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  1. Arithmetic is Necessary.Zachary Goodsell - 2024 - Journal of Philosophical Logic 53 (4).
    (Goodsell, Journal of Philosophical Logic, 51(1), 127-150 2022) establishes the noncontingency of sentences of first-order arithmetic, in a plausible higher-order modal logic. Here, the same result is derived using significantly weaker assumptions. Most notably, the assumption of rigid comprehension—that every property is coextensive with a modally rigid one—is weakened to the assumption that the Boolean algebra of properties under necessitation is countably complete. The results are generalized to extensions of the language of arithmetic, and are applied to answer a question (...)
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  • (1 other version)The Necessity of Mathematics.Juhani Yli-Vakkuri & John Hawthorne - 2020 - Noûs 54 (3):549-577.
    Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.
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  • Theories of truth for countable languages which conform to classical logic.Seppo Heikkilä - forthcoming - Nonlinear Studies.
    Every countable language which conforms to classical logic is shown to have an extension which has a consistent definitional theory of truth. That extension has a consistent semantical theory of truth, if every sentence of the object language is valuated by its meaning either as true or as false. These theories contain both a truth predicate and a non-truth predicate. Theories are equivalent when sentences of the object lqanguage are valuated by their meanings.
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  • (1 other version)The Necessity of Mathematics.Juhani Yli‐Vakkuri & John Hawthorne - 2018 - Noûs 52 (3):549-577.
    Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.
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