Aristotle's philosophically most explicit and sophisticated account of the concept of a (primary-)universal proof is found, not in "Analytica Posteriora" 1.4, where he introduces the notion, but in 1.5. In 1.4 Aristotle merely says that a universal proof must be of something arbitrary as well as of something primary and seems to explain primacy in extensional terms, as concerning the largest possible domain. In 1.5 Aristotle improves upon this account after considering three ways in which we may delude ourselves into (...) thinking we have a primary-universal proof. These three sources of delusion are shown to concern situations in which our arguments do establish the desired conclusion for the largest possible domain, but still fail to be real primary-universal proofs. Presupposing the concept of what may be called an immediate proof, in which something is proved of an arbitrary individual, Aristotle in response now demands that a proof be immediate of the primary thing itself and goes on to sketch a framework in which an intensional criterion for primacy can be formulated. For the most part this article is a comprehensive and detailed commentary on Aristotle's very concise exposition in 1.5. One important result is that the famous passage 74a17-25 referring to two ways of proving the alternation of proportions cannot be used as evidence for the development of pre-Euclidean mathematics. (shrink)

This paper highlights an important distinction underlying the possibility of inquiry, between first _identifying the subject of inquiry and ultimately _explaining it: that the former can be achieved before and without the latter is a presupposition of inquiry. I believe Aristotle is keenly aware of this in _Posterior Analytics, II.8, where he shows how a scientific demonstration can "manifest" a definition. I argue that such a demonstration consists of two sorts of syllogisms, one identifying the definiendum, the other explaining it. (...) Further, this distinction is tied in crucial ways to two others: between existence and essence, and between particular and universal. (shrink)

This paper highlights an important distinction underlying the possibility of inquiry, between first _identifying the subject of inquiry and ultimately _explaining it: that the former can be achieved before and without the latter is a presupposition of inquiry. I believe Aristotle is keenly aware of this in _Posterior Analytics, II.8, where he shows how a scientific demonstration can "manifest" a definition. I argue that such a demonstration consists of two sorts of syllogisms, one identifying the definiendum, the other explaining it. (...) Further, this distinction is tied in crucial ways to two others: between existence and essence, and between particular and universal. (shrink)

David Bronstein sheds new light on Aristotle's Posterior Analytics--one of the most important, and difficult, works in the history of western philosophy--by arguing that it is coherently structured around two themes of enduring philosophical interest: knowledge and learning. He argues that the Posterior Analytics is a sustained examination of scientific knowledge, an elegantly organized work in which Aristotle describes the mind's ascent from sense-perception of particulars to scientific knowledge of first principles. Bronstein goes on to highlight Plato's influence on Aristotle's (...) text, and argues against current orthodoxy that Aristotle is committed to the Socratic Picture of inquiry, according to which one should seek what a thing's essence is before seeking its demonstrable attributes and their causes. (shrink)

I discuss an important feature of the notion of cause in Post. An. 1. 13, 78b13–28, which has been either neglected or misunderstood. Some have treated it as if Aristotle were introducing a false principle about explanation; others have understood the point in terms of coextensiveness of cause and effect. However, none offers a full exegesis of Aristotle's tangled argument or accounts for all of the text's peculiarities. My aim is to disentangle Aristotle's steps to show that he is arguing (...) in favour of a logical requirement for a middle term's being the appropriate cause of its explanandum. Coextensiveness between the middle term and the attribute it explains is advanced as a sine qua non condition of a middle term's being an appropriate or primary cause. This condition is not restricted either to negative causes or to middle terms in second‐figure syllogisms, but ranges over all primary causes qua primary. (shrink)