From real analysis to the sorites paradox via Reverse Mathematics
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909845448294400 |
|---|---|
| author | Dean, Walter Sanders, Sam |
| author_facet | Dean, Walter Sanders, Sam |
| contents | This paper presents a reverse mathematical analysis of several forms of the sorites paradox. We first illustrate how traditional formulations are reliant on Hölder's Representation Theorem for ordered Archimedean groups. While this is provable in RCA$_0$, we also consider two forms of the sorites which rest on non-constructive principles: the continuous sorites of Weber & Colyvan (2010) and a variant we refer to as the covering sorites. We show in the setting of second-order arithmetic that the former depends on the existence of suprema and thus on arithmetical comprehension (ACA$_0$) while the latter depends on the Heine-Borel Theorem and thus on Weak König's Lemma (WKL$_0$). We finally illustrate how recursive counterexamples to these principles provide resolutions to the corresponding paradoxes which can be contrasted with supervaluationist, epistemicist, and constructivist approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From real analysis to the sorites paradox via Reverse Mathematics Dean, Walter Sanders, Sam Logic History and Overview This paper presents a reverse mathematical analysis of several forms of the sorites paradox. We first illustrate how traditional formulations are reliant on Hölder's Representation Theorem for ordered Archimedean groups. While this is provable in RCA$_0$, we also consider two forms of the sorites which rest on non-constructive principles: the continuous sorites of Weber & Colyvan (2010) and a variant we refer to as the covering sorites. We show in the setting of second-order arithmetic that the former depends on the existence of suprema and thus on arithmetical comprehension (ACA$_0$) while the latter depends on the Heine-Borel Theorem and thus on Weak König's Lemma (WKL$_0$). We finally illustrate how recursive counterexamples to these principles provide resolutions to the corresponding paradoxes which can be contrasted with supervaluationist, epistemicist, and constructivist approaches. |
| title | From real analysis to the sorites paradox via Reverse Mathematics |
| topic | Logic History and Overview |
| url | https://arxiv.org/abs/2502.06596 |