First-order modal logic in the necessary framework of objects

Journal article


Fritz, Peter. (2016). First-order modal logic in the necessary framework of objects. Canadian Journal of Philosophy. 46(4-5), pp. 584 - 609. https://doi.org/10.1080/00455091.2015.1132976
AuthorsFritz, Peter
Abstract

I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson's argument.

Keywordsfirst-order modal logic; necessitism; metaphysical universality; two-cardinal theorems; Kreisel’s principle
Year2016
JournalCanadian Journal of Philosophy
Journal citation46 (4-5), pp. 584 - 609
PublisherRoutledge
ISSN0045-5091
Digital Object Identifier (DOI)https://doi.org/10.1080/00455091.2015.1132976
Scopus EID2-s2.0-84961391543
Page range584 - 609
Research GroupDianoia Institute of Philosophy
Publisher's version
File Access Level
Controlled
Place of publicationUnited Kingdom
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https://acuresearchbank.acu.edu.au/item/880w6/first-order-modal-logic-in-the-necessary-framework-of-objects

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