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Epistemic Modality, Mind, and Mathematics

Khudairi, Hasen (2017) Epistemic Modality, Mind, and Mathematics. [Preprint]

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Abstract

This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; the types of mathematical modality; to the epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the apriori-aposteriori distinction; to the modal profile of rational propositional intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Each essay is informed by either epistemic logic, modal and cylindric algebra or coalgebra, intensional semantics or hyperintensional semantics. The book's original contributions include theories of: (i) epistemic modal algebras and coalgebras; (ii) cognitivism about epistemic modality; (iii) two-dimensional truthmaker semantics, and interpretations thereof; (iv) the ground-theoretic ontology of consciousness; (v) fixed-points in vagueness; (vi) the modal foundations of mathematical platonism; (vii) a solution to the Julius Caesar problem based on metaphysical definitions availing of notions of ground and essence; (viii) the application of epistemic two-dimensional semantics to the epistemology of mathematics; and (ix) a modal logic for rational intuition. I develop, further, a novel approach to conditions of self-knowledge in the setting of the modal $\mu$-calculus, as well as novel epistemicist solutions to Curry's and the liar paradoxes. Solutions to previously intransigent issues concerning the first-person concept, the distinction between fundamental and derivative truths, and the unity of intention and its role in decision theory, are developed along the way.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Khudairi, Hasenhasen.khudairi@gmail.com
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Specific Sciences > Artificial Intelligence > Classical AI
Specific Sciences > Cognitive Science > Concepts and Representations
Specific Sciences > Cognitive Science > Consciousness
Depositing User: Hasen Khudairi
Date Deposited: 02 Feb 2021 03:04
Last Modified: 02 Feb 2021 03:04
Item ID: 18669
Official URL: https://philpapers.org/rec/HASFOL-2
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Specific Sciences > Artificial Intelligence > Classical AI
Specific Sciences > Cognitive Science > Concepts and Representations
Specific Sciences > Cognitive Science > Consciousness
Date: 2017
URI: http://philsci-archive.pitt.edu/id/eprint/18669

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