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424This sentence does not contain the symbol XThe Reasoner 7 (9): 108. 2013.A suprise may occur if we use a similar strategy to the Liar's paradox to mathematically formalize "This sentence does not contain the symbol X".
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675An axiomatic version of Fitch’s paradoxSynthese 190 (12): 2015-2020. 2013.A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the paradox
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422Biologically Unavoidable SequencesElectronic Journal of Combinatorics 20 (1): 1-13. 2013.A biologically unavoidable sequence is an infinite gender sequence which occurs in every gendered, infinite genealogical network satisfying certain tame conditions. We show that every eventually periodic sequence is biologically unavoidable (this generalizes König's Lemma), and we exhibit some biologically avoidable sequences. Finally we give an application of unavoidable sequences to cellular automata.
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863A Machine That Knows Its Own CodeStudia Logica 102 (3): 567-576. 2014.We construct a machine that knows its own code, at the price of not knowing its own factivity
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585Fast-Collapsing TheoriesStudia Logica (1): 1-21. 2013.Reinhardt’s conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and transfinite induction up to a smaller ordinal
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