Modality and Hyperintensionality in Mathematics

Download Edit this record How to cite View on PhilPapers
Abstract
This paper aims to contribute to the analysis of the nature of mathematical modality, and to the applications of the latter to unrestricted quantification and absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the priority and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance a topic-sensitive epistemic two-dimensional truthmaker semantics, if hyperintensional approaches are to be preferred to possible worlds semantics. I examine the relation between two-dimensional hyperintensional states and epistemic set theory.
Keywords
No keywords specified (fix it)
PhilPapers/Archive ID
KHUADA
Upload history
First archival date: 2017-06-14
Latest version: 56 (2022-05-25)
View other versions
Added to PP index
2017-06-14

Total views
227 ( #31,619 of 69,167 )

Recent downloads (6 months)
43 ( #19,150 of 69,167 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.