Meaning in Classical Mathematics
Is it at odds with Intuitionism
Bibliographic Data
| ID | 12110237 |
|---|---|
| Authors | Karin Usadi Katz, Mikhail G Katz (0000-0002-3489-0158) |
| Year | 2011 |
| Volume | 56 |
| Issue | 2 |
| Pages | 223-302 |
| Publication date | 2011-01-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | Intellectica Revue de l Association pour la Recherche Cognitive (JOURNAL) |
| Journal identifiers | ISSN: 0769-4113 • E-ISSN: 2273-9262 |
| Publisher | PERSEE Program (PUBLISHER) |
| DOI | 10.3406/intel.2011.1154 |
| OpenAlex | W1675643752 |
| Language | EN |
| Citations received | 1 |
| References cited | 12 |
We examine the classical/ intuitionist divide, and how it reflects on modern theories of infinitesimals. When leading intuitionist Heyting announced that “ the creation of non-standard analysis is a standard model of important mathematical research”, he was fully aware that he was breaking ranks with Brouwer. Was Errett Bishop faithful to either Kronecker or Brouwer ? Through a comparative textual analysis of three of Bishop’s texts, we analyze the ideological and/ or pedagogical nature of his objections to infinitesimals à la Robinson. Bishop’s famous “ debasement” comment at the 1974 Boston workshop, published as part of his Crisis lecture, in reality was never uttered in front of an audience. We compare the realist and the anti-realist intuitionist narratives, and analyze the views of Dummett, Pourciau, Richman, Shapiro, and Tennant. Variational principles are important physical applications, currently lacking a constructive framework. We examine the case of the Hawking– Penrose singularity theorem, already analyzed by Hellman in the context of the Quine-Putnam indispensability thesis
Constructive · Context (archaeology · Epistemology · Intuitionism · Quine · Statistician · Computer Science · History · History and Theory of Mathematics · Mathematical and Theoretical Analysis · Mathematics · Philosophy · Relativity and Gravitational Theory
The Large Scale Structure of Space-Time
Renaissance notions of number and magnitude
Preservice Teachers' Understanding of the Relation Between a Fraction or Integer and Its Decimal Expansion
The wake of Berkeley's analyst
Intuitionism as a (failed) Kuhnian revolution in mathematics
Response to Questionnaire
Applied Constructive Mathematics
Cauchy, Convergence and Continuity
Mathematical Constructivism in Spacetime
| Unique citing works | 1 |
|---|---|
| Citations per year | 0,17 |
| Citation span | 2020 - 2020 (1) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 1 |