Khudairi (Bowen), Hasen (Tim) (2019) Hyperintensional Ω-Logic. Matteo Vincenzo D'Alfonso and Don Berkich (eds.), \textit{On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence}. pp. 65-82.
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Abstract
This essay examines the philosophical significance of the consequence relation defined in the $\Omega$-logic for set-theoretic languages. I argue that, as with second-order logic, the hyperintensional profile of validity in $\Omega$-Logic enables the property to be epistemically tractable. Because of the duality between coalgebras and algebras, Boolean-valued models of set theory can be interpreted as coalgebras. In Section \textbf{2}, I demonstrate how the hyperintensional profile of $\Omega$-logical validity can be countenanced within a coalgebraic logic. Finally, in Section \textbf{3}, the philosophical significance of the characterization of the hyperintensional profile of $\Omega$-logical validity for the philosophy of mathematics is examined. I argue (i) that $\Omega$-logical validity is genuinely logical, and (ii) that it provides a hyperintensional account of formal grasp of the concept of `set'. Section \textbf{4} provides concluding remarks.
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Item Type: | Published Article or Volume | ||||||
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Additional Information: | In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence, Springer. pp. 65-82. 2019 | ||||||
Keywords: | Hyperintensional Ω-Logic; Logical Consequence; Large Cardinals; Modal Coalgebra; Set-theoretic Realism; Topic-sensitive Epistemic Two-dimensional Truthmaker Semantics | ||||||
Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic |
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Depositing User: | David Elohim | ||||||
Date Deposited: | 01 Mar 2024 03:44 | ||||||
Last Modified: | 01 Mar 2024 03:44 | ||||||
Item ID: | 23145 | ||||||
Journal or Publication Title: | Matteo Vincenzo D'Alfonso and Don Berkich (eds.), \textit{On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence} | ||||||
Publisher: | Springer | ||||||
Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic |
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Date: | 2019 | ||||||
Page Range: | pp. 65-82 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/23145 |
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