Elohim, David (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 $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The categorical duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The hyperintensional profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal and hyperintensional profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical. Second, the foregoing provides a hyperintensional account of the interpretation of mathematical and metamathematical vocabulary.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Elohim, David hasen.khudairi@gmail.com 0000-0003-1726-6123
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 Specific Sciences > Mathematics > Ontology
Depositing User:	David Elohim
Date Deposited:	05 May 2024 23:59
Last Modified:	05 May 2024 23:59
Item ID:	23371
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 Specific Sciences > Mathematics > Ontology
Date:	2019
Page Range:	pp. 65-82
URI:	https://philsci-archive.pitt.edu/id/eprint/23371

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• Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 09 Aug 2018 22:54)

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