Topoi

, Volume 13, Issue 2, pp 127–133

Intuitionistic mathematics does not needex falso quodlibet

Authors

  • Neil Tennant
    • The Ohio State University and Churchill College
Article

DOI: 10.1007/BF00763511

Cite this article as:
Tennant, N. Topoi (1994) 13: 127. doi:10.1007/BF00763511

Abstract

We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX. Thus IR establishes the same inconsistencies and theorems as intuitionistic logic, and allows one to prove every intuitionistic consequence of any consistent set of premisses.

Copyright information

© Kluwer Academic Publishers 1994