Temporal and atemporal truth in intuitionistic mathematics Export

@article{citeulike:5704981, 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.}, author = {Martino, Enrico and Usberti, Gabriele}, citeulike-article-id = {5704981}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/BF00763507}, citeulike-linkout-1 = {http://www.springerlink.com/content/q38323075216t332}, day = {1}, doi = {10.1007/BF00763507}, journal = {Topoi}, keywords = {constructivism, tense}, month = {September}, number = {2}, pages = {83--92}, posted-at = {2009-09-02 02:17:30}, priority = {2}, title = {Temporal and atemporal truth in intuitionistic mathematics}, url = {http://dx.doi.org/10.1007/BF00763507}, volume = {13}, year = {1994} }

TY - JOUR ID - citeulike:5704981 L3 - citeulike-article-id:5704981 N2 - 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. IS - 2 JF - Topoi EP - 92 TI - Temporal and atemporal truth in intuitionistic mathematics VL - 13 SP - 83 KW - constructivism KW - tense AU - Martino, Enrico AU - Usberti, Gabriele PY - 1994/09/01/ UR - http://dx.doi.org/10.1007/BF00763507 ER -