Higher-order metaphysics is in full swing. One of its principle aims is to show that higher-order logic can be our foundational metaphysical theory. A foundational metaphysical theory would be a simple, powerful, systematic theory which would ground all of our metaphysical theories from modality, to grounding, to essence, and so on. A satisfactory account of its epistemology would in turn yield a satisfactory epistemology of these theories. And it would function as the final court of appeals for metaphysical questions. It would play the role for our metaphysical community that ZFC plays for the mathematical community.
I think there is much promise in this project. There is clear value in having a shared foundational theory to which metaphysicians can appeal. And there is reason to think that higher-order logic can play this role. After all, it has long been known that one can do math in higher-order logic. And there is growing reason to think that one can do metaphysics in higher-order logic in much the same way. However, most of the research approaches higher-order logic from a monist perspective, according to which there is 'one true' higher-order logic. And in the midst of the enthusiasm, metaphysicians seem to have overlooked that this approach leaves the program susceptible to epistemological problems that plague monism about other areas, like set theory.
The most significant of these is the Benacerraf Problem. This is the problem of explaining the reliability of our higher-order-logical beliefs. The problem is sufficiently serious that, in the set-theoretic case, it has led to a reconception of the foundations of mathematics, known as pluralism. In this dissertation I investigate a pluralist approach to higher-order metaphysics. The basic idea is that any higher-order logic which can play the role of our foundational metaphysical theory correctly describes the metaphysical structure of the world, in much the way that the set-theoretic pluralist maintains that any set theory which can play the role of our foundational mathematical theory is true of a mind-independent platonic universe of sets. I outline my view about what it takes for a higher-order logic to play this role, what it means for such a logic to correctly describe the metaphysical structure of the world, and how it is that different higher-order logics which seem to disagree with each other can meet both of these conditions.
I conclude that higher-order logical pluralism is the most tenable version of the higher-order logic as metaphysics program. Higher-order logical pluralism constitutes a radical departure from conventional wisdom, requiring a significant reconception of the nature of validity, modality, and metaphysics in general. It renders moot some of the most central questions in these domains, such as: Is the law of excluded middle valid? Is it the case that necessarily everything is necessarily something? Is the grounding relation transitive? On this picture, these questions no longer have objective answers. They become like the question of whether the Continuum Hypothesis is true, according to the set-theoretic pluralist. The only significant question in the neighborhood of the aforementioned questions is: which metaphysical principles are best suited to the task at hand?
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/9zn3-2244 |
| Date | January 2023 |
| Creators | McCarthy, William Kevin |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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