@mastersthesis {492, title = {Entre Provas e Experimentos. Uma leitura wittgensteiniana das controv{\'e}rsias em torno da prova do Teorema das Quatro Cores}, year = {2013}, school = {Pontif{\'\i}cia Universidade Cat{\'o}lica do Rio de Janeiro}, type = {PhD Thesis}, address = {Rio de Janeiro}, abstract = {

Resumo

O advento do uso maci{\c c}o de computadores em provas matem{\'a}ticas, ocorrido ao final da d{\'e}cada de setenta com a solu{\c c}{\~a}o de um famoso problema matem{\'a}tico {\textendash} a prova do Teorema das Quatro Cores {\textendash} ocasionou disputas filos{\'o}ficas que ainda hoje demandam esclarecimentos. O objetivo principal da tese consiste em elaborar alguns dos referidos esclarecimentos desde uma perspectiva motivada pela filosofia da matem{\'a}tica de Ludwig Wittgenstein, especialmente no que diz respeito {\`a} distin{\c c}{\~a}o continuamente manuseada e depurada pelo fil{\'o}sofo ao longo do desenvolvimento de seu pensamento entre provas e experimentos. Ap{\'o}s apresentar as principais ideias da prova do Teorema das Quatro Cores em termos hist{\'o}ricos, algumas distin{\c c}{\~o}es conceituais metodologicamente significativas s{\~a}o elaboradas. A seguir o trabalho analisa, a partir da concep{\c c}{\~a}o funcional de a priori de Arthur Pap, o argumento da introdu{\c c}{\~a}o da experimenta{\c c}{\~a}o nas matem{\'a}ticas de Thomas Tymoczko. A leitura das controv{\'e}rias filos{\'o}ficas que se seguiram ao argumento de Tymoczko {\'e} ent{\~a}o apresentada, aplicando-se as distin{\c c}{\~o}es conceituais anteriormente elaboradas. Por fim algumas ideias wittgensteinianas sobre da disitin{\c c}{\~a}o entre provas e experimentos s{\~a}o exploradas em conex{\~a}o com a no{\c c}{\~a}o de sinopticidade de provas, considerando menos os pap{\'e}is espec{\'\i}ficos de tais no{\c c}{\~o}es na filosofia da matem{\'a}tica de Wittgenstein, do que investigando as vantagens de suas poss{\'\i}veis aplica{\c c}{\~o}es no esclarecimento de t{\'o}picos cr{\'\i}ticos das referidas disputas.

Palavras-chave:
Experimento; Prova; Teorema das Quatro Cores; Wittgenstein.

Abstract

Between proofs and experiments: a wittgensteinean reading of the philosophical controversies surrounding the Four Color Theorem proof. Rio de Janeiro, 2013. 203p. Thesis - Departamento de Filosofia, Pontif{\'\i}cia Universidade Cat{\'o}lica do Rio de Janeiro.

The massive use of computers in mathematical proofs, which started in the end of the seventies trough the solution of one famous mathematical problem {\textendash} the Four-Color Theorem {\textendash} entailed philosophical disputes still in need of elucidation. The central aim of this thesis consists in elaborating some of these elucidations from a point of view motivated by Ludwig Wittgenstein{\textquoteright}s philosophy of mathematics, mainly in what concerns the distinction between proofs and experiments, which was continuously used and elaborated by the philosopher in the course of the development of his thought. After the presentation of the main ideas involved in the proof of the Four-Color Theorem from a historical perspective, some methodological conceptual distinctions are elaborated. The thesis then shifts to an analysis of the introduction of experiment in mathematics argument, by Thomas Tymoczko, from the point of view of Arthur Pap{\textquoteright}s conception of functional a priori. An interpretation of the controversies that followed that argument is developed trough the application of the conceptual distinctions previously elaborated. At last, some wittgensteinian ideas about the distinction between proofs and experiments are explored in connection with the notion of surveyability of proofs, concerned less with its specific roles in Wittgenstein{\textquoteright}s philosophy of mathematics than with investigating the advantages of its possible applications in the elucidation of some critical points in the referred controversies.

Key-Words:
Experiment; Proof; Four-Color Theorem; Wittgenstein.

}, author = {SECCO, Gisele Dalva}, editor = {PEREIRA, Luiz Carlos Dias Pinheiro} }