O-propositions and Ockham's theory of supposition.
Alfred J. Freddoso · Notre Dame Journal of Formal Logic · 1979
In their recent article "The Formalization of Ockham's Theory of Supposition" Priest and Read [4] make the following two claims:1.In propositions 1 of the form of ' (ΞUXPxΛΓ & ~P2 x)' the predicate term, in this case P 2 , has merely confused supposition, although Ockham mistakenly thought it to have confused and distributive supposition.2. Contrary to the opinion of those who, like Geach, maintain that merely confused supposition is superfluous, there is at least one type of propositions (viz., negative indefinite exclusive propositions such as'Only pigs don't fly') in which both the subject and the predicate have merely confused supposition, and in dealing with them the notion of merely confused supposition is ineliminable.I will try to show in what follows that both of these claims are false.Further, in my discussion of the first claim I will construct an alternative, though Ockhamistic, account of the supposition of the predicate in a particular negative proposition (O-proposition).I will then use this account in constructing an explication of negative indefinite exclusive propositions without recourse to the notion of merely confused supposition.Since my purpose is not explicitly to discuss or evaluate the formalization of Ockham's theory proposed by Priest and Read, I will make use instead of the sort of schematization employed by Loux in "Ockham on Generality" ([3], pp.23-46).Thus, '{AD/'A 9 }' will stand for the appellative domain of A, i.e., for all those things which A can supposit for in a present-tense non-modal proposition.Also, the symbol v will be used as both a terminal and propositional connective, with the context of its occurrence making clear which use is intended.Finally, although I agree with Priest and Read that an adequate formalization of Ockham's theory must be given in an infinitary language, that issue is not germane to the points I wish to make here.So I will simplify the following discussion by treating the appellative domains of general terms as finite.2 According to Priest and Read an O-proposition, schematically represented by