In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer. pp. 65-82 (2019)
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This essay examines the philosophical significance of Ω-logic in Zermelo-Fraenkel set theory with choice (ZFC). The dual isomorphism between algebra and coalgebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of Ω-logical validity can then be countenanced within a coalgebraic logic, and Ω-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 Ω-logical validity correspond to those of second-order logical consequence, Ω-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets.
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DOI | 10.1007/978-3-030-01800-9_4 |
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References found in this work BETA
The Emergent Multiverse: Quantum Theory According to the Everett Interpretation.David Wallace - 2012 - Oxford University Press.
Warrant for Nothing (and Foundations for Free)?Crispin Wright - 2004 - Aristotelian Society Supplementary Volume 78 (1):167–212.
Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics.Peter J. Lewis - 2016 - Oxford University Press USA.
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