Open AccessA Two-Part Defense of Intuitionistic Mathematics
Author(s) -
Sam Elliott
Publication year - 2021
Publication title -
stance
Language(s) - English
Resource type - Journals
eISSN - 1943-1899
pISSN - 1943-1880
DOI - 10.33043/s.14.1.27-39
Subject(s) - intuitionism , schema (genetic algorithms) , interpretation (philosophy) , epistemology , computer science , truth value , philosophy , information retrieval , linguistics
The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.