Abstract
The proof-theoretic analysis of logical semantics undermines the received view of proof theory as being concerned with symbols devoid of meaning, and of model theory as the sole branch of logical theory entitled to access the realm of semantics. The basic tenet of proof-theoretic semantics is that meaning is given by some rules of proofs, in terms of which all logical laws can be justified and the notion of logical consequence explained. In this paper an attempt will be made to unravel some aspects of the issue and to show that this justification as it stands is untenable, for it relies on a formalistic conception of meaning and fails to recognise the fundamental distinction between semantic definitions and rules of inference. It is also briefly suggested that the profound connection between meaning and proofs should be approached by first reconsidering our very notion of proof.
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References
M. Dummett (1991) The Logical Basis of Metaphysics Duckworth London
G. Gentzen (1935) ArticleTitle‘Untersuchungen über das logische Schließen’ Mathematische Zeitschrift 39 IssueID176–210 405–431 Occurrence Handle10.1007/BF01201363
S. MacLane (1998) Categories for the Working Mathematician EditionNumber2 Springer Berlin
P. Martin-Löf (1984) Intuitionistic Type Theory Bibliopolis Napoli
Martin-Löf, P.: 1985, ‘On the Meanings of the Logical Constants and the Justifications of the Logical Laws’, repr. in Nordic Journal of Philosophical Logic 1(1996), 11–60.
D. Prawitz (1965) Natural Deduction: A Proof-Theoretical Study Almqvist & Wiksell Stockholm
D. Prawitz (1985) ArticleTitle‘Remarks on Some Approaches to the Concept of Logical Consequence’ Synthese 62 153–171 Occurrence Handle10.1007/BF00486044
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Contu, P. The Justification of the Logical Laws Revisited. Synthese 148, 573–588 (2006). https://doi.org/10.1007/s11229-004-6270-y
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DOI: https://doi.org/10.1007/s11229-004-6270-y