Cheng, Yong (2025) Isaacson's thesis on arithmetical truth. Synthese, 206 (140). ISSN 1573-0964
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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: | Published Article or Volume | ||||||
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| Keywords: | Isaacson's thesis, Arithmetical truth, The incompleteness phenomenon, Coding, Higher order concept | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic |
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| Depositing User: | Dr. YONG CHENG | ||||||
| Date Deposited: | 01 Oct 2025 18:08 | ||||||
| Last Modified: | 01 Oct 2025 18:08 | ||||||
| Item ID: | 26800 | ||||||
| Journal or Publication Title: | Synthese | ||||||
| Publisher: | Springer (Springer Science+Business Media B.V.) | ||||||
| Official URL: | https://doi.org/10.1007/s11229-025-05229-7 | ||||||
| DOI or Unique Handle: | 10.1007/s11229-025-05229-7 | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic |
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| Date: | 18 August 2025 | ||||||
| Volume: | 206 | ||||||
| Number: | 140 | ||||||
| ISSN: | 1573-0964 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/26800 |
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Isaacson's thesis on arithmetical truth. (deposited 20 Aug 2025 17:08)
- Isaacson's thesis on arithmetical truth. (deposited 01 Oct 2025 18:08) [Currently Displayed]
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