Boole, criador da lógica moderna
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jean-yves beziau
Jul 20, 2021, 10:14:13 PM7/20/21
to Lista acadêmica brasileira dos profissionais e estudantes da área de LOGICA
Estou finalizando a preparação de um livro que vai compilar os melhores artigos de 10 anos do workshop
La Logique en Question / Logic-in-Question
que estou organizando na Sorbonne em Paris desde 2011, com meu colega Jean-Pierre Desclés (que foi durante muitos anos o diretor do departamento de matemática e de informática da Sorbonne).
Nesses artigos achei dois comentários interessantes relativamente ao Boole:
"Symbolism in Boole - Its inability to be interpreted" artigo de Michel Serfati
Frege considered that Boolean calculus, for which he had little sympathy, (unlike that of Peano, which he judged to be closer to his own conceptions), was, as he said in Leibnizian terms, only a Calculus ratiocinator, without being a lingua characteristica. The future of the history of science and logic prove that both Boole's contemporaries and Frege were wrong, by depreciating the procedures and mathematical contents of Boole's work. Today, despite some shortcomings, (which we have identified above), it embodies the real break in the history of the Laws of Thought. Note Bourbaki's opinion: Boole must be considered the true creator of modern logic.
"Boole’s symbolized laws of thought facing empiricism" artigo de Marie-José Durand-Richard
Even if Gottlob Frege (1848-1925) is often considered as the founder of modern logic – for his formalisation of logical inference, and of universal and existential propositions with quantifiers – Boole realised the first essential jump form analysis of language to mathematical formalisation of this analysis. His work was supported by the same will as that of the Cambridge algebraists to close the debates between theory and practices in mathematics. Moreover, as evidenced by the whole text, and specially by the last chapter of the Laws of Thought, Boole grasped empirical critics on logics, and, as the Cambidge algebraists, he was alarmed at the dangers of a mechanization of thought by algebraic or formal reasoning, and at the frailness and the lack of universality of human practices. He partook the methodology of those who tried to found algebra on symbolical methods, and introduced a median thought so as to close the debates about the competition between logic and mathematics in the system of human knowledge.
Marie-José Durand-Richard fez o doutorado sobre Boole, ela é uma das melhores especialistas mundial de Boole.
Michel Serfati (30/09/1938 - 30/09/2018) dirigiu durante muitos o seminário de epistemologia e história das idéias matemáticas (Institut Henri-Poincaré, Paris) e ele autor de um livro bem importante:
La révolution symbolique. La constitution de l'écriture symbolique mathématique
Este livro não foi ainda traduzido em inglês mas vem aí um artigo que é um resumo deste livro
"Symbolic revolution, scientific revolution: mathematical and philosophical aspects"
que foi publicado no excelente livro
Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics
Quero apontar que além de
“Review Essay of Van Heijenoort - Logic and its History in the Work and Writings of Jean van Heijenoort by I.H.Anellis”, Modern Logic, 8 (2000), pp.105-117.
eu escrevi também:
"Review Essay of The Search for Mathematical Roots 1870-1940 (Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel)" by I. Grattan-Guiness, The Review of Modern Logic, 10 (2005), pp.135-138.
e
"Review Essay of From Peirce to Skolem – A neglected chapter in the history of logic by G.Brady", The Review of Modern Logic, 11 (2007), pp.155-161.
e
"A History of Truth-Values"
Handbook of the History of Logic, Volume 11 ( Logic: A History of its Central Concepts), 2012, Pages 235-307
Neste artigo faço uma análise comparativa de Boole, Peirce e Frege.
JYB
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