PhilSci Archive

Hyperintensional Ω-Logic

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.

This is the latest version of this item.

[img]
Preview
Text
Modal Ω-Logic.pdf

Download (518kB) | Preview

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.


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

Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Elohim, Davidhasen.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
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

Available Versions of this Item

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item