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Mathematical progress

Philip Kitcher

Revue Internationale de Philosophie 42 (167):518-540 (1988)

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Mathematical Progress — On Maddy and Beyond.Simon Weisgerber - 2023 - Philosophia Mathematica 31 (1):1-28.details A key question of the ‘maverick’ tradition of the philosophy of mathematical practice is addressed, namely what is mathematical progress. The investigation is based on an article by Penelope Maddy devoted to this topic in which she considers only contributions ‘of some mathematical importance’ as progress. With the help of a case study from contemporary mathematics, more precisely from tropical geometry, a few issues with her proposal are identified. Taking these issues into consideration, an alternative account of ‘mathematical importance’, broadly (...) Download Export citation Bookmark 2 citations
The Role of Intuition and Formal Thinking in Kant, Riemann, Husserl, Poincare, Weyl, and in Current Mathematics and Physics.Luciano Boi - 2019 - Kairos 22 (1):1-53.details According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that nevertheless (...) Download Export citation Bookmark 1 citation
Argument and explanation in mathematics.Michel Dufour - 2013 - In Dima Mohammed and Marcin Lewiński (ed.), Virtues of Argumentation. Proceedings of the 10th International Conference of the Ontario Society for the Study of Argumentation (OSSA), 22-26 May 2013. pp. pp. 1-14..details Are there arguments in mathematics? Are there explanations in mathematics? Are there any connections between argument, proof and explanation? Highly controversial answers and arguments are reviewed. The main point is that in the case of a mathematical proof, the pragmatic criterion used to make a distinction between argument and explanation is likely to be insufficient for you may grant the conclusion of a proof but keep on thinking that the proof is not explanatory. Download Export citation Bookmark 1 citation
The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today.Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.) - 2006 - Dordrecht, Netherland: Springer.details This book explores the interplay between logic and science, describing new trends, new issues and potential research developments. Download Export citation Bookmark 2 citations
What is categorical structuralism?Geoffrey Hellman - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today. Dordrecht, Netherland: Springer. pp. 151--161.details Download Export citation Bookmark 5 citations

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