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 (Sect. 2). 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 (Sect. 3), that is, the ways similarities and regularities are sought, in order to understand how theoretical novelty is constructed and heuristic reasoning is put forward

Manufacturing a mathematical group: a study in heuristics / Ippoliti, Emiliano. - In: TOPOI. - ISSN 1572-8749. - 39:4(2020), pp. 963-971. [10.1007/s11245-018-9549-1]

Manufacturing a mathematical group: a study in heuristics

Ippoliti, Emiliano
2020

Abstract

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 (Sect. 2). 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 (Sect. 3), that is, the ways similarities and regularities are sought, in order to understand how theoretical novelty is constructed and heuristic reasoning is put forward
2020
heuristics; hypotheses; inference; inferential micro-structures; logic; discovery
01 Pubblicazione su rivista::01a Articolo in rivista
Manufacturing a mathematical group: a study in heuristics / Ippoliti, Emiliano. - In: TOPOI. - ISSN 1572-8749. - 39:4(2020), pp. 963-971. [10.1007/s11245-018-9549-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1068938
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