The Structuralist Thesis Reconsidered
Bibliographic Data
| ID | 8399607 |
|---|---|
| Authors | Georg Schiemer (0000-0003-1197-4532, University of Vienna, corresponding author), John Wigglesworth (0000-0002-7305-6844, University of Vienna, corresponding author) |
| Year | 2019 |
| Volume | 70 |
| Issue | 4 |
| Pages | 1201-1226 |
| Publication date | 2019-12-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | The British Journal for the Philosophy of Science (JOURNAL) |
| Journal identifiers | ISSN: 0007-0882 • E-ISSN: 1464-3537 |
| Publisher | Oxford University Press (PUBLISHER • GB) |
| DOI | 10.1093/bjps/axy004 |
| OpenAlex | W2757608074 |
| Language | EN |
| Citations received | 5 |
| References cited | 19 |
Øystein Linnebo and Richard Pettigrew ([2014]) have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They argue that their theory of abstract structures proves a consistent version of the structuralist thesis that positions in abstract structures only have structural properties. They do this by defining a subset of the properties of positions in structures, so-called fundamental properties, and argue that all fundamental properties of positions are structural. In this article, we argue that the structuralist thesis, even when restricted to fundamental properties, does not follow from the theory of structures that Linnebo and Pettigrew have developed. To make their account work, we propose a formal framework in terms of Kripke models that makes structural abstraction precise. The formal framework allows us to articulate a revised definition of fundamental properties, understood as intensional properties. Based on this revised definition, we show that the restricted version of the structuralist thesis holds. 1. Introduction2. The Structuralist Thesis3. LP-Structuralism4. Purity5. A Formal Framework for Structural Abstraction6. Fundamental Relations7. The Structuralist Thesis Vindicated8. Conclusion
Abstraction · Epistemology · Structuralism (philosophy of science) · Computability, Logic, AI Algorithms · Computer Science · Philosophy · Philosophy and History of Science · Philosophy and Theoretical Science
| Unique citing works | 5 |
|---|---|
| Citations per year | 0.71 |
| Citation span | 2019 - 2025 (7) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 5 |