Abduction and the process of scientific discovery

TitleAbduction as a strategy for concept formation in mathematics: Cardano postulating a negative.
Publication TypeBook Chapter (with title)
Year of Publication2007
AuthorsHeeffer, A
Secondary AuthorsPombo, O, Gerner, A
Book TitleAbduction and the process of scientific discovery
Pages179–194
PublisherCentro de Filosofia das Ciências da Universidade de Lisboa
Abstract

When dealing with abductive reasoning in scientific discovery, historical case studies are focused mostly on the physical sciences, as with the discoveries of Kepler, Galilei and Newton. We will present a case study of abductive reasoning in early algebra. Two new concepts introduced by Cardano in his Ars Magna, imaginary numbers and a negative solution to a linear problem, can be explained as a result of a process of abduction. We will show that the first appearance of these new concepts fits very well Peirce’s original description of abductive reasoning. Abduction may be regarded as one important strategy for the formation of new concepts in mathematics.

Citation Key381663
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