Gabriel Shapiro

In Metaphysics Γ.3, Aristotle argues that it is impossible to deny the PNC. However, as several commentators—including Code, Barnes, Priest, Kirwan, and Dancy—have objected, Aristotle’s argument appears to rely on the invalid inference from 1 to 2 as follows: 1. For all p, it is impossible to believe that p and not-p. 2. Therefore, it is impossible to believe that it is possible that there is a p such that p and not-p. We argue that this objection turns on a misunderstanding of Aristotle’s text, and that Aristotle's argument is valid and quite strong.

abstract: In the Categories, Aristotle relies on the truth of claims like ‘Socrates is an individual’ and ‘human is a species,’ but it is not clear how terms like ‘species’ and ‘individual’ fit into the framework of the Categories. Do these terms introduce substances or accidents? When we truly apply them to a subject, is the predication we express essential or accidental? These questions puzzled ancient commentators on the Categories but have largely been neglected in modern scholarship. My central contention is that these terms correspond to entities outside of the categories. An upshot of my account is that sentences like ‘human is a species’ and ‘Socrates is an individual’ express neither essential nor accidental predications.

According to the Categories, predicates can be ‘said of’ their subjects or they can be ‘present in’ their subjects. The said-of relation has received relatively little scholarly attention, and scholars disagree on the answers to four foundational questions about the relation. (i) What is it? (ii) Is it an essential relation? (iii) How is it related to predication? (iv) Is it primitive? I argue that A is said-of B just in case A is a formal part of B. On this account, said-of is an essential relation and it is definable, but it is not defined in terms of predication.