Joshua Mendelsohn

This paper offers an interpretation of Aristotle’s claim that epistēmē haplōs requires the knower to be ‘incapable of being persuaded otherwise’ (ametapeistos). The claim is interpreted as a requirement that a scientist with fully settled knowledge not undergo rational belief revision, itself a version of the Socratic idea that true knowledge is not subject to refutation or elenchos. Aristotle reduces this requirement to a pair of conditions regarding the knowledge and conviction (pistis) the scientist has in her principles. It is shown that these conditions serve to rule out precisely the types of refutation Aristotle takes to be incompatible with scientific knowledge.

In a series of recent papers, Emily Katz has argued that on Aristotle's view mathematical sciences are in an important respect no different from most natural sciences: They study sensible substances, but not qua sensible. In this paper, I argue that this is only half the story. Mathematical sciences are distinctive for Aristotle in that they study things ‘from’, ‘through’ or ‘in’ abstraction, whereas natural sciences study things ‘like the snub’. What this means, I argue, is that natural sciences must study properties as they occur in the subjects from which they are originally abstracted, even where they reify these properties and treat them as subjects. The objects of mathematical sciences, on the other hand, can be studied as if they did not really occur in an underlying subject. This is because none of the properties of mathematical objects depend on their being in reality features of the subjects from which they are abstracted, such as bodies and inscriptions. Mathematical sciences are in this way able to study what are in reality non-substances as if they were substances.

Recent formalizations of Aristotle's modal syllogistic have made use of an interpretative assumption with precedent in traditional commentary: That Aristotle implicitly relies on a distinction between two classes of terms. I argue that the way Rini (2011. Aristotle's Modal Proofs: Prior Analytics A8–22 in Predicate Logic, Dordrecht: Springer) employs this distinction undermines her attempt to show that Aristotle gives valid proofs of his modal syllogisms. Rini does not establish that Aristotle gives valid proofs of the arguments which she takes to best represent Aristotle's modal syllogisms, nor that Aristotle's modal syllogisms are instances of any other system of schemata that could be used to define an alternative notion of validity. On the other hand, I argue, Robert Kilwardby's ca. 1240 commentary on the Prior Analytics makes use of a term-kind distinction so as to provide truth conditions for Aristotle's necessity propositions which render Aristotle's conversion rules and first figure modal syllogisms formally valid. I reconstruct a suppositio semantics for syllogistic necessity propositions based on Kilwardby's text, and yield a consequence relation which validates key results in the assertoric, pure necessity and mixed necessity-assertoric syllogistics.