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Absolute Decidability and Mathematical Modality

By Khudairi, Hasen

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Book Id: WPLBN0100003130
Format Type: PDF (eBook)
File Size: 197.36 KB.
Reproduction Date: 9/2/2018

Title: Absolute Decidability and Mathematical Modality  
Author: Khudairi, Hasen
Volume:
Language: English
Subject: Non Fiction, Philosophy
Collections: Authors Community, Philosophy
Historic
Publication Date:
2018
Publisher: Gutenberg
Member Page: Hasen Khudairi

Description
This paper aims to contribute to the analysis of the nature of mathematical modality, and to the applications of the latter to unrestricted quantification and absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of multi-dimensional intensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the priority and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the multi-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I demonstrate, finally, how the duality axioms of the epistemic logic for the semantics can be availed of, in order to defuse the paradox of knowability.

 

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