Prospects for Triviality

  • Luis Estrada-González
Part of the Trends in Logic book series (TREN, volume 45)


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.


Triviality Atomic triviality Real number theory Degenerate categories Internal logic 


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© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Instituto de Investigaciones FilosóficasUniversidad Nacional Autónoma de MéxicoCoyoacanMexico

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