Temporal and atemporal truth in intuitionistic mathematics

Topoi 13 (2):83-92 (1994)
Abstract
In section 1 we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of theclassical meaning of the logical constants, and consequently is incompatible with the antirealism of orthodox intuitionism. In section 2 we show how what we call the potential intuitionistic meaning of the logical constants can be defined, on the one hand, by means of the notion of atemporal provability and, on the other, by means of the operator K of epistemic logic. Intuitionistic logic, as reconstructed within this perspective, turns out to be a part of epistemic logic, so that it loses its traditional foundational role, antithetic to that of classical logic. In section 3 we uphold the view that certain consequences of the adoption of atemporal notion of truth, despite their apparent oddity, are quite acceptable from an antirealist point of view.
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References found in this work BETA
Michael Dummett (1987). Reply to Dag Prawitz. In Barry Taylor (ed.), Michael Dummett: Contributions to Philosophy. Distributors for the United States and Canada, Kluwer Academic Publishers. 281--316.
Stewart Shapiro (ed.) (1985). Intentional Mathematics. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
Timothy Williamson (1988). Knowability and Constructivism. Philosophical Quarterly 38 (153):422-432.
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