Esta disponivel meu ultimo artigo “Is modern logic non-Aristotelian?" relativo a palestra que apresentei em Moscou em 2012 no congresso dedicado a Vasiliev http://www.jyb-logic.org/papers.html Comentarios sao bemvindos
Abstract In this paper we examine up to which point Modern logic can be qualified as non-Aristotelian. After clarifying the difference between logic as reasoning and logic as a theory of reasoning, we compare syllogistic with propositional and first-order logic. We touch the question of formal validity, variable and mathematization and we point out that Gentzen’s cut-elimination theorem can be seen as the rejection of the central mechanism of syllogistic – the cut-rule has been first conceived as a modus Barbara by Hertz. We then examine the non-Aristotelian aspect of some non-classical logics, in particular paraconsistent logic. We argue that a paraconsistent negation can be seen as neo-Aristotelian since it corresponds to the notion of subcontrary in Boethius’ square of opposition. We end by examining if the comparison promoted by Vasiliev between non-Aristotelian logic and non-Euclidian geometry makes sense. 1. The two-stage history of logic 2. Non-Aristotelian logic and Non-Aristotelian Logic 3. Syllogistic, propositional and first-order logic 4. Aristotelian logic, formal logic and mathematical logic 5. Farewell to Barbara 6. Are non-classical logics non-Aristotelian? 7. The square of opposition and neo-Aristotelian logic 8. Non-Aristotelian logic and Non-Euclidian geometry 9. Bibliography _______________________________________________ Logica-l mailing list [email protected] http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
