David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Erkenntnis 43 (1):81 - 109 (1995)
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 BETA
Michael A. E. Dummett (1978). Truth and Other Enigmas. Harvard University Press.
Michael A. E. Dummett (2000). Elements of Intuitionism. Oxford University Press.
W. V. Quine (1986). Philosophy of Logic. Harvard University Press.
K. R. Popper (1966). Conjectures and Refutations. Les Etudes Philosophiques 21 (3):431-434.
Citations of this work BETA
Claudio Garola & Sandro Sozzo (2013). Recovering Quantum Logic Within an Extended Classical Framework. Erkenntnis 78 (2):399-419.
Claudio Garola & Luigi Solombrino (1996). The Theoretical Apparatus of Semantic Realism: A New Language for Classical and Quantum Physics. [REVIEW] Foundations of Physics 26 (9):1121-1164.
Daniele Chiffi (2012). Idiolects and Language. Axiomathes 22 (4):417-432.
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