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Temporal and Atemporal Truth in Intuitionistic Mathematics

  • Enrico MartinoEmail author
Chapter
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Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 42)

Abstract

In Sect. 11.2, 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 the classical meaning of the logical constants and consequently is incompatible with the antirealism of orthodox Intuitionism. In Sect. 11.3, 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 hand, 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 Sect. 11.4, we uphold the view that certain consequences of the adoption of a temporal notion of truth, despite their apparent oddity, are quite acceptable from an antirealist point of view.

Keywords

Atemporal Truth Notion Oftruth Logical Constants Intuitive Potential Heyting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.FISPPA DepartmentUniversity of PaduaPaduaItaly

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