I examine the question why in Proclus' view genetic processes provide demonstrative explanations, in light of the interpretation of Aristotle's theory of demonstration in late antiquity. I show that in this interpretation mathematics is not an explanatory science in the strict sense because its objects, being immaterial, do not admit causal explanation. Placing Proclus' account of demonstrative explanation in this context, I argue that this account is aimed at answering the question whether mathematical proofs provide causal explanation as opposed to (...) grounds. I show further that Proclus can answer this question in the affirmative due to his realist view of mathematical objects and the priority he ascribes to causal relations over logical relations. (shrink)

In this article I explain three puzzling features of Simplicius’ use of syllogistic reconstructions in his commentary on Aristotle’s Physics: (1) Why does he reconstruct Aristotle’s non-argumentative remarks? (2) Why does he identify the syllogistic figure of an argument but does not explicitly present its reconstruction? (3) Why in certain lemmata does he present several reconstructions of the same argument? Addressing these questions, I argue that these puzzling features are an expression of Simplicius’ assumption that formal reasoning underlies Aristotle’s prose, (...) hence they reflect his attempt to capture as faithfully as possible Aristotle’s actual mode of reasoning. I show further that, as a consequence of this seemingly descriptive use of syllogistic reconstructions, logic serves Simplicius not only as an expository and clarificatory tool of certain interpretations or philosophical views, but also motivates and shapes his exegetical stances and approach. (shrink)

This paper examines the widely accepted contention that geometrical constructions serve in Greek mathematics as proofs of the existence of the constructed figures. In particular, I consider the following two questions: first, whether the evidence taken from Aristotle's philosophy does support the modern existential interpretation of geometrical constructions; and second, whether Euclid's Elements presupposes Aristotle's concept of being. With regard to the first question, I argue that Aristotle's ontology cannot serve as evidence to support the existential interpretation, since Aristotle's ontological (...) discussions address the question of the relation between the whole and its parts, while the modern discussions of mathematical existence consider the question of the validity of a concept. In considering the second question, I analyze two syllogistic reformulations of Euclidean proofs. This analysis leads to two conclusions: first, it discloses the discrepancy between Aristotle's view of mathematical objects and Euclid's practice, whereby it will cast doubt on the historical and theoretical adequacy of the existential interpretation. Second, it sets the conceptual background for an alternative interpretation of geometrical constructions. I argue, on the basis of this analysis that geometrical constructions do not serve in the Elements as a means of ascertaining the existence of geometrical objects, but rather as a means of exhibiting spatial relations between geometrical figures. (shrink)

I examine Alexander of Aphrodisias’ theory of action, addressing the question how his view that human actions are determined by reason accounts for the capacity of doing otherwise. Calling into question the standard view that Alexander frees agents from internal determination, I argue that (1) the capacity of doing otherwise is a consequence of determination by reason, since it enables agents to do something different from what they would have done had they followed external circumstances; and (2) this capacity is (...) compatible with causal determination by reason because as a case of potentiality for opposites, it grants agents the qualified possibility of doing otherwise insofar as their nature as human beings is concerned – a possibility which remains also when their actions are causally determined by reason and by their internal disposition. I show further that these elements of Alexander’s theory of action are ultimately based on his conception of the soul, specifically on his commitment to Aristotle’s view that the human soul is not purely rational, as the Stoics hold, but has nonrational and rational parts. (shrink)

I argue that Aristotle’s late-antique commentators read into his theory of demonstration the notion of tekmeriodic proofs in attempt to integrate into the theory of demonstration the assumption that the principles of demonstration should be evident. In so doing, I trace the late antique commentators’ view to Alexander of Aphrodisias’ discussion of the principles of demonstration, showing how his assumption that the principles of demonstration should be evident underlies their notions of tekmeriodic proofs.

We mourn the loss of Yehuda Elkana, founding editor of this journal. Setting science in context was a mission of his life. For him this did not mean to relativize and historicize science to the point where it is no longer distinguishable as central to the human quest for knowledge. Rather, an understanding of science as being rooted in social, material, and cultural contexts was for him the key to its central role for solving the problems of humanity with which (...) he was so deeply concerned. (shrink)

After more than a decade Alexandre Métraux is leaving his post as a co-editor of Science in Context and will remain as a member of the editorial board.