The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...) problems. (shrink)

Leibniz had a well-known argument against the existence of infinite wholes that is based on the part-whole axiom: the whole is greater than the part. The refutation of this argument by Russell and others is equally well known. In this note, I argue (against positions recently defended by Arthur, Breger, and Brown) for the following three claims: (1) Leibniz himself had all the means to devise and accept this refutation; (2) This refutation does not presuppose the consistency of Cantorian set (...) theory; (3) This refutation does not cast doubt on the part-whole axiom. Hence, should there be an obstacle to Gödel's wish to integrate Cantorian set theory within Leibniz' philosophy, it will not be this famous argument of Leibniz'. (shrink)

Simon Blackburn defends a 'quasi-realist' view intended to preserve much of what realists want to say about moral discourse. According to error theory, moral discourse is committed to indefensible metaphysical assumptions. Quasi-realism seems to preserve ontological frugality, attributing no mistaken commitments to our moral practices. In order to make good this claim, quasi-realism must show that (a) the seemingly realist features of the 'surface grammar' of moral discourse can be made compatible with projectivism; and (b) certain realist-sounding statements which we (...) might use in describing the nature of our moral commitments can be understood in projectivist terms. Much attention has been devoted to whether quasi-realism can deliver (a). I raise an important difficulty with regard to (b). (shrink)

Consider the following argument written on the board in room 227: 1 = 1. So, the argument on the board in room 227 is not valid. This argument generates a paradox. The aim of this paper is to present a resolution of this paradox and related paradoxes of validity, including a version of the Curry paradox. The proposal stresses the close connections between these validity paradoxes and paradoxes of truth and paradoxes of denotation. So a more general aim is to (...) provide a unified response to semantic paradox. The positive proposal is in part inspired by a brief, tantalizing suggestion of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concept of validity, for example, is everywhere applicable except for certain singular points or singularities. A second central claim is that ‘valid’ is a context-sensitive predicate. The key notions of this contextual-singularity theory are presented and applied to a variety of cases. Any purported solution to paradox must deal with the phenomenon of revenge, and a response to revenge is outlined. The paper closes with remarks about the accommodation of Tarski’s claim that natural languages are universal. (shrink)

I argue for an account of semantic paradox that requires minimal logical revision. I first consider a phenomenon that is common to the paradoxes of definability, Russell’s paradox and the Liar. The phenomenon—which I call Repetition—is this: given a paradoxical expression, we can go on to produce a semantically unproblematic expression composed of the very same words. I argue that Kripke’s and Field’s theories of truth make heavy weather of Repetition, and suggest a simpler contextual account. I go on to (...) outline a ‘singularity’ theory of semantical predicates in the spirit of remarks of Gödel. According to this theory, ‘denotes’, ‘extension’ and ‘true’ are context-sensitive expression that apply almost everywhere on a given occasion of use, except for certain singular points. I then turn to revenge paradoxes, and argue that even the dialetheist is subject to revenge. I then examine how the singularity theory responds to revenge. (shrink)

Cet ouvrage de Pascal Engel doit être fortement recommandé pour plusieurs raisons. On est d'abord frappé par l'ampleur du travail accompli et l'étendue du domaine couvert. La documentation est fouillée, l'exposé est clair et un équilibre est toujours maintenu entre les questions générales et les questions de détail. Engel ne perd jamais de vue la perspective d'ensemble qu'il s'est donnée et qui concerne la nature de la logique, y compris lorsqu'il s'emploie à faire certaines nuances ou à proposer une distinction (...) subtile. Il aurait été facile en pareille matière de proposer un mauvais choix de thèmes. Là encore, Engel s'est bien acquitté de sa tâche. On a affaire à un ouvrage dans lequel l'auteur va toujours droit à l'essentiel. Plusieurs sujets sont à peine effleurés, mais cette décision est très souvent heureuse puisqu'elle permet à l'auteur d'établir des liens entre des problématiques qui, de prime abord, semblent très éloignées les unes des autres. L'auteur fait montre d'un étonnant esprit de synthèse et plusieurs thèmes font, à ma connaissance, une première apparition dans la littérature philosophique francophone. Il s'agit donc d'une contribution à la philosophie de la logique qui mérite d'être signalée. On regrettera peut-être la présence d'un assez grand nombre d'erreurs typographiques. Dans la plupart des cas, il ne s'agit que de coquilles mais, dans d'autres cas, elles risquent de nuire à la compréhension du texte surtout lorsqu'elles interviennent dans des formules ou des définitions. (shrink)

This paper considers how to best relate the competing accounts of scientific knowledge that Russell and Reichenbach proposed in the 1930s and 1940s. At the heart of their disagreements are two different accounts of how to best combine a theory of knowledge with scientific realism. Reichenbach argued that a broadly empiricist epistemology should be based on decisions. These decisions or “posits” informed Reichenbach’s defense of induction and a corresponding conception of what knowledge required. Russell maintained that a scientific realist must (...) abandon empiricism in favor of knowledge of some non-demonstrative principles with a non-empirical basis. After identifying the best versions of realism offered by Reichenbach and Russell, the paper concludes with a brief discussion of the limitations of these two approaches. (shrink)

Structured propositions are often invoked to explain why intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. As the semantics is standardly developed—for example, in Salmon, Soames :47–87, 1987) and King :516–535, 1995), the semantic value of a complex expression is an ordered complex consisting of the semantic values of its components. Such views, however, trivialize semantic composition since they do not allow for independent constraints on the meaning of complexes. Trivializing semantic composition risks “trivializing semantics” Semantics versus (...) pragmatics, Oxford University Press, Oxford, 2005). Yet, proponents of structured propositions suggest a route to reimpose substantive compositionality. While the mapping from a sentence to the structured proposition it expresses is trivially compositional, there is a non-trivial mapping from the structured proposition to its truth-value. This non-trivial level of semantic composition allows the meanings assigned to complex expressions to impose substantive constraints on the meanings of the simple ones. I first articulate the basic desiderata: an account of structured propositions capable of explaining attitude attributions and of delivering a non-trivially compositional semantics. I then show that the two-stage semantics proposed by standard proponents of structured propositions does not satisfy these joint goals. (shrink)

This paper is a critical examination of Stephen Neale's *The Philosophical Significance of Godel's slingshot*. I am sceptical of the philosophical significance of Godel’s Slingshot (and of Slingshot arguments in general). In particular, I do not believe that Godel’s Slingshot has any interesting and important philosophical consequences for theories of facts or for referential treatments of definite descriptions. More generally, I do not believe that any Slingshot arguments have interesting and important philosophical consequences for theories of facts or for referential (...) treatments of definite descriptions. Friends of facts and referential treatments of definite descriptions can, and should, proceed with the construction of their theories, blithely ignoring the many Slingshots which now litter the landscape. (Of course, there may be other considerations which should give such theorists pause -- but those are other considerations.). (shrink)

This is the introductory essay to a collection commemorating the 100th anniversary of the publication in Mind of Bertrand Russell’s paper ‘On Denoting’.

Despite the renown of ‘On Denoting’, much criticism has ignored or misconstrued Russell's treatment of scope, particularly in intensional, but also in extensional contexts. This has been rectified by more recent commentators, yet it remains largely unnoticed that the examples Russell gives of scope distinctions are questionable or inconsistent with his own philosophy. Nevertheless, Russell is right: scope does matter in intensional contexts. In Principia Mathematica, Russell proves a metatheorem to the effect that the scope of a single occurrence of (...) a description in an extensional context does not matter, provided existence and uniqueness conditions are satisfied. But attempts to eliminate descriptions in more complicated cases may produce an analysis with more occurrences of descriptions than featured in the analysand. Taking alternation and negation to be primitive (as in the first edition of Principia), this can be resolved, although the proof is non-trivial. Taking the Sheffer stroke to be primitive (as proposed by Russell in the second edition), with bad choices of scope the analysis fails to terminate. (shrink)

Part 1 sets out the logical/semantical background to ‘On Denoting’, including an exposition of Russell's views in Principles of Mathematics, the role and justification of Frege's notorious Axiom V, and speculation about how the search for a solution to the Contradiction might have motivated a new treatment of denoting. Part 2 consists primarily of an extended analysis of Russell's views on knowledge by acquaintance and knowledge by description, in which I try to show that the discomfiture between Russell's semantical and (...) epistemological commitments begins as far back as 1903. I close with a non-Russellian critique of Russell's views on how we are able to make use of linguistic representations in thought and with the suggestion that a theory of comprehension is needed to supplement semantic theory. (shrink)

Russell is often accused of having a naive ‘Fido’–Fido theory of meaning of the sort Wittgenstein attacked at the beginning of the Philosophical Investigations. In this paper I argue that he never held such a theory though I concede that, prior to 1918, he said various things that might lead a very careless reader to suppose that he had. However, in The Analysis of Mind, a book which we know Wittgenstein studied closely, Russell put forward an account of understanding an (...) utterance which clearly anticipates the use theory of meaning usually attributed to Wittgenstein. The paper concludes with some problems for understanding the use theory of meaning as presented by both Russell and, derivatively, Wittgenstein. (shrink)

In this paper I describe the birth of Russell’s notion of a propositional function on 3 May 1902 and its immediate context and implications. In particular, I consider its significance in relation to the development of his views on analysis.

Einstein considered fallibilist methodology obvious and metaphysics the challenging heuristic of physics. This philosophy is a minority view in academic philosophy. Most commentators on Einstein reject it and either refuse to ascribe it to him or declare it an impediment to his researches, his own opinion to the contrary notwithstanding.

This Companion to the philosophy of science reflects fairly well the gloomy state of affairs in this subfield at its best—concerns, problems, prejudices, and all. The field is still stuck with the problem of justification of science, refusing to admit that there is neither need nor possibility to justify science and forbid dissent from it.

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

The Institute Vienna Circle held a conference in Vienna in 2003, Cambridge and Vienna a?

This thesis explores the development of Bertrand Russell‘s theory of definite descriptions. It aims at demonstrating the connection between Russell‘s views on the subject of denoting and his attempt, in the period 1903-05, to develop a solution to 'the Contradiction'. The thesis argues that the discovery of the theory of descriptions, and the way in which it works, are best understood against the backdrop of Russell‘s work on the paradoxes. A new understanding of Russell‘s seminal paper 'On Denoting' is presented, (...) including a novel interpretation of the notorious 'Gray‘s Elegy Argument', in which Russell argues against his earlier theory of denoting. That Russell‘s work on denoting is connected to his work on the paradoxes is reasonably well-known: the nature of the connection has not, however, been adequately brought out in the literature. This is addressed through demonstrating the relationship between Russell‘s work on denoting and his development of the 'substitutional theory' of classes and relations. This theory eliminates classes and propositional functions in favour of matrices and substitutions. The role of the theory of descriptions in the development of the substitutional theory is commonly supposed to be merely that the theory of descriptions facilitates the ontological elimination of classes. But this elimination was equally possible on Russell‘s earlier theory of denoting. In the thesis it is suggested that the theory of descriptions brings with it a new conception of analysis, and that it is through the introduction of this new form of analysis—rather than through the elimination of classes—that the theory of descriptions facilitates the substitutional approach. (shrink)

Russell's nonchalant response to Newman's apparently devastating critique of his structural realism presents a puzzle: if Russell conceded the point why did he not alter his theory or address the problem in print? I argue that Newman had merely pointed out an ambiguity in the formulation of Russell's theory in Analysis of Matter, and Russell already had the resources to avoid the problem through his contention that some relations are perceived. This concession gives his criterion of structural equivalence enough empirical (...) purchase to avoid Newman's triviality objection without the need to make stronger claims of knowledge of external relations than are present in Analysis of Matter. This provides a precise criterion of structural equivalence that explains exactly how the structural realist may escape Newman's objection by taking relations in intension. (shrink)