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Aristotle on Demonstration by reductio ad impossibile

Pro.Dr Marko Malink (New York University)


Abstract: In the first book of the Posterior Analytics, Aristotle develops a theory of scientific knowledge and demonstration. He argues that direct demonstrations are superior to demonstrations by reductio ad impossibile on the grounds that the former, but not the latter, proceed from premises which are prior in nature to the conclusion (Posterior Analytics 1.26). While this view has been widely influential throughout the history of philosophy, Aristotle's argument for it is not straightforward and has been deemed problematic since antiquity. The purpose of this talk is to shed new light on this argument. I argue that it relies on a specific relation of priority in nature among scientific propositions that is determined by the theory of predication presented in Posterior Analytics 1.19-23. I show how this relation of priority in nature allows us to make sense of Aristotle's thesis concerning demonstration by reductio ad impossibile. I conclude by indicating how Aristotle's thesis is related to analogous results in contemporary theories of grounding.


Marko Malink是纽约大学哲学系和古典系的双聘副教授,当下最杰出的亚里士多德和古代逻辑学的研究者之一。他在莱比锡大学学习了逻辑学和古希腊语,并于2004年取得了人文硕士学位,2008年,他在柏林洪堡大学取得了哲学博士学位。他的主要研究领域是古代哲学,尤其是古代逻辑和形而上学。 Malink还对逻辑史,语言哲学和语言学有兴趣。他的著作“Aristotle’s Modal Syllogistic”于2013年由哈佛大学出版社出版。他与Jacob Rosen的合著文章“A Method of Modal Proof in Aristotle”(in Oxford Studies in Ancient Philosophy )被The Philosopher’s Annual为2012年哲学界发表的十佳论文之一。他的文章“The Beginnings of Formal Logic: Deduction in Aristotle’s Topics vs. Prior Analytics”(in Phronesis)和“Aristotle on Principles as Elements”(in Oxford Studies in Ancient Philosophy)分别又于2015和2017年入选年度十佳哲学论文。2014年加入纽约大学之前,Malink曾在柏林洪堡大学和芝加哥大学任职。