Intensional type theory for higher-order contingentism

Dissertation, University of Oxford (2015)

Authors
Peter Fritz
Australian Catholic University
Abstract
Things could have been different, but could it also have been different what things there are? It is natural to think so, since I could have failed to be born, and it is natural to think that I would then not have been anything. But what about entities like propositions, properties and relations? Had I not been anything, would there have been the property of being me? In this thesis, I formally develop and assess views according to which it is both contingent what individuals there are and contingent what propositions, properties and relations there are. I end up rejecting these views, and conclude that even if it is contingent what individuals there are, it is necessary what propositions, properties and relations there are. Call the view that it is contingent what individuals there are first-order contingentism, and the view that it is contingent what propositions, properties and relations there are higher-order contingentism. I bring together the three major contributions to the literature on higher-order contingentism, which have been developed largely independently of each other, by Kit Fine, Robert Stalnaker, and Timothy Williamson. I show that a version of Stalnaker's approach to higher-order contingentism was already explored in much more technical detail by Fine, and that it stands up well to the major challenges against higher-order contingentism posed by Williamson. I further show that once a mistake in Stalnaker's development is corrected, each of his models of contingently existing propositions corresponds to the propositional fragment of one of Fine's more general models of contingently existing propositions, properties and relations, and vice versa. I also show that Stalnaker's theory of contingently existing propositions is in tension with his own theory of counterfactuals, but not with one of the main competing theories, proposed by David Lewis. Finally, I connect higher-order contingentism to expressive power arguments against first-order contingentism. I argue that there are intelligible distinctions we draw with talk about "possible things", such as the claim that there are uncountably many possible stars. Since first-order contingentists hold that there are no possible stars apart from the actual stars, they face the challenge of paraphrasing such talk. I show that even in an infinitary higher-order modal logic, the claim that there are uncountably many possible stars can only be paraphrased if higher-order contingentism is false. I therefore conclude that even if first-order contingentism is true, higher-order contingentism is false.
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References found in this work BETA

Ontological Pluralism.Jason Turner - 2010 - Journal of Philosophy 107 (1):5-34.
The Problem of Possibilia.Kit Fine - 2003 - In Michael J. Loux & Dean W. Zimmerman (eds.), The Oxford Handbook of Metaphysics. Oxford University Press. pp. 161-179.
Class and Membership.Kit Fine - 2005 - Journal of Philosophy 102 (11):547 - 572.
An Actualistic Semantics for Quantified Modal Logic.Thomas Jager - 1982 - Notre Dame Journal of Formal Logic 23 (3):335-349.

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