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Made available in DSpace on 2014-12-17T14:35:50Z (GMT). No. of bitstreams: 1 GiselleCS_tese.pdf: 1424263 bytes, checksum: 0a3b291c39e9d1dfd7f82f5c1ef897a3 (MD5) Previous issue date: 2008-06-13 / The present study has as objective to explaining about the origins of the mathematical logic. This has its beginning attributed to the autodidactic English mathematician George Boole (1815-1864), especially because his books The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854) are recognized as the inaugural works of the referred branch. However, surprisingly, in the same time another mathematician called Augutus of Morgan (1806-1871) it also published a book, entitled Formal Logic (1847), in defense of the mathematic logic. Even so, times later on this same century, another work named Elements of Logic (1875) it appeared evidencing the Aristotelian logic with Richard Whately (1787-1863), considered the better Aristotelian logical of that time. This way, our research, permeated by the history of the mathematics, it intends to study the logic produced by these submerged personages in the golden age of the mathematics (19th century) to we compare the valid systems in referred period and we clarify the origins of the mathematical logic. For that we looked for to delineate the panorama historical wrapper of this study. We described, shortly, biographical considerations about these three representatives of the logic of the 19th century formed an alliance with the exhibition of their point of view as for the logic to the light of the works mentioned above. In this sense, we aspirated to present considerations about what effective Aristotelian?s logic existed in the period of Boole and De Morgan comparing it with the new emerging logic (the mathematical logic). Besides of this, before the textual analysis of the works mentioned above, we still looked for to confront the systems of Boole and De Morgan for we arrive to the reason because the Boole?s system was considered better and more efficient. Separate of this preponderance we longed to study the flaws verified in the logical system of Boole front to their contemporaries' production, verifying, for example, if they repeated or not. We concluded that the origins of the mathematical logic is in the works of logic of George Boole, because, in them, has the presentation of a new logic, matematizada for the laws of the thought similar to the one of the arithmetic, while De Morgan, in your work, expand the Aristotelian logic, but it was still arrested to her / O presente estudo tem como objetivo uma elucida??o das origens da l?gica matem?tica. Esta tem seu in?cio atribu?do ao matem?tico ingl?s autodidata George Boole (1815-1864), especialmente porque seus livros The Mathematical Analysis of Logic (1847) e An Investigation of the Laws of Thought (1854) s?o reconhecidos como as obras inaugurais do referido ramo. Contudo, curiosamente, na mesma ?poca um outro matem?tico chamado Augutus de Morgan (1806-1871) tamb?m lan?ou um livro, intitulado Formal Logic (1847), em defesa da matematiza??o da l?gica. Mesmo assim, tempos depois neste mesmo s?culo, uma outra obra nomeada Elements of Logic (1875) surgiu evidenciando a l?gica aristot?lica a partir da figura de Richard Whately (1787-1863), considerado o maior l?gico aristot?lico da ?poca. Desta forma, nossa pesquisa, permeada pela hist?ria da matem?tica, prop?e estudar a l?gica produzida por estes personagens imersos na idade ?urea da matem?tica (s?culo XIX) a fim de compararmos os sistemas vigentes no referido per?odo e clarificarmos as origens da l?gica matem?tica. Para isso buscamos delinear o panorama hist?rico envolt?rio deste estudo. Descrevemos, brevemente, considera??es biogr?ficas destes tr?s representantes da l?gica do s?culo XIX aliadas ? exposi??o de seus pontos de vista quanto ? l?gica ? luz das obras citadas acima. Neste sentido, aspiramos ainda apresentar considera??es acerca do que existia de l?gica aristot?lica vigente no per?odo de Boole e De Morgan comparando-a com a nova l?gica emergente (a l?gica matem?tica). Al?m disso, diante da an?lise textual das obras citadas acima, buscamos ainda confrontar os sistemas de Boole e De Morgan a fim de chegarmos ao motivo pelo o qual o de Boole ter sido considerado melhor e mais eficiente. ? parte desta preponder?ncia, almejamos estudar as falhas constatadas no sistema l?gico de Boole frente ? produ??o de seus contempor?neos, verificando, por exemplo, se elas se repetiram ou n?o. Conclu?mos que as origens da l?gica matem?tica residem nas obras de l?gica de George Boole, visto que, nelas, h? a apresenta??o de uma nova l?gica, matematizada pelas leis do pensamento an?logas ?s da aritm?tica, enquanto De Morgan conseguiu em seu trabalho expandir a l?gica aristot?lica, mas ainda esteve preso a ela

Made available in DSpace on 2014-06-11T19:24:52Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-02-25Bitstream added on 2014-06-13T19:52:43Z : No. of bitstreams: 1 000755405.pdf: 721229 bytes, checksum: a665c9ee190d3a2675b924dd4bb2c525 (MD5) / As origens da Teoria dos Invariantes na Inglaterra e o Mécanique Analytique de Lagrange (1788), é um trabalho voltado principalmente a entender uma possível influência que levou George Boole em 1841, a escrever o artigo Exposition of a General Theory of Linear Transformations e verificar se a motivação que o fez produzir este trabalho é igual ou diferente da motivação que ele exerceu sobre Arthur Cayley e consequentemente sobre James Joseph Sylvester. O presente trabalho apresenta um estudo das origens da Teoria dos Invariantes, no século XIX na Inglaterra. De acordo com os historiadores da Matemática o marco do início desta Teoria foi a publicação de George Boole em 1841. Assumimos este artigo como referência principal para realizar nossa pesquisa. Analisamos “antes” e “após” esta publicação de 1841. Concluímos que o Mécanique Analytique de Lagrange, foi a principal motivação para George Boole escrever seu trabalho e, certamente, George Boole foi uma grande influência para Arthur Cayley no que condiz com a escolha do assunto “invariantes” bem como o desenvolvimento desta Teoria por Cayley / The origins of the theory of invariants in England and Mécanique Analytique of Lagrange (1788), is a work geared primarily to understand a possible influence that led George Boole in 1841, writing the article Exposition of the General Theory of Linear Transformations and verify that the motivation that did produce this work is equal or different of the motivation that he exerted on Arthur Cayley and James Joseph Sylvester consequently. This paper presents a study of the Invariant Theory origins, in the nineteenth century in England. According to historians of Mathematics the beginning of this Theory was the publication in 1841 of George Boole. We have taken this article as a reference to our research. We have proposed to analyzed before and after this publication, 1841. We conclude that the Mécanique Analytique Lagrange, was the essential motivation for George Boole write his work, and certainly George Boole was a great influence to Arthur Cayley in which matches the choice of subject invariants as well as the development of this Theory by Cayley