@incollection {381663,
	title = {Abduction as a strategy for concept formation in mathematics: {C}ardano postulating a negative.},
	booktitle = {Abduction and the process of scientific discovery},
	year = {2007},
	pages = {179{\textendash}194},
	publisher = {Centro de Filosofia das Ci{\^e}ncias da Universidade de Lisboa},
	abstract = {<p>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 <em>Ars Magna</em>, 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 Peirces original description of abductive reasoning. Abduction may be regarded as one important strategy for the formation of new concepts in mathematics.</p>},
	author = {Heeffer, Albrecht},
	editor = {Pombo, Olga and Gerner, Alexander}
}
