Truth, Existence and Explanation: FilMat 2016 Studies in the Philosophy of Mathematics

0496697 - FLÚ 2019 RIV CH eng M - Část monografie knihy
Peregrin, Jaroslav
Intensionality in Mathematics.
Truth, Existence and Explanation: FilMat 2016 Studies in the Philosophy of Mathematics. Cham: Springer, 2018 - (Piazza, M.; Pulcini, G.), s. 57-70. Boston Studies in the Philosophy and History of Science, 334. ISBN 978-3-319-93341-2
Grant CEP: GA ČR(CZ) GA17-15645S
Institucionální podpora: RVO:67985955
Klíčová slova: intensionality * mathematical logic * Gödel’s theorems * possible worlds
Obor OECD: Philosophy, History and Philosophy of science and technology

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.
Trvalý link: http://hdl.handle.net/11104/0289834