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Intuitionistic Truth
No full textTopos: Intuitionistic Truth. Papers by C. COZZO; A. GEORGE; E. MARTINO G. USBERTI; P. PAGIN; W. RABINOWICZ K. SEGERBERG; G. SUNDHOLM; N. TENNANT; T. WILLIAMSO
Introduction
No full textPrima facie, the intuitive notion of truth seems to be¬long entirely to the realist conceptual framework, while the an¬tirealist's very enterprise appears to be, in its essence, an attempt to eliminate that notion from his own framework. However, there are some reasons to argue that the notion of truth - some notion of truth - is indispensable for the antirealistic conceptual framework. Two notions of intuitionistic truth seem possible: truth as the existence of a proof, and truth as knowability. framework
Significato e conoscenza
No full textIl libro rintraccia in primo luogo l'origine delle teorie neoverificazioniste del significato nell'intuizionismo matematico, da un lato, e in particolare nella concezione della matematica e della logica di Brouwer e Heyting, e dall'altro nelle idee di Gentzen sul modo di caratterizzare il significato delle costanti logiche mediante regole per il loro uso corretto. In secondo luogo descrive come le due tradizioni, intuizionista e formalista, confluiscono nel pensiero di Dummett, Prawitz e Martin-Löf, concorrendo nell'articolazione di una teoria antirealista del significato. Infine mette in evidenza alcuni nodi problematici irrisolti della teoria, e suggerisce spunti per uno sviluppo della teoria più aderente all'ispirazione intuizionista
Towards a semantics based on the notion of justification
No full textSuppose we want to take seriously the neoverificationist idea that an intuitionistic theory of meaning can be generalized in such a way as to be applicable not only to mathematical but also to empirical sentences. The paper explores some
consequences of this attitude and takes some steps towards the realization of this program. The general idea is to develop a meaning theory, and consequently a formal semantics, based on the idea that knowing the meaning of a sentence is
tantamount to having a criterion for establishing what is a justification for it. Section 1 motivates a requirement of epistemic transparency imposed onto justifications
conceived as mental states. In Section 2, the formal notion of justification for an atomic formula is defined, in terms of the notion of cognitive state. In Section 3, the definition is extended to logically complex formulas. In Section 4, the notion of truth-ground is introduced and is used to give a definition of logical validity
Constructivism in logic
No full textA constructive conception of logic is nowadays essentially a theory of the meaning of the logical constants. While the building of such a theory is an essentially philosophical enterprise, it presupposes a considerable amount of work both on the mathematical and on the philosophical side. The main purpose of this book is to supply the reader with the essential of such work, in order to make him able to grasp the real questions at issue in an important area of the actual philosophical debate
Names: Sense, Epistemic Content, and Denotation
No full textMy suggestion in the paper is that to know the sense of a name n is not to know some facts about the bearer of the name: it is to know a classification criterion of cognitive states. This criterion is not variable, and not contextual: it is ideally the same for every time and context, and its difference from the sense of every other name rests ultimately upon the syntactical identity of the name. This does not mean that we don’t attach information to names: we do attach it, but it is more properly qualified as the epistemic content we associate to them; epistemic content varies with the empirical situations in which a subject is involved, with his temporal and spatial location, with what he believes or knows, and so on; it accounts for what is variable and contextual to a speaker’s knowledge of his own language, and just for this reason it cannot be what we must know in order to understand the name
Logica, verità e paradosso
No full textNel corso di oltre venti secoli i paradossi semantici non hanno cessato di apparire dei mostri, generati non dal sonno della ragione ma dalla sua stessa attività, dai suoi reiterati tentativi di caratterizzare la nozione di verità. Per questo sono stati spesso relegati tra i 'capricci' del linguaggio quotidiano, e quindi di fatto accantonati. La prima parte di questo libro intende mettere in luce l'illegittimità di questa operazione di rimozione, mostrando come il problema del mentitore sorga tanto nelle lingue naturali che nelle teorie formalizzate. Una seconda parte è dedicata all'illustrazione e alla discussione delle principali linee di soluzione del problema, mentre una terza parte sviluppa un'argomentazione filosofica a sostegno della tesi che nelle lingue naturali ci sono enunciati privi di valore di verità
On the notion of justification
No full textSuppose we are prepared to conceive the meaning of a sentence as a classification criterion which enables us to establish whether something is or is not a justification to believe that sentence. Which properties of the intuitive notion of justification to believe a sentence are essential from this point of view? And how might a theoretical notion of justification for a sentence be defined? In Sections 2-5 some properties are suggested as essential, in particular Intentionality (a justification is always a justification for a sentence), Defeasibility (a justification for a sentence A can cease to be a justification for A as new information is received), and Epistemic transparency (a justification for A is not a justification for A unless it is recognized as such by an idealized knowing subject). In Section 6 the sketch of a definition is proposed, according to which a justification for a sentence A is a cognitive state in which the subject has at his disposal a certain amount of information, and the hypothesis that A is the best explanation of that information. Section 7 shows how the notion defined escapes a crucial objection to defeasible justifications recently stated by P. Casalegno
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