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theses

The goal of my dissertation is to bring insights from branches of logic that are not well-discussed in the literature, notably modal model theory, to bear on questions in the metaphysics of time and modality. This occurs on both the meta-level and on the level of first order philosophical questions.

On the meta-level, I mount a defense of the ongoing usefulness of modal logic, considered as a branch of mathematics, in the face of recent views in metametaphysics that consider modal tools too crude to usefully state metaphysical theses or adjudicate metaphysical disputes. In doing so, I draw on the study of expressive power in languages and Bayesian epistemology to formulate a new criterion for ideological parsimony: if two ideologies are expressively equivalent, then they are equally parsimonious. After explicating this principle, I show how it blocks arguments against the use of modal logic (among other consequences for parsimony arguments in the literature). I go beyond purely negative arguments by then showing how to use modal logic to study things other than necessity and possibility, and use it to unearth a hitherto unappreciated parallel between grounding and provability.

On the first order level, I focus on A-theories of time. Tense logic and modal logic are mathematically similar; their model theory is typically studied together. I address several problems with A-theories. First, I argue that the standard way of setting up tense logic is hostile to open future views, and propose an alternative that is not. I show that my alternative can provide a logical setting for evaluating arguments about whether the future is open, and prove that the standard setup is a special case of my framework. Second, I argue that (a) presentists can consistently adopt a counterpart theory of identity across time, and (b) that they can solve several problems if they do so.

ETD_10142

Ph.D.

Includes bibliographical references

doi:10.7282/t3-6mg0-x861

ETD doctoral

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