Understanding in mathematics
The case of mathematical proofs
Bibliographic Data
| ID | 21364048 |
|---|---|
| Authors | Yacin Hamami (0000-0002-0780-7996, Philosophy Department University of Liège Liège Belgium, corresponding author), Robert L Morris (0000-0002-1216-6900, Independent Scholar Minneapolis Minnesota US, corresponding author) |
| Year | 2024 |
| Volume | 58 |
| Issue | 4 |
| Pages | 1073-1106 |
| Publication date | 2024-12-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Noûs (JOURNAL) |
| Journal identifiers | ISSN: 0029-4624 • E-ISSN: 1468-0068 |
| Publisher | Wiley (PUBLISHER • GB) |
| DOI | 10.1111/nous.12489 |
| OpenAlex | W4394012392 |
| Language | EN |
| References cited | 53 |
Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a simple idea, namely that understanding a proof amounts to rationally reconstructing its underlying plan. This characterization is fleshed out by specifying the relevant notion of plan and the associated process of rational reconstruction, building in part on Bratman's theory of planning agency. It is argued that the proposed account can explain a significant range of distinctive phenomena commonly associated with proof understanding by mathematicians and philosophers. It is further argued, on the basis of a case study, that the account can yield precise diagnostics of understanding failures and can suggest ways to overcome them. Reflecting on the approach developed here, the essay concludes with some remarks on how to shape a general methodology common to the study of mathematical and scientific understanding and focused on human agency
Calculus (dental) · Geometry · Mathematical practice · Mathematical proof · Mathematics education · Computer Science · History and Theory of Mathematics · Logic, Reasoning, and Knowledge · Mathematics · Philosophy and History of Science
The Value of Knowledge and the Pursuit of Understanding
Understanding, Explanation, and Scientific Knowledge
Understanding Scientific Understanding
Recovering Understanding
Toward a Theory of Understanding
Mathematical Explanation in Practice
The Mark of Understanding
Rationality in Mathematical Proofs
The Oxford Handbook of the Epistemology of Theology
Functional explanation in mathematics
A Contextual Approach to Scientific Understanding
Understanding phenomena
No understanding without explanation
Beyond Explanation
Agency, Time, and Sociality
Considered Judgment
The Value of Understanding
Risk, Responsibility, and Blame
| Citation velocity | historical |
|---|---|
| Highly cited | No |