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Document Details : Title: Intuitions in the Mathematical Practice of Conjecturing Author(s): BÜCHI, Romain Journal: Logique et Analyse Volume: 266 Date: 2024-2025 Pages: 341-366 DOI: 10.2143/LEA.266.0.3294843 Abstract : The topic of this paper is the role intuition can play in the mathematical practice of conjecturing. More precisely, it addresses the question of how intuitions can serve to rationally form fruitful conjectures. To succeed in making fruitful conjectures, various conditions must be fulfilled. Syntactic capacities paired with unwarranted truth claims are not sufficient. Conjecturing is not guesswork and not all intuitions are of the same relevance to it. The kind of intuition that can and often does play a leading role in the practice of conjecturing is typically invoked by experts. But even if a statement is suggested by expert intuition, the attempt to conjecture it may still fail due to insufficient justification. In such cases, one has to offer other reasons why the statement should be considered probably true and worth investigating. Although an established conjecture may of course still prove to be false, this need not undermine its fruitfulness. For in mathematics, the refutation of an interesting claim can be the proof of an equally intriguing statement. And when it comes to identifying what is potentially fruitful, intuition has again a crucial role to play. This paper aims to show that the unwritten rules, implicit criteria and intellectual powers at work in the art of conjecturing are indeed a valuable field of investigation for epistemology. It is also an attempt to contribute to the larger issue of how intuition relates to knowledge and truth in mathematics. |
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