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Intensionality in Mathematics

  • Jaroslav PeregrinEmail author
Chapter
Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 334)

Abstract

Do mathematical expressions have intensions, or merely extensions? If we accept the standard account of intensions based on possible worlds, it would seem that the latter is the case – there is no room for nontrivial intensions in the case of non-empirical expressions. However, some vexing mathematical problems, notably Gödel’s Second Incompleteness Theorem, seem to presuppose an intensional construal of some mathematical expressions. Hence, can we make room for intensions in mathematics? In this paper we argue that this is possible, provided we give up the standard approach to intensionality based on possible worlds.

Notes

Acknowledgements

Work on this paper was supported by Grant No. 17-15645S of the Czech Science Foundation.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of PhilosophyCzech Academy of SciencesPragueCzech Republic
  2. 2.Faculty of PhilosophyUniversity of Hradec KrálovéHradec KrálovéCzech Republic

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