William of Ockham on Particular Negative Propositions

Abstract

My aim in this paper is to show that the views of Priest and Read on these three points themselves need some correction.' Commenting on points (a) and (b)(i), which are focused on Ockham's treatment of particular negative propositions, I shall not follow the way Priest and Read have chosen to formalize Ockham's supposition theory. Instead I shall use, following R. Price, a 'sorted calculus of individuals with identity as its only predicate'.2 Let the singular terms fl, f2, . . . be the substituends of the individual variable 'f', the values of which are those and only those objects to which the general term F applies, let the singular terms gl, g2, . . . be the substituends of the individual variable 'g', the values of which are those and only those objects to which the general term G applies, and so on, to the effect that all predicates other than that of identity can be dispensed with in favour of lists of singular terms denoting individuals of certain kinds, over which our sorted variables 'f', 'g', . . . are to range. In terms of such a 'many-sorted logic with identity'3 the four categorical propositions (A) 'Every F is a G', (E) 'No F is a G', (I) 'Some F is a G', and (0) 'Some F is not a G' can be symbolized in a manner which not only takes into account the fact that Ockham adheres to what has been called a 'two-name' (or identity) theory of predication (as opposed to a 'inherence' theory), but also allows a faithful rendering of the so-called 'descent to singulars', which is characteristic of Ockham's supposition theory.4