PhilSci Archive

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

Khudairi, Hasen (2017) Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. [Preprint]

[img]
Preview
Text
Khudairi - Modal Ω-Logic.pdf

Download (226kB) | Preview

Abstract

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.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Creators:
CreatorsEmailORCID
Khudairi, Hasenhasen.khudairi@gmail.com0000-0003-1726-6123
Keywords: Ω-Logic; Modal Logic; Logical Consequence; Large Cardinals; Coalgebra; Automata; Neo-Logicism; Set-theoretic Realism
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Computation/Information
Depositing User: Hasen Khudairi
Date Deposited: 09 Aug 2018 22:54
Last Modified: 09 Aug 2018 22:54
Item ID: 14904
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Computation/Information
Date: 2017
URI: http://philsci-archive.pitt.edu/id/eprint/14904

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item