<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Heeffer, Albrecht</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">Pombo, Olga</style></author><author><style face="normal" font="default" size="100%">Gerner, Alexander</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Abduction as a strategy for concept formation in mathematics: Cardano postulating a negative.</style></title><secondary-title><style face="normal" font="default" size="100%">Abduction and the process of scientific discovery</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year></dates><publisher><style face="normal" font="default" size="100%">Centro de Filosofia das Ciências da Universidade de Lisboa</style></publisher><pages><style face="normal" font="default" size="100%">179–194</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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 &lt;em&gt;Ars Magna&lt;/em&gt;, 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.&lt;/p&gt;</style></abstract></record></records></xml>