The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new (...) realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of prooftheoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones. (shrink)

In the spirit of B. C. van Fraassen's view of science called Constructive Empiricism, we propose a scientific criterion to decide whether a concrete object is observable, as well as a coextensive scientific-philosophical definition of observability, and we sketch a rigorous account of modal language occurring in science. We claim that our account of observability solves three problems to which current accounts of observability, notably van Fraassen's own accounts, give rise. We further claim that our account of modal propositions (subjunctive (...) conditionals included), which proceeds wholly within the framework of the semantic view on scientific theories, grounds his claim that such an account is possible without relying on ‘inflationary metaphysics’, notably without postulating an infinitude of different universes besides the universe we inhabit. We thus claim to solve a fourth problem: how to give a precise nominalist account of modal language in science tailor-made for Constructive Empiricism. Introduction: Rough Guides The semantic view and the wave theory of light A scientific guide and a scientific criterion A New Rough Guide and a definition The Context Problem and Psillos' Problem Musgrave's Problem Modality without inflationary metaphysics Exitum. (shrink)

In this paper it is argued that herzberger's general theory of presupposition may be successfully applied to category mistakes. The study offers an alternative to thomason's supervaluation treatment of sortal presupposition and as an indirect measure of the relative merits of the two-Dimensional theory to supervaluations. Bivalent, Three-Valued matrix, And supervaluation accounts are compared to the two-Dimensional theory according to three criteria: (1) abstraction from linguistic behavior, (2) conformity of technical to preanalytic distinctions, And (3) ability to capture classical logic. (...) A matrix like characterization of thomason's theory is reported. (shrink)

In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n<ω, for da Costa's hierarchy of propositional paraconsistent logics Cn, 1≤n<ω. In our tableaux formulation, we introduce da Costa's “ball” operator “o”, the generalized operators “k” and “(k)”, for 1≤k, and the negations “~k”, for k≥1, as primitive operators, differently to what has been done in the literature, where these operators are usually defined operators. We prove a version of Cut Rule for the TNDC n, 1≤n<ω, (...) and also prove that these systems are logically equivalent to the corresponding systems Cn, 1≤n<ω. The systems TNDC n constitute completely automated theorem proving systems for the systems of da Costa's hierarchy Cn, 1≤n<ω. (shrink)

In this paper, we define some consequence relations based on supervaluation semantics for partial models, and we investigate their properties. For our main consequence relation, we show that natural versions of the following fail: upwards and downwards Lowenheim-Skolem, axiomatizability, and compactness. We also consider an alternate version for supervaluation semantics, and show both axiomatizability and compactness for the resulting consequence relation.

In “The Myth of Factive Verbs” (Hazlett 2010), I had four closely related goals. The first (pp. 497-99, p. 522) was to criticize appeals to ordinary language in epistemology. The second (p. 499) was to criticize the argument that truth is a necessary condition on knowledge because “knows” is factive. The third (pp. 507-19) – which was the intended means of achieving the first two – was to defend a semantics for “knows” on which <S knows p> can be true (...) even if p isn’t true. The fourth (Ibid.) – which seemed necessary for the success of the third – was to defend a pragmatic account of the fact that utterances of <S knows p> typically imply p, on which the implication in those cases is down to conversational implicature. In this paper I’ll go after these goals again, with an emphasis on the second. Our topic will be whether the factivity of “knows” (whatever this amounts to) supports the truth condition on knowledge. A new goal will be to defend my argument against some criticisms from John Turri (2011) and Savas Tsohatzidis (forthcoming). We’ll first look at the truth condition (§1) and factive presupposition (§§2 – 3), before turning to replies to Turri and Tsohatzidis (§§4 – 7). (shrink)

The aim of the article is to outline the historical background and the present state of the methodology of deductive systems invented by Alfred Tarski in the thirties. Key notions of Tarski's methodology are presented and discussed through, the recent development of the original concepts and ideas.

The paper describes in detail the procedure of identification of the inner language and an inner logico of a physical theory. The procedure is a generalization of the original ideas of J. von Neuman and G. Birkhoff about quantum logic.

Atomists explain properties of wholes as compositions of properties of their parts; in particular properties of complex expressions as composed of properties of their parts. Especially, semantic atomists explain meanings of complex expressions as composed of meanings of their parts. Holists deny themselves this way: they insist that at least in some cases properties of wholes are more basic than, or not reducible to, properties of their parts; in particular, semantic holists claim that meanings of (at least some) wholes are (...) more basic than meanings of parts. Now as atomists have composition as the way of getting themselves from the meanings of parts to the meanings of wholes, holists need something to get them from the meanings of wholes to those of their parts. What is usually invoked in this context is the concept of intersubstitutivity, which is, however, not always wholly clear. (shrink)