In Posterior Analytics 71b9 12, we find Aristotle’s definition of scientific knowledge. The definiens is taken to have only two informative parts: scientific knowledge must be knowledge of the cause and its object must be necessary. However, there is also a contrast between the definiendum and a sophistic way of knowing, which is marked by the expression “kata sumbebekos”. Not much attention has been paid to this contrast. In this paper, I discuss Aristotle’s definition paying due attention to this contrast (...) and to the way it interacts with the two conditions presented in the definiens. I claim that the “necessity” condition ammounts to explanatory appropriateness of the cause. (shrink)

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)

_ Source: _Volume 63, Issue 1, pp 64 - 86 Five times in the extant corpus, Aristotle refers to a distinction between two ways of being a ‘that for the sake of which’ that he sometimes marks by using genitive and dative pronouns. Commentators almost universally say that this is the distinction between an aim and beneficiary. I propose that Aristotle had a quite different distinction in mind, namely: that which holds between something and the aim or objective it is (...) in the business of producing or achieving, and that which holds between some instrument and the user of that instrument. (shrink)