Is Modern Logic Non-Aristotelian ? Jean-Yves Beziau Department of Philosophy – PPGF-UFRJ Federal University of Rio de Janeiro Brazilian Research Council Brazilian Academy of Philosophy 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 mathematizatioŶ aŶd ǁe poiŶt out that GeŶtzeŶs Đut-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