All Brutes are Subhuman:

Aristotle and Ockham on Privative Negation

Synthese 134 (2003), 429-461.

Abstract

The mediaeval logic of Aristotelian privation, represented by Ockham’s exposition of All A is non-P as All S is of a type T that is naturally P and no S is P,  is critically evaluated as an account of privative negation.  It is argued that there are two senses of privative negation: (1) an intensifier (as in subhuman), the inverse of Neoplatonic hypernegation (superhuman), which is studied in linguistics as an operator on scalar adjectives, and (2) a (often lexicalized) Boolean complement relative to the extension of a privative negation in sense (1) (e.g. Brute).  This second sense, which is that of privative negation in modern linguistics,  is shown to be Aristotle’s.  It is argued that Ockham’s exposition fails to capture the full  logic of Aristotelian privation due to limitations in the expressive power of the syllogistic.