth relative to a conceptual scheme. He defines the notion of a conceptual scheme as something ordering, organizing, and rendering intelligible empirical content, and calls the position that employs both notions scheme-content dualism. He argues that such dualism is untenable since: not only can we not parcel out empirical content sentence per sentence but also the notion of uninterpreted content to which several schemes are relative, and the related notion of a (...) theory ”fitting the evidence’, can be shown to lack intelligibility too. Davidson argues further that belief in incommensurable schemes or non-intertranslatable languages is possible only on violating a correct understanding of interpretability : if we succeed in interpreting someone else then we have shown there is no need to speak of two conceptual schemes, while if we fail ”there is no ground for speaking of two.’. (shrink)

We describe in some detail how to build an infinite computing machine within a continuous Newtonian universe. The relevance of our construction to the Church-Turing thesis and the Platonist-Intuitionist debate about the nature of mathematics is also discussed.

Comprehensive account of constructive theory of first-order predicate calculus. Covers formal methods including algorithms and epi-theory, brief treatment of Markov’s approach to algorithms, elementary facts about lattices and similar algebraic systems, more. Philosophical and reflective as well as mathematical. Graduate-level course. 1963 ed. Exercises.

In “The Runabout Inference Ticket” AN Prior (1960) examines the idea that logical connectives can be given a meaning solely in virtue of the stipulation of a set of rules governing them, and thus that logical truth/consequence.

This paper examines the paradox of revisability. This paradox was proposed by Jerrold Katz as a problem for Quinean naturalised epistemology. Katz employs diagonalisation to demonstrate what he takes to be an inconsistency in the constitutive principles of Quine's epistemology. Specifically, the problem seems to rest with the principle of universal revisability which states that no statement is immune to revision. In this paper it is argued that although there is something odd about employing universal revisability to revise itself, there (...) is nothing paradoxical about this. At least, there is no paradox along the lines suggested by Katz. (shrink)

How should one react when one has a belief, but knows that other people—who have roughly the same evidence as one has, and seem roughly as likely to react to it correctly—disagree? This paper argues that the disagreement of other competent inquirers often requires one to be much less confident in one’s opinions than one would otherwise be.

How much should your confidence in your beliefs be shaken when you learn that others – perhaps 'epistemic peers' who seem as well-qualified as you are – hold beliefs contrary to yours? This article describes motivations that push different philosophers towards opposite answers to this question. It identifies a key theoretical principle that divides current writers on the epistemology of disagreement. It then examines arguments bearing on that principle, and on the wider issue. It ends by describing some outstanding questions (...) that thinking about this issue raises. (shrink)

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

The relation between linguistics and logic has been discussed in a, recent paper by Bar-Hillel} where it is argued that a disregard for workin logical syntax and semantics has caused linguists to limit themselves too narrowly in their inquiries, and to fall into several errors. In particular, Bar-Hillel asserts, they have attempted to derive relations of synonymy and so-called ‘rules of transfOI`1'Il8.tiOH,, such as the active—pussive relation, from distributional studies alone, and they have hesitated to rely on considerations of meaning (...) in linguistic analysis. No one can quarrel with the suggestion that linguists interest themselves in meaning or transformation rules, but the relevance of logical syntax and semsmticsz (at least as we now know them) to this study is very dubious. I think that a closer investigation of the assumptions and concems of logical syntax and semantics will show that the hope of applying the results which have been achieved in these fields to the solution of linguistic problems is illusory. (shrink)

Chomsky proposes a reformulation of the theory of transformational generative grammar that takes recent developments in the descriptive analysis of particular ...

This is identical with the first edition (see 21: 2716) except for the addition of a Supplement containing 5 previously published articles and the bringing of the bibliography (now 73 items) up to date. The 5 added articles present clarifications or modifications of views expressed in the first edition. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

Three experiments are reported which show that in certain contexts subjects reject instances of the valid modus ponens and modus tollens inference form in conditional arguments. For example, when a conditional premise, such as: If she meets her friend then she will go to a play, is accompanied by a conditional containing an additional requirement: If she has enough money then she will go to a play, subjects reject the inference from the categorical premise: She meets her friend, to the (...) conclusion: She will go to a play. Other contexts suppress the conditional fallacies. The first experiment demonstrates the effects of context on conditional reasoning. The second experiment shows that the inference suppression disappears when the categorical premise refers to both of the antecedents, such as: She meets her friend and she has enough money. In this case, subjects make both the valid inferences and the fallacies, regardless of the contextual information. The third experiment establishes that when subjects are given general information about the duration of a situation in which a conditional inducement was uttered, such as: If you shout then I will shoot you, they reject both the valid inferences and the fallacies. The results suggest that the interpretation of premises plays an even more central role in reasoning than has previously been admitted. Trois expériences montrent que dans certains contextes les sujets rejettent des instances valides de modus ponens et de modus tollens dans des énoncés conditionnels. Par exemple, quand une prémisse conditionnelle comme: Si elle rencontre son ami, alors elle ira jouer, est accompagnée par une phrase contenant une condition supplémentaire: Si elle a assez d'argent, alors elle ira jouer, les sujets rejettent l'inférence liant la prémisse catégorielle: Elle rencontre son ami, à la conclusion: Elle ira jouer. D'autres contextes éliminent également les inférences conditionnelles fallacieuses. La premiére expérience démontre l'effet du contexte sur la raisonnement conditionnel. La deuxiéme expérience montre que la suppression de l'inférence disparait quand la prémisse catégorielle fait référence aux deux antécédants, comme: Elle rencontre son ami et elle a assez d'argent. Dans ce cas, les sujets font aussi bien les inférences valides et fallacieuses, quelle que soit l'information contextuelle. La troisiéme expérience établit que quand l'on donne aux sujets des informations générales à propos de la durée d'une situation dans laquelle une conditionnelle a été prononcée, comme Si tu cries, alors je te tire dessus, ils rejettent autant les inférences valides que les inférences fallacieuses. Ces résultats suggèrent que l'interprétation des prémisses joue un rŏle encore plus central dans le raisonnement que l'on admettait auparavant. (shrink)

Quine correctly argues that Carnap's distinction between internal and external questions rests on a distinction between analytic and synthetic, which Quine rejects. I argue that Quine needs something like Carnap's distinction to enable him to explain the obviousness of elementary mathematics, while at the same time continuing to maintain as he does that the ultimate ground for holding mathematics to be a body of truths lies in the contribution that mathematics makes to our overall scientific theory of the world. Quine's (...) arguments against the analytic/synthetic distinction, even if fully accepted, still leave room for a notion of pragmatic analyticity sufficient for the indicated purpose. (shrink)

Reasoning is a process through which premise-attitudes give rise to a conclusion-attitude. When you reason actively you operate on the propositions that are the contents of your premise-attitudes, following a rule, to derive a new proposition that is the content of your conclusion-attitude. It may seem that, when you follow a rule, you must, at least implicitly, have the normative belief that you ought to comply with the rule, which guides you to comply. But I argue that to follow a (...) rule is to manifest a particular sort of disposition, which can be interpreted as an intention. An intention is itself a guiding disposition. It can guide you to comply with a rule, and no normative belief is required. (shrink)

This new work provides an approachable introduction to the complex system that Making It Explicit mapped out.

The problem of this paper is the discovery of criteria to identify conventions and the description of some of the more general properties of conventions with particular reference to scientific inquiry. Numerous specialized methodological investigations testify to the importance of conventions in inquiry, but none provide a general account of their operation. This paper aims to provide a necessary, if not sufficient, basis for such an account. The discussion falls into three parts: common senses of the term ‘convention’, a provisional (...) formulation of conditions under which a certain type of behavior, which we shall call conventional, occurs, as well as a description of its characters, and a brief consideration of one context of inquiry in which it appears. (shrink)

What are the philosophical views of contemporary professional philosophers? We surveyed many professional philosophers in order to help determine their views on 30 central philosophical issues. This article documents the results. It also reveals correlations among philosophical views and between these views and factors such as age, gender, and nationality. A factor analysis suggests that an individual's views on these issues factor into a few underlying components that predict much of the variation in those views. The results of a metasurvey (...) also suggest that many of the results of the survey are surprising: philosophers as a whole have quite inaccurate beliefs about the distribution of philosophical views in the profession. (shrink)

In some previous work, I tried to give a concept-based account of the nature of our entitlement to certain very basic inferences (see the papers in Part III of Boghossian 2008b). In this previous work, I took it for granted, along with many other philosophers, that we understood well enough what it is for a person to infer. In this paper, I turn to thinking about the nature of inference itself. This topic is of great interest in its own right (...) and surprisingly understudied by philosophers. A correct understanding of inference promises to shed light on a number of important topics. In particular, it threatens to undermine the sort of concept-based story about entitlement to which I had previously been attracted. (shrink)

I. Recent years have witnessed a great resurgence of interest in the writings of the later Wittgenstein, especially with those passages roughly, Philosophical Investigations p)I 38 — 242 and Remarks on the Foundations of mathematics, section VI that are concerned with the topic of rules. Much of the credit for all this excitement, unparalleled since the heyday of Wittgenstein scholarship in the early IIJ6os, must go to Saul Kripke's I4rittgenstein on Rules and Private Language. It is easy to explain why. (...) To begin with, the dialectic Kripke uncovered from Wittgenstein's.. (shrink)

Epistemic relativism has the contemporary academy in its grip. Not merely in the United States, but seemingly everywhere, most scholars working in the humanities and the social sciences seem to subscribe to some form of it. Even where the label is repudiated, the view is embraced. Sometimes the relativism in question concerns truth, sometimes justification. The core impulse appears to be a relativism about knowledge. The suspicion is widespread that what counts as knowledge in one cultural, or broadly ideological, setting (...) need not count as knowledge in another. (shrink)

Relativist and constructivist conceptions of knowledge have become orthodoxy in vast stretches of the academic world in recent times. This book critically examines such views and argues that they are fundamentally flawed. The book focuses on three different ways of reading the claim that knowledge is socially constructed, one about facts and two about justification. All three are rejected. The intuitive, common sense view is that there is a way things are that is independent of human opinion, and that we (...) are capable of arriving at belief about how things are that is objectively reasonable, and is binding on anyone capable of appreciating the relevant evidence, regardless of their social or cultural perspective. Difficult as these notions may be, it is a mistake to think that recent philosophy has uncovered powerful reasons for rejecting them. (shrink)

This essay distinguishes between metaphysical and epistemological conceptions of analyticity. The former is the idea of a sentence that is ‘true purely in virtue of its meaning’ while the latter is the idea of a sentence that ‘can be justifiably believed merely on the basis of understanding its meaning’. It further argues that, while Quine may have been right to reject the metaphysical notion, the epistemological notion can be defended from his critique and put to work explaining a priori justification. (...) Along the way, a number of further distinctions relevant to the theory of analyticity and the theory of apriority are made and their significance is explained. (shrink)

Skyrms, building on the work of Dretske, has recently developed a novel information-theoretic account of propositional content in simple signalling systems. Information-theoretic accounts of content traditionally struggle to accommodate the possibility of misrepresentation, and I show that Skyrms’s account is no exception. I proceed to argue, however, that a modified version of Skyrms’s account can overcome this problem. On my proposed account, the propositional content of a signal is determined not by the information that it actually carries, but by the (...) information that it would carry at the nearest separating equilibrium of the underlying evolutionary dynamics. I show that this amended account yields reasonable ascriptions of false propositional content in a well-known formal model of the evolution of communication , and close with a discussion of the serious but perhaps not insuperable difficulties we face in applying the account to examples of signalling in the real world. (shrink)

This paper argues that the prominent accounts of logical knowledge have the consequence that they conflict with ordinary reasoning. On these accounts knowing a logical principle, for instance, is having a disposition to infer according to it. These accounts in particular conflict with so-called ‘reasoned change in view’, where someone does not infer according to a logical principle but revise their views instead. The paper also outlines a propositional account of logical knowledge which does not conflict with ordinary reasoning.

In this paper I will argue that Tait’s axiomatic conception of mathematics implies that it is in principle impossible to be justified in believing a mathematical statement without being justified in believing that statement to be provable. I will then show that there are possible courses of experience which would justify acceptance of a mathematical statement without justifying belief that this statement is provable.

What Numbers Could Not Be’) that an adequate account of the numbers and our arithmetic practice must satisfy not only the conditions usually recognized to be necessary: (a) identify some w-sequence as the numbers, and (b) correctly characterize the cardinality relation that relates a set to a member of that sequence as its cardinal number—it must also satisfy a third condition: the ‘<’ of the sequence must be recursive. This paper argues that adding this further condition was a mistake—any w-sequence (...) would do, no matter how undecidable its ‘<’ relation. (shrink)

The only way to settle conclusively what any part of a language means is to discover the circumstances, both linguistic and non-linguistic, in which the speakers of the language are prepared to use it. This is not a new doctrine, but Wittgenstein gave it new life by dramatising the following question: If someone used an expression in a radically non-standard way, could anything he said about his state of mind convince us that he nevertheless meant it in a standard way? (...) To answer ‘No’ to this, and to generalize that answer, is to say that the last-resort criteria for what something means lie in the way in which it is used - a fairly plain statement which I shall call ‘the behavioural theory (of meaning)’ and with which I shall here have no quarrel at all. What I wish to do in the following pages is to consider the relationship between the behavioural theory and some aspects of the concept of proof. It is beyond dispute that one can be led, by one’s acceptance of certain premisses, to accept a certain conclusion. There is, though, a problem about the nature of this ‘leading’. On the one hand, it is usual to think of it as sometimes having the nature of a forcing: ‘If you say that, you are committed to admitting this also; you cannot accept the one and reject the other.’ On the other hand, the behavioural theory of meaning makes it difficult to see how there can possibly be such a relationship between the premisses and the conclusion of any proof. There are many ways of bringing out the apparent clash between the behavioural theory and the notion of logical forcing or committal. Perhaps the clearest of them arises from asking how there can be room for a concept of committal in a purely behavioural study. In this spirit, we might grant that our knowledge of some of the ways in which the parts of a language are used may lead us to expect to find certain sorts of further use and not others; and we could compare such expectations with those of an anthropologist who finds that a certain society has a matriarchal system of authority and then proceeds to investigate its inheritance laws.. (shrink)