Open AccessMathematical Understanding and the role of Counterexamples and Pathologies: a case study in Mathematical Analysis.
Author(s) -
Carmen Martínez-Adame
Publication year - 2018
Publication title -
revista colombiana de filosofía de la ciencia/revista colombiana de filosofía y ciencia
Language(s) - English
Resource type - Journals
eISSN - 2463-1159
pISSN - 0124-4620
DOI - 10.18270/rcfc.v18i36.2334
Subject(s) - counterexample , object (grammar) , epistemology , subject (documents) , philosophical analysis , function (biology) , cognitive science , computer science , mathematics , psychology , artificial intelligence , philosophy , biology , discrete mathematics , evolutionary biology , library science
Pathological objects and counterexamples play an important role in mathematical understanding even though there is no precise definition of them.What is a pathological object? What makes a mathematical object pathological?The aim of this paper is to try to give a partial response to these questions from the standpoint of mathematical analysis in the nineteenth and twentieth centuries. We will describe briefly how the notion of function changed dramatically in the nineteenth century and we will study how this change brought on important philosophical consequences for the subject implying that the notion of pathology relies upon certain properties occurring only in a few instances.