Handbook of the History of Logic: - Fordham University Faculty

272 Terence Parsons
Change every main denoting phrase of the form ‘No T ’into‘every T
not’, and every main denoting phrase of the form ‘a T’into‘some T ’,.
This leaves ‘every’ and ‘some’ as the only quantifier signs on main
terms.
Remove any double not’s anywhere in the formula whenever they appear.
Starting at the left, replace each ‘not every T ’by‘some T not’, and
each ‘not some T ’by‘every T not’, and each ’not D’ by‘D not’.
Remove double not’s whenever they appear.
Every categorical proposition has a unique prenex-convert produced by these rules.
Call the quantifier signs ‘every’ and ‘some’ opposites. We can then define:
a main term has (wide)/(narrow) quantificational import in a proposition
iff when the proposition is converted into prenex form the term
(is not)/(is) preceded by a main term with the opposite quantifier sign
a main term has (universal)/(existential) global quantificational import
in a proposition iff when the proposition is converted into prenex
form the term ends up with (’every’)/(’some’) as its quantifier sign
This defines global quantificational import for all main terms in any categorical
proposition.
9.4.2 Causes of the Modes
One can now establish the following equivalence between the classifications above
in terms of global quantificational import and the refined modes of supposition
that are yielded by the rules governing causes of the modes in the last section. If
these rules are applied to the forms we have been discussing:
A term has Determinate supposition according to the rules iff it has
wide existential quantificational import
A term has Merely Confused supposition according to the rules iff it
has narrow existential quantificational import
A term has Wide Distributive supposition according to the rules iff it
has wide universal quantificational import
A term has Narrow Distributive supposition according to the rules iff
it has narrow universal quantificational import
Illustration: Let us test ‘donkey’ for its mode of supposition in ‘Some donkey is
a predator’. ‘Donkey’ has determinate supposition here, because it is already in
prenex form, existentially quantified:
Some donkey is a predator
It has wide distributive supposition here, for the same reason: