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Hyperintensional Ω-Logic

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
Creators:
CreatorsEmailORCID
Khudairi (Bowen), Hasen (Tim)hasen.khudairi@gmail.com0000-0003-1726-6123
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
Depositing User: Timothy (Hasen) Bowen (Khudairi)
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
Date: 2019
Page Range: pp. 65-82
URI: https://philsci-archive.pitt.edu/id/eprint/23145

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