Chapter

Logical Studies of Paraconsistent Reasoning in Science and Mathematics

Volume 45 of the series Trends in Logic pp 81-89

Date:

Prospects for Triviality

  • Luis Estrada-GonzálezAffiliated withInstituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México Email author 

Abstract

In this paper I argue, contra Mortensen, that there is a case, namely that of a degenerate topos, an extremely simple mathematical universe in which everything is true, in which no mathematical “catastrophe” is implied by mathematical triviality. I will show that either one of the premises of Dunn’s trivialization result for real number theory –on which Mortensen mounts his case– cannot obtain (from a point of view “external” to the universe) and thus the argument is unsound, or that it obtains in calculations “internal” to such trivial universe and the theory associated, yet the calculations are possible and meaningful albeit extremely simple.

Keywords

Triviality Atomic triviality Real number theory Degenerate categories Internal logic