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Previous issue date: 2005-10-14 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics / O presente estudo tem como objetivo fazer uma reavalia??o do pensamento l?gico do matem?tico ingl?s George Boole (1815 1864). Desta forma, nossa pesquisa versa sobre reflex?es concernentes a an?lise matem?tica da l?gica permeada pela hist?ria da matem?tica. Para isso, realizamos uma colet?nea de considera??es biogr?ficas deste personagem ? luz de um estudo dos acontecimentos ocorridos no s?culo XIX e seu reflexo na produ??o matem?tica. Descrevemos brevemente as inova??es feitas por Boole nas ?reas de equa??es diferenciais e da teoria de invariantes. Fizemos ainda uma an?lise da l?gica de Boole, especialmente como formulada no livro The Mathematical Analysis of Logic, fazendo uma compara??o desta tanto com a l?gica aristot?lica tradicional, quanto ? l?gica moderna. Conclu?mos que Boole, como pretendia, expandiu a l?gica, n?o somente em termos do seu conte?do, mas tamb?m em termos dos seus m?todos e elabora??o formal. Conclu?mos ainda que o seu prop?sito foi a modelagem matem?tica do racioc?nio dedutivo, o que o levou a apresentar um formalismo que marcou ?poca para a l?gica e que, atrav?s de suas interpreta??es distintas, levou Boole a uma nova conceitua??o do que ? a pr?pria matem?tica
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/14224 |
| Date | 14 October 2005 |
| Creators | Souza, Giselle Costa de |
| Contributors | CPF:13056476453, http://lattes.cnpq.br/2466525106349625, Sad, Ligia Arantes, CPF:2957525768, http://lattes.cnpq.br/1714140036102231, Mendes, Iran Abreu, CPF:12432962249, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4704236U8, Fossa, John Andrew |
| Publisher | Universidade Federal do Rio Grande do Norte, Programa de P?s-Gradua??o em Educa??o, UFRN, BR, Educa??o |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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