Handbook of the History of Logic: - Fordham University Faculty

228 Terence Parsons
supposition whenever it supposits either for many things or for one thing taken
repeatedly. (He is worried about the second ‘man’ in‘Every man sees a man’
when everyone sees the same man — so that it is false that many men are seen.)
So the ‘many’ is merely a way of denying that we have a case of ‘one’, that
is, of determinate supposition. This reduces the characterization of distributive
supposition to:
A term has distributive supposition when it does not have determinate
supposition and it supposits for any.
It is clear in context that ‘supposits for any’ means that the term supposits for
any of its supposita; I will take this limitation for granted. The trick is to see how
to get this to mean anything other than a tautology. After all, how could a term
not “supposit for any” of its supposita? The answer must be that for a term to
supposit for something in a proposition requires more than just that the thing in
question be among the term’s supposita. I suggest that a term “supposits for any
of its supposita in a proposition” just in case that proposition’s being true entails
that it (that very proposition) is true for any of the supposita of the term (with
respect to the term in question), in the sense of ‘true for’ discussed above. Thus,
a necessary and sufficient condition for:
is:
‘T ’ supposits for any of its supposita in a proposition ‘. . . T ...’
the proposition ‘. . . QT ...’ entails that ‘. . . QT . . . ’ is true for any of
T ’s supposita.
This can then be further spelled out as follows:
Necessarily, if ‘. . . QT ...’, then for any x that is T : ‘...x...’ is true
For example, the term ‘dog’ has distributive supposition in ‘every dog is spotted’
because it does not have determinate supposition there, and:
Necessarily: if every dog is spotted, then, for any x that is a dog: x is
spotted.
(Again, this is an explanation of how to understand William’s account, not a
proposal for how to replace his account with something clearer. His account was
already fully stated above, and I have not suggested revising it.)
One can check that this account also gives the intended results for the subject
and predicate terms of universal negatives. It also classifies the predicates of
particular negatives as distributed, because
Necessarily: if some dog is not spotted, then, for any x that is spotted,
some dog is not x.