In Logical Forms Part II, Chateaubriand begins the Chapter on “Propositional Logic” by considering the reading of the ‘conditional’ by ‘implies’; in fact he states that:There is a confusion, as a matter of fact, and it runs deep, but it is a confusion in propositional logic itself, and the mathematician’s reading is a rather sensible one.After a careful, erudite analysis of various philosophical viewpoints of logic, Chateaubriand comes to the conclusion that:Pure propositional logic, as just cha…
Read moreIn Logical Forms Part II, Chateaubriand begins the Chapter on “Propositional Logic” by considering the reading of the ‘conditional’ by ‘implies’; in fact he states that:There is a confusion, as a matter of fact, and it runs deep, but it is a confusion in propositional logic itself, and the mathematician’s reading is a rather sensible one.After a careful, erudite analysis of various philosophical viewpoints of logic, Chateaubriand comes to the conclusion that:Pure propositional logic, as just characterized, belongs to ontological logic, and it does not include a theory of deduction as a human activity. This is a part of epistemological logic, and is more closely connected to the applications of pure propositional logic.An implicit assumption in Chateaubriand’s reasoning appears to be that propositions have a timeless status. I will present arguments for the opposite viewpoint which leads to an analysis of Propositional Logic not covered under Chateaubriand’s monograph and perhaps resolves some conflicts therein; much as the conflict between the Intuitionist and Classical Mathematician on whether every function on the Reals is continuous is resolved by the realization that they are talking about different “entities”.Em Logical Forms II, Chateaubriand inicia o capítulo “Lógica Proposi-cional” considerando a leitura do ‘condicional’ como ‘implica’. De fato, ele diz o seguinte:Na verdade, existe uma confusão, e ela é profunda, mas é uma confusão na lógica proposicional ela mesma, e a leitura de um matemático é bastante sensível.Depois de uma análise cuidadosa e erudita dos vários pontos de vista filosóficos da lógica , Chateaubriand chega à conclusão que:A lógica proposicional pura, tal como aqui caracterizada, pertence à lógica ontológica, e não inclui uma teoria da dedução como atividade humana. Isto é parte da lógica epistemológica, e é mais intimamente conectada às aplicações da lógica proposicional.Uma premissa implícita no raciocínio de Chateaubriand parece ser a de que proposições têm um estatuto atemporal. Eu argumentarei em favor da visão oposta, que leva a uma análise da Lógica Proposicional não abordada no texto de Chateaubriand e que talvez resolva alguns conflitos. Muito do conflito entre Intuicionistas e Matemáticos Clássicos sobre se toda função sobre os números reais é contínua é resolvido pela compreensão de que eles estão falando de “entidades” diferentes
