Journal of Philosophical Logic

, Volume 42, Issue 1, pp 195-219

First online:

Paradox and Potential Infinity

  • Charles McCartyAffiliated withThe Logic Program, Indiana University Email author 

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We describe a variety of sets internal to models of intuitionistic set theory that (1) manifest some of the crucial behaviors of potentially infinite sets as described in the foundational literature going back to Aristotle, and (2) provide models for systems of predicative arithmetic. We close with a brief discussion of Church’s Thesis for predicative arithmetic.


Potential infinity Intuitionism Predicative arithmetic Church’s thesis