1,234 research outputs found
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 textThe volume collects contributions on the question of the nature of mathematical, empirical and ethical statements, most of which were originally at the Conference "Justification and Meaning" held at the University of Siena, Certosa di Pontignano, on June 15th-17th 2000. Papers by M Dummett, G. Soldati, C. Cozzo, C. Penco, E. Martino, W.W. Tait, P. Casalegno, D. Prawitz, F. Pataut, G. Usberti, J. Skorupski, C. Bagnoli, R. Wedgwood, T. Magri, V. Tiberius, J. Taylor, J. Bransen, P.W. Ross, M. van Roojen, E. Millgra
Gettier Problems, C-Justifications, and C-Truth-Grounds
No full textThis paper is a continuation of Usberti (forthcoming), in which I proposed, as the key notion of an anti-realist theory of the meaning of empirical statements, the theoretical notion of C-justification for A, where A is an empirical statement that can be translated into a sentence of first order logic. Here I suggest, first, an extension of the definition of C-justification to statements of the forms “s justifiedly believes that A” and “s knows that A”; second, a characterization of the assertibility conditions of all the statements for which the notion of C-justification has been defined. The definition of C-justifications for “s knows that A” will involve and an analysis of Gettier problems and the definition of the notion of C-truth-ground of A
Inference and Epistemic Transparency
No full textIn his paper â Explaining Deductive Inferenceâ Prawitz states what he calls «a fundamental problem of logic and the philosophy of logic»: the problem of explaining «Why do certain inferences have the epistemic power to confer evidence on the conclusion when applied to premisses for which there is evidence already?». In this paper I suggest a way of articulating, and partly modifying, the intuitionistic answer to this problem in such a way as to both answer Prawitzâ s problem and satisfy a requirement I argue to be crucial for any epistemic theory of the meaning of the logical constants: the requirement that evidence is epistemically transparent
A Notion of C-Justification for Empirical Statements
No full textAfter having argued that Prawitz’s notion of ground for A is not epistemically transparent when A is an empirical statement (§1), a non-factive and defeasible notion of C-justification (“C” for “computational”) for empirical statements is defined and proposed as the key notion of the theory of meaning. C-justifications for A are conceived as cognitive states (§2), and are defined by recursion on the logical complexity of A. In the atomic case (§3) they are defined in terms of two other concepts: the one of C- authorization to use a name to refer to a given entity, and the one of C-authorization to use a predicate in order to apply an accessible concept to objects. In the logically complex cases (§4) the meaning of the logical constants as applied to empirical statements is discussed, and the necessity is shown of Nelson’s strong negation besides intuitionistic negation. In the conclusion (§5) it is argued that the notion defined is epistemically transparent and not exposed to traditional objections
Anti-Realist Truth and Truth-Recognition
No full textI will be concerned with the following question: are there compelling arguments for postulating a distinction between the truth of a statement and the recognition of its truth, when truth is conceived along the lines of a suitable generalization of the intuitionistic idea that it should be characterized as the existence of a proof? I will argue that the distinction is not necessary within the conceptual framework of intuitionism by replying to two arguments to the contrary, one based on the paradox of inference, the other on considerations concerning the content of a statement
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
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