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117Explanation And Solution In The Inclosure ArgumentAustralasian Journal of Philosophy 88 (2): 353-357. 2010.In a recent article, Emil Badici contends that the inclosure schema substantially fails as an analysis of the paradoxes of self-reference because it is question-begging. The main purpose of this note is to show that Badici's critique highlights a necessity condition for the success of dialectic about paradoxes. The inclosure argument respects this condition and remains solvent
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139A Note on Contraction-Free Logic for ValidityTopoi 34 (1): 63-74. 2015.This note motivates a logic for a theory that can express its own notion of logical consequence—a ‘syntactically closed’ theory of naive validity. The main issue for such a logic is Curry’s paradox, which is averted by the failure of contraction. The logic features two related, but different, implication connectives. A Hilbert system is proposed that is complete and non-trivial.
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318Transfinite Cardinals in Paraconsistent Set TheoryReview of Symbolic Logic 5 (2): 269-293. 2012.This paper develops a (nontrivial) theory of cardinal numbers from a naive set comprehension principle, in a suitable paraconsistent logic. To underwrite cardinal arithmetic, the axiom of choice is proved. A new proof of Cantor’s theorem is provided, as well as a method for demonstrating the existence of large cardinals by way of a reflection theorem.
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148On closure and truth in substructural theories of truthSynthese 199 (Suppl 3): 725-739. 2016.Closure is the idea that what is true about a theory of truth should be true in it. Commitment to closure under truth motivates non-classical logic; commitment to closure under validity leads to substructural logic. These moves can be thought of as responses to revenge problems. With a focus on truth in mathematics, I will consider whether a noncontractive approach faces a similar revenge problem with respect to closure under provability, and argue that if a noncontractive theory is to be genuin…Read more
Dunedin, Otago, New Zealand
Areas of Specialization
| Logic and Philosophy of Logic |
| Philosophy of Mathematics |
Areas of Interest
| Logic and Philosophy of Logic |
| Philosophy of Mathematics |