Khudairi, Hasen (2019) Modal 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 modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical. Second, the foregoing provides a modal account of the interpretation of mathematical vocabulary.
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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: | Ω-Logic; Modal Logic; Logical Consequence; Large Cardinals; Coalgebra; Automata; Set-theoretic Realism | ||||||
Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Computation/Information |
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Depositing User: | Hasen Khudairi | ||||||
Date Deposited: | 25 Nov 2022 17:02 | ||||||
Last Modified: | 25 Nov 2022 17:02 | ||||||
Item ID: | 21460 | ||||||
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 > Computation/Information |
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Date: | 2019 | ||||||
Page Range: | pp. 65-82 | ||||||
URI: | http://philsci-archive.pitt.edu/id/eprint/21460 |
Available Versions of this Item
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 09 Aug 2018 22:54)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 17 May 2021 16:43)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 21 May 2021 01:36)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 03 Jun 2021 18:41)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 23 Jun 2021 19:04)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 29 Jun 2021 19:34)
- Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 09 May 2022 22:47)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 22 Jul 2021 16:35)
- Modal Ω-Logic. (deposited 25 Nov 2022 17:02) [Currently Displayed]
- Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 22 Nov 2022 16:03)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 29 Jun 2021 19:34)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 23 Jun 2021 19:04)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 03 Jun 2021 18:41)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 21 May 2021 01:36)
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Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. (deposited 17 May 2021 16:43)
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