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Title: Existence and modality
Author: McCarthy, Andrew Joseph
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2013
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In this dissertation I defend the non-contingency of objecthood: whatever is something is necessarily something; whatever there could have been is actually something. My defence begins by establishing that the non-contingency of objecthood is connected to the Barcan Formulas of first-order modal logic: the latter are valid schemas exactly if objecthood is non-contingent. Furthermore, the Barcan Formulas are themselves theorems of a particularly attractive system of first-order modal logic. Nevertheless, the presence of intuitive inform al counter-examples raises doubts over their form al validity. Since questions of validity are most naturally investigated in the formal semantics, 1 note that although firs t-order modal logic with the Barcan Formulas is correct over an attractively simple class of models, Kripke famously identified models on which they are untrue. Nevertheless, I argue that the existence of such models fails undermine the thought that that Barcan Formulas are valid on their intended interpretations. I diagnose this failure as resulting from the use in Kripke's semantics of a non-modal meta-language in which facts about validity' for modal logic are reduced to non-modal facts. Although this reduction is wholly warranted in terms of advancing the technical study of modal logics. it is inadequate to the ambition of explaining the alleged invalidity of the Barcan Formulas. This motivates the thought that a more homophonic sort of semantics for modal logic might be a better tool to adjudicate the dispute. I develop a natural homophonic semantics for first-order modal logic and argue that it validates the Barcan Fonnulas. A modification to this theory designed to avoid this consequence is found unacceptable. This completes the logical case for the non-contingency of objecthood. In the remainder of the dissertation I consider how the Barcan Formulas interact with some other issues in modal metaphysics. First, I consider whether they are incompatible with Actualism, the much espoused view that everything actually exists. I argue that on the relevant reading of 'exists' Actualism is itself a logical truth, with the result that it offers no constraint on theories in modal metaphysics. Fin ally, I consider Predication Actualism, the view that objects cannot have properties without existing. I argue that only with ad hoc restrictions on the logic of predicate abstraction can one combine this view with the denial of the Barcan Formulas; and that further difficulties for this combination emerge when Predication Actualism is formulated in second order modal logic.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available