Emiliano Ippoliti

Mathematical knowledge and its construction. The heuristic stance

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Keywords: Discovery, Heuristics, Logic, Mathematics, Method, Rationality.

In this paper I examine the heuristic view of mathematics focussing on an updated version of it. I discuss how the seminal work of Lakatos has been improved under several respects and I point at four issues that are particularly relevant for the philosophy of mathematics and mathematical practice from a heuristic point of view: 1. the quest for a method of discovery (§ 2); 2. the construction of heuristic procedure, that is rational and inferential ways of producing a hypothesis to solve a problem (§ 3); 3. the nature of mathematical objects (§ 4); 4. the relation between mathematics, evolution, and reality (§ 5).

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