Abstract
Conspicuously missing some planks, a latter-day Ship of Theseus catches the eye when one picks up this Book of Three Authors. Teasingly, differentiated prepositions between their names on the title page hint at its complex history. The result is a formidable achievement, exemplifying contemporary metaphysics at its best. Puzzles of variation arise from pre-reflectively plausible tolerance principles, on which an artefact survives any small variation in its constituents but no large variation in them: unfortunately, many small variations make a large variation. The variations may be across times or across possibilities, though
Key takeaways
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- BOP exemplifies contemporary metaphysics, addressing puzzles of modal variation with higher-order logic.
- Tolerance and Non-Contingency premises underpin BOP's exploration of modal puzzles.
- Higher-order logic extends classical systems, allowing unrestricted comprehension principles for predicates.
- BOP critiques first-order logic's limitations, demonstrating the necessity of higher-order frameworks in mathematics and semantics.
- The book serves as an introduction to formal metaphysics, bridging foundational theories and contemporary debates.
References (10)
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- Kripke, S. 1980. Naming and Necessity. Oxford: Blackwell.
- Salmón, N. 1989. The logic of what might have been. Philosophical Review 98: 3-34.
- Williamson, T. 1990. Identity and Discrimination. Oxford: Blackwell.
- Williamson, T. 2003. Everything. Philosophical Perspectives 17: 415-65.
- Williamson, T. 2013. Modal Logic as Metaphysics. Oxford: Oxford University Press.
- Williamson, T. 2016. Modal science. Canadian Journal of Philosophy 46: 453-92.
- Williamson, T. 2020. Suppose and Tell: The Semantics and Heuristics of Conditionals. Oxford: Oxford University Press.
FAQs
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What are the implications of higher-order logic for modal variation puzzles?
The research suggests that higher-order frameworks enhance clarity in modal puzzles, revealing nuanced relationships between properties and modalities, as illustrated by the modal tolerance principle.
How does formal metaphysics differ from traditional philosophical approaches?
This work articulates that formal metaphysics utilizes interpreted formal systems to systematically explore metaphysical questions, contrasting its approach with classical philosophical discourse that often lacks rigorous structure.
What role do tolerance principles play in addressing modal puzzles?
The study establishes that tolerance principles, combined with non-contingency assumptions, generate significant insights into modal variation, especially when exploring the implications of small differences.
Why is the unrestricted comprehension principle considered crucial in higher-order logic?
The unrestricted comprehension principle is vital as it allows mapping across all predicate types, thereby circumventing limitations present in first-order logic, particularly regarding general comprehension issues.
What challenges arise from the contrast between first-order and higher-order logic?
The analysis indicates that while first-order logic encounters non-standard models and limitations in capturing certain mathematical truths, higher-order logic provides a more robust framework for encompassing these complexities.