Cheng, Yong (2025) Isaacson's thesis on arithmetical truth. [Preprint]

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Abstract

Isaacson's thesis claims that Peano arithmetic is complete with respect to arithmetical truth as defined by Isaacson. According to this thesis, the incompleteness phenomenon revealed in Goedel's incompleteness theorems does not pertain to arithmetical incompleteness. In our analysis, we discuss both the advantages and disadvantages of Isaacson's thesis. Additionally, we propose seven case examples that may pose potential challenges to Isaacson's thesis. To effectively defend Isaacson's thesis, one must address these case examples. We conclude that either Isaacson's notion of arithmetical truth is not right, or that it is difficult to defend Isaacson's thesis.

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Item Type:	Preprint
Creators:	Creators Email ORCID Cheng, Yong world-cyr@hotmail.com 0000-0003-2408-3886
Additional Information:	Accepted and to appear in Synthese
Keywords:	Isaacson's thesis, Arithmetical truth, The incompleteness phenomenon, Coding, Higher order concept
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic
Depositing User:	Dr. YONG CHENG
Date Deposited:	20 Aug 2025 17:08
Last Modified:	20 Aug 2025 17:08
Item ID:	26252
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic
Date:	18 August 2025
URI:	https://philsci-archive.pitt.edu/id/eprint/26252

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