Journal of Philosophical Logic

, Volume 33, Issue 4, pp 421-436

First online:

Routes to Triviality

  • Susan RogersonAffiliated withSchool of Philosophy and Bioethics School of Computer Science and Software Engineering, Monash University
  • , Greg RestallAffiliated withDepartment of Philosophy, University of Melbourne

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It is known that a number of inference principles can be used to trivialise the axioms of naïve comprehension – the axioms underlying the naïve theory of sets. In this paper we systematise and extend these known results, to provide a number of general classes of axioms responsible for trivialising naïve comprehension.

Abelian logic contraction Curry's paradox naïve comprehension Non-classical implicational logics Peirce's law