Ian Rumfitt

According to Quine, in any disagreement over basic logical laws the contesting parties must mean different things by the connectives or quantifiers implicated in those laws; when a deviant logician ‘tries to deny the doctrine he only changes the subject’. The standard semantics for intuitionism offers some confirmation for this thesis, for it represents an intuitionist as attaching quite different senses to the connectives than does a classical logician. All the same, I think Quine was wrong, even about the dispute between classicists and intuitionists. I argue for this by presenting an account of consequence, and a cognate semantic theory for the language of the propositional calculus, which respects the meanings of the connectives as embodied in the familiar classical truth-tables, does not presuppose Bivalence, and with respect to which the rules of the intuitionist propositional calculus are sound and complete. Thus the disagreement between classicists and intuitionists, at least, need not stem from their attaching different senses to the connectives; one may deny the doctrine without changing the subject. The basic notion of my semantic theory is truth at a possibility, where a possibility is a way that things might be, but which differs from a possible world in that the way in question need not be fully specific or determinate. I compare my approach with a previous theory of truth at a possibility due to Lloyd Humberstone, and with a previous attempt to refute Quine’s thesis due to John McDowell

It seems beyond doubt that a thinker can come to know a conclusion by deducing it from premisses that he knows already, but philosophers have found it puzzling how a thinker could acquire knowledge in this way. Assuming a broadly externalist conception of knowledge, I explain why judgements competently deduced from known premisses are themselves knowledgeable. Assuming an exclusionary conception of judgeable content, I further explain how such judgements can be informative. (According to the exclusionary conception, which I develop from some remarks in Ramsey, a judgement's content is given by the hitherto live possibilities that it excludes or rules out.) I propose that the value of logic lies in its allowing us to combine different sources of knowledge, so that we can learn things that we could not learn from those sources individually. I conclude by arguing that while single-conclusion logics possess that value, multiple-conclusion logics do not.

In his essay ‘“Wang’s Paradox”’, Crispin Wright proposes a solution to the Sorites Paradox (in particular, the form of it he calls the ‘Paradox of Sharp Boundaries’) that involves adopting intuitionistic logic when reasoning with vague predicates. He does not give a semantic theory which accounts for the validity of intuitionistic logic (and the invalidity of stronger logics) in that area. The present essay tentatively makes good the deficiency. By applying a theorem of Tarski, it shows that intuitionistic logic is the strongest logic that may be applied, given certain semantic assumptions about vague predicates. The essay ends with an inconclusive discussion of whether those semantic assumptions should be accepted.

In developing his alternative, Brandom starts from a version of inferential-role semantics according to which an assertion's content is constituted by its place in a field of inferential relations. It is because we have "an independent theoretical grip on the notion of an inference", and of its goodness or badness, that we are able to attain a notion of content that is prior to any of the representational concepts. He stresses that the relevant assessment of inferences is not whether they are logically valid, but whether they are "materially correct," in a sense that Sellars is said to have succeeded in explaining. "As examples, consider the inference from 'Pittsburgh is to the West of Philadelphia' to 'Philadelphia is to the East of Pittsburgh', the inference from 'Today is Wednesday' to 'Tomorrow is Thursday', and that from 'Lightning is seen now' to 'Thunder will be heard soon'. It is the contents of the concepts West and East that make the first a good inference... and the contents of the concepts lightning and thunder, as well as the temporal concepts, that underwrite the third". Subsentential contents are extracted from the sentential contents thereby identified using substitutional methods derived from Frege.

Many prominent writers on the philosophy of logic, including Michael Dummett, Dag Prawitz, Neil Tennant, have held that the introduction and elimination rules of a logical connective must be ‘in harmony ’ if the connective is to possess a sense. This Harmony Thesis has been used to justify the choice of logic: in particular, supposed violations of it by the classical rules for negation have been the basis for arguments for switching from classical to intuitionistic logic. The Thesis has also had an influence on the philosophy of language: some prominent writers in that area, notably Dummett and Robert Brandom, have taken it to be a special case of a more general requirement that the grounds for asserting a statement must cohere with its consequences. This essay considers various ways of making the Harmony Thesis precise and scrutinizes the most influential arguments for it. The verdict is negative: all the extant arguments for the Thesis are weak, and no version of it is remotely plausible.

[Ian Rumfitt] Frege's logicism in the philosophy of arithmetic consisted, au fond, in the claim that in justifying basic arithmetical axioms a thinker need appeal only to methods and principles which he already needs to appeal in order to justify paradigmatically logical truths and paradigmatically logical forms of inference. Using ideas of Gentzen to spell out what these methods and principles might include, I sketch a strategy for vindicating this logicist claim for the special case of the arithmetic of the finite cardinals. /// [Timothy Williamson]The paper defends the intelligibility of unrestricted quantification. For any natural number n, 'There are at least n individuals' is logically true, when the quantifier is unrestricted. In response to the objection that such sentences should not count as logically true because existence is contingent, it is argued by consideration of cross-world counting principles that in the relevant sense of 'exist' existence is not contingent. A tentative extension of the upward Löwenheim-Skolem theorem to proper classes is used to argue that a sound and complete axiomatization of the logic of unrestricted universal quantification results from adding all sentences of the form 'There are at least n individuals' as axioms to a standard axiomatization of the first-order predicate calculus

In what does the sense of a sentential connective consist? Like many others, I hold that its sense lies in rules that govern deductions. In the present paper, however, I argue that a classical logician should take the relevant deductions to be arguments involving affirmative or negative answers to yes-or-no questions that contain the connective. An intuitionistic logician will differ in concentrating exclusively upon affirmative answers. I conclude by arguing that a well known intuitionistic criticism of classical logic fails if the answer "No" is accorded parity with the answer "Yes".

The paper addresses itself to the "Homeric struggle" in the theory of meaning between those (e.g., Grice) who try to analyze declarative meaning in terms of an intention to induce a belief and those (e.g., Davidson) for who declarative meaning consists in truth conditions. (The point of departure is Strawson's celebrated discussion of this issue, in his Inaugural Lecture.) I argue that neither style of analysis is satisfactory, and develop a "hybrid" that may be-although what I take from the Gricean side in the struggle is not the notion of an intention, but that of somebody's reason for speaking as he does. The paper applies the hybrid analysis to resolve certain problems connected with the rationale for compositional, truth-theoretic semantics

In developing his alternative, Brandom starts from a version of inferential-role semantics according to which an assertion's content is constituted by its place in a field of inferential relations. It is because we have "an independent theoretical grip on the notion of an inference", and of its goodness or badness, that we are able to attain a notion of content that is prior to any of the representational concepts. He stresses that the relevant assessment of inferences is not whether they are logically valid, but whether they are "materially correct," in a sense that Sellars is said to have succeeded in explaining. "As examples, consider the inference from 'Pittsburgh is to the West of Philadelphia' to 'Philadelphia is to the East of Pittsburgh', the inference from 'Today is Wednesday' to 'Tomorrow is Thursday', and that from 'Lightning is seen now' to 'Thunder will be heard soon'. It is the contents of the concepts West and East that make the first a good inference... and the contents of the concepts lightning and thunder, as well as the temporal concepts, that underwrite the third". Subsentential contents are extracted from the sentential contents thereby identified using substitutional methods derived from Frege.

In his 'paratactic' analysis of indirect speech reports, Davidson took the occurrence of 'that' in 'Galileo said that the Earth moves' to be a demonstrative expression which refers to the reporter's subsequent utterance of 'the Earth moves'. Ian McFetridge used his 'counting problem' to argue that we get a better version of the paratactic theory if we take the demonstrative 'that' to refer to the proposition expressed by the reporter's utterance, rather than to the utterance itself. In this note, I defend McFetridge's argument against an objection of Richard Holton's.

In his book The Things We Mean, Stephen Schiffer advances a subtle defence of what he calls the ‘face-value’ analysis of attributions of belief and reports of speech. Under this analysis, ‘Harold believes that there is life on Venus’ expresses a relation between Harold and a certain abstract object, the proposition that there is life on Venus. The present essay first proposes an improvement to Schiffer’s ‘pleonastic’ theory of propositions. It then challenges the face-value analysis. There will be such things as propositions only if they possess conditions of identity and distinctness. By analyzing Frege’s theory of propositions (Gedanken), I argue that such conditions may be found for the special case of beliefs and sayings advanced as premises and conclusions of deductive arguments. These conditions, however, are not applicable to most ordinary beliefs and sayings. Ordinary attributions and reports, then, do not place thinkers and speakers in relations to propositions. A bonus is exposure of the fallacy in the Putnam-Taschek objection to Frege’s theory of sense and reference.

Book synopsis: The philosophy of modality investigates necessity and possibility, and related notions--are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This volume presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the papers address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal logic and its relations to necessary existence and to counterfactual reasoning. The general introduction locates the individual contributions in the wider context of the contemporary discussion of the metaphysics and epistemology of modality