Temporal and atemporal truth in intuitionistic mathematics

Topoi 13 (2):83-92 (1994)
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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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Author Profiles

Gabriele Usberti
Università degli Studi di Siena

References found in this work

Elements of Intuitionism.Michael Dummett - 1977 - New York: Oxford University Press. Edited by Roberto Minio.
The Philosophical Basis of Intuitionistic Logic.Michael Dummett - 1978 - In Truth and other enigmas. Cambridge: Harvard University Press. pp. 215--247.
Knowability and constructivism.Timothy Williamson - 1988 - Philosophical Quarterly 38 (153):422-432.
Knowability and Constructivism.Timothy Williamson - 1988 - Philosophical Quarterly 38 (53):422-432.
Intensional Mathematics.Stewart Shapiro - 1989 - Philosophy of Science 56 (1):177-178.

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