A pragmatic interpretation of intuitionistic propositional logic

Erkenntnis 43 (1):81-109 (1995)
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Abstract

We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined classically, and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic.

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References found in this work

Philosophy of Logic.Willard Van Orman Quine - 1970 - Harvard University Press.
Truth and Other Enigmas.Michael Dummett - 1978 - Cambridge, MA, USA: Harvard University Press.
Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
Meaning and the Moral Sciences.Hilary Putnam - 1978 - Routledge and Kegan Paul.
Elements of Symbolic Logic.Hans Reichenbach - 1947 - London: Dover Publications.

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