Topoi 39 (4):963-971 (2020)

Emiliano Ippoliti
Università degli Studi di Roma La Sapienza
I examine the way a relevant conceptual novelty in mathematics, that is, the notion of group, has been constructed in order to show the kinds of heuristic reasoning that enabled its manufacturing. To this end, I examine salient aspects of the works of Lagrange, Cauchy, Galois and Cayley. In more detail, I examine the seminal idea resulting from Lagrange’s heuristics and how Cauchy, Galois and Cayley develop it. This analysis shows us how new mathematical entities are generated, and also how what counts as a solution to a problem is shaped and changed. Finally, I argue that this case study shows us that we have to study inferential micro-structures, that is, the ways similarities and regularities are sought, in order to understand how theoretical novelty is constructed and heuristic reasoning is put forward.
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DOI 10.1007/s11245-018-9549-1
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Rethinking Knowledge.Carlo Cellucci - 2015 - Metaphilosophy 46 (2):213-234.
Revolutions in Mathematics.Donald Gillies (ed.) - 1992 - Oxford University Press.
Proofs and Refutations: The Logic of Mathematical Discovery.Daniel Isaacson - 1978 - Philosophical Quarterly 28 (111):169-171.

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