Canadian Journal of Philosophy 46 (4-5):584-609 (2016)

Peter Fritz
Australian Catholic University
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.
Keywords First-Order Modal Logic  Necessitism  Metaphysical Universality  Two-Cardinal Theorems
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DOI 10.1080/00455091.2015.1132976
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References found in this work BETA

Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford University Press.
On the Plurality of Worlds.William G. Lycan - 1988 - Journal of Philosophy 85 (1):42-47.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.

View all 35 references / Add more references

Citations of this work BETA

The Broadest Necessity.Andrew Bacon - 2018 - Journal of Philosophical Logic 47 (5):733-783.
An Argument For Necessitism.Jeremy Goodman - 2016 - Philosophical Perspectives 30 (1):160-182.
Reply to Fritz.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):610-612.
Epistemic Modality, Mind, and Mathematics.Hasen Khudairi - 2020 - Dissertation, University of St Andrews

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