In this paper I explore the ways in which Alexander of Aphrodisias employs and develops so-called ‘common notions’ as reliable starting points of deductive arguments. He combines contemporary developments in the Stoic and Epicurean use of common notions with Aristotelian dialectic, and axioms. This more comprehensive concept of common notions can be extracted from Alexander’s commentary on Metaphysics A 1–2. Alexander puts Aristotle’s claim that ‘all human beings by nature desire to know’ in a larger deductive framework, and adds weight to Aristotle’s use of the common understanding of the notion of ‘wisdom’. Finally I will indicate how these upgraded common notions are meant to play an important role in the general framework of metaphysics as a science.
Olympiodorus led the Platonist school of philosophy at Alexandria for several decades in the sixth century, and both Platonic and Aristotelian commentaries ascribed to him survive. During this time the school’s attitude to the teaching of Aristotelian syllogistic, originally owing something to Ammonius, changed markedly, with an early tendency to reinforce the teaching of syllogistic even in Platonist lectures giving way to a greater awareness of its limitations. The vocabulary for arguments and their construction becomes far commoner than the language of syllogistic and syllogistic figures, and also of demonstration. I discuss the value of these changes for the dating of certain works, especially where the text lectured on does not demand different emphases. The commitment to argument rather than to authority continues, but a greater emphasis eventually falls on the establishment of the premises than on formal validity.
In late antiquity, logic developed into what Ebbesen calls the LAS, the Late Ancient Standard. This paper discusses the Neoplatonic use of LAS, as informed by epistemological and metaphysical concerns. It demonstrates this through an analysis of the late ancient debate about hypothetical and categorical logic as manifest in the practice of syllogizing Platonic dialogues. After an introduction of the Middle Platonist view on Platonic syllogistic as present in Alcinous, this paper presents an overview of its application in the syllogizing practice of Proclus and others. That overview shows that the two types were considered two sides of the same coin, to be used for the appropriate occasions, and both relying on the methods of dialectic as revealing the structure of knowledge and reality. Pragmatics, dialectic, and didactic choices determine which type or combination is selected in syllogizing Plato. So even though there is no specific Neoplatonic logic, there is a specific Neoplatonic use of LAS.
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.
This paper provides a case study for the use of syllogistic reconstructions in the commentaries on Plato by the fifth-century commentator Proclus. The paper discusses Proclus’ reconstruction of the argument about the range of the Forms in Plato’s Parmenides (130b–e). In his commentary on this dialogue, Proclus reports a syllogistic reconstruction of the argument proposed by some of his predecessors. In this reconstruction, the argument as a whole is interpreted as a straightforward attack on the existence of Forms, while the different premises of the hypothetical syllogism represent the respective positions of Parmenides and Socrates in the discussion. For Proclus, however, the argument about the range of Forms is not meant to be critical of the Forms, but rather provides a positive instruction about their range of application. I argue that while Proclus finds the syllogism a useful tool to reconstruct the different positions in the exegetical history of the argument, he does not accept it as an adequate reconstruction on his own account. The argument can be traced back most likely to the so-called ‘logical’ interpretations of the Parmenides that Proclus discusses – and dismisses – in the prologue to his commentary.