| _version_ | 1866901604154736640 |
|---|---|
| author | Cao, Runlin |
| author_facet | Cao, Runlin |
| contents | <p>This paper develops a structural occupancy model to challenge the principle of tolerance in the sorites paradox and to critique the assumption of sharp boundaries. Standard formulations of tolerance assume that each step in a sorites sequence constitutes a small and negligible change, typically grounded in similarity. I argue that this assumption fails once we consider the role of structural configuration. In my model, objects are represented as occupying regions within a structured space, where the significance of any local change depends on its position within the overall configuration. As a result, incremental changes are not uniformly negligible: identical quantitative additions can produce different classificatory outcomes depending on their structural placement. This undermines the stability of similarity relations required for tolerance and shows that there is no principled basis for treating each step as preserving predicate application. Furthermore, the model challenges sharp boundary views, such as those defended by Timothy Williamson, by arguing that no single point can stably serve as a boundary when truth-conditions depend on global structural features. Even if all structural facts are fixed, they do not determine a unique extension of vague predicates such as “bald.” I conclude that both tolerance and sharp boundary approaches rely on assumptions that fail under structurally sensitive analysis.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20059159 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Structural Occupancy, Non-Uniform Change, and the Instability of Tolerance Cao, Runlin <p>This paper develops a structural occupancy model to challenge the principle of tolerance in the sorites paradox and to critique the assumption of sharp boundaries. Standard formulations of tolerance assume that each step in a sorites sequence constitutes a small and negligible change, typically grounded in similarity. I argue that this assumption fails once we consider the role of structural configuration. In my model, objects are represented as occupying regions within a structured space, where the significance of any local change depends on its position within the overall configuration. As a result, incremental changes are not uniformly negligible: identical quantitative additions can produce different classificatory outcomes depending on their structural placement. This undermines the stability of similarity relations required for tolerance and shows that there is no principled basis for treating each step as preserving predicate application. Furthermore, the model challenges sharp boundary views, such as those defended by Timothy Williamson, by arguing that no single point can stably serve as a boundary when truth-conditions depend on global structural features. Even if all structural facts are fixed, they do not determine a unique extension of vague predicates such as “bald.” I conclude that both tolerance and sharp boundary approaches rely on assumptions that fail under structurally sensitive analysis.</p> |
| title | Structural Occupancy, Non-Uniform Change, and the Instability of Tolerance |
| url | https://doi.org/10.5281/zenodo.20059159 |