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This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) |
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This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) |
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According to Weyl, “‘inexhaustibility’ is essential to the infinite”. However, he distinguishes two kinds of inexhaustible, or merely potential, domains: those that are “extensionally determinate” and those that are not. This article clarifies Weyl's distinction and explains its enduring logical and philosophical significance. The distinction sheds lights on the contemporary debate about potentialism, which in turn affords a deeper understanding of Weyl. |
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What explains the truth of a universal generalization? Two types of explanation can be distinguished. While an ‘instance-based explanation’ proceeds via some or all instances of the generalization, a ‘generic explanation’ is independent of the instances, relying instead on completely general facts about the properties or operations involved in the generalization. This intuitive distinction is analyzed by means of a truthmaker semantics, which also sheds light on the correct logic of quantification. On the most natural version of the semantics, this (...) |
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This paper investigates two intuitionistic mereological systems based on Tarski’s axiomatisation of general mereology. These systems use two intuitionistically non-equivalent formalisations of the notion of fusion. I study extensionality and supplementation properties as well as some variants of these systems, and defend parthood as a suitable primitive notion for intuitionistic mereology if working with Tarski’s axiomatisation. Furthermore, I arrive at an equi-interpretability result for one of the atomistic variants with intuitionistic plural logic. I discuss to what extent these results support (...) |
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After a critical presentation of the debate between absolutists and relativists regarding generality where I show that the debate is framed in a way that is bound to be harmful to the relativist’s position, I examine critically one of the customary arguments advanced against the relativist: the expressibility objection (according to which the relativist would be logically unable to express her own position). I then propose a radical way out of this debate-usually centered on semantic paradoxes-by arguing that it rests (...) |
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