Handbook of the History of Logic: - Fordham University Faculty

242 Terence Parsons
is similar to a quantifier generalization step.) Each of the three modes has a
distinctive pattern of allowable ascents and descents.
What follows is an account that takes what is most common to the views of
Burley, Ockham, and Buridan. The theory consists of three definitions; they give
necessary and sufficient conditions for a term’s having determinate, distributive,
or merely confused supposition. Begin with determinate supposition:
Determinate supposition 99
A term F has determinate supposition in a proposition P if and only
if
[Descent]: you may descend under F to a disjunction of
propositional instances of all the F s, and
[Ascent]: from any such instance you may ascend back to
the original proposition P
A propositional instance of a proposition with respect to F is the proposition you
get by replacing the quantifier word of the denoting phrase containing F by ‘this’
or ‘that’, and adding a ‘not’ if the quantifier word is negative. Descent and ascent
are inferences, picturesquely expressed in terms of the directions in which the
inferences go. As an example, we validate the claim that ‘donkey’ has determinate
supposition in ‘Some donkey is spotted’ by establishing these two claims:
Descent: You may descend under ‘donkey’ in ‘Some donkey is spotted’
to a disjunction of instances of all donkeys. That is, from:
Some donkey is spotted
you may infer:
This donkey is spotted or that donkey is spotted or ...and
so on for all the donkeys.
99 This account is common to both Ockham and Buridan. Burley omits the ascent clause.
Buridan SD 4.3.5 (262-63) says “. . . there are two conditions for the determinate supposition
of some common term. The first is that from any suppositum of that term it is possible to infer
the common term, the other parts of the proposition remaining unchanged. For example, since,
in ‘A man runs’, the term ‘man’ supposits determinately, it follows that ‘Socrates runs; therefore,
a man runs’, ‘Plato runs; therefore, a man runs’, and so on for any singular contained under the
term ‘man’. The second condition is that from a common term suppositing in this manner all
singulars can be inferred disjunctively, by a disjunctive proposition. For example, ‘A man runs;
therefore, Socrates runs, or Plato runs or John runs ...’ and so on for the rest.”
Ockham SL I.70 (200) says: “. . . whenever it is possible to descend to the particulars under
a general term by way of a disjunctive proposition and whenever it is possible to infer such a
proposition from a particular, the term in question has personal determinate supposition.”
Burley PAL 1.1.3 para.82 (102) says: ‘Supposition is determinate when a common term supposits
disjunctively for its supposita in such a way that one can descend to all of its supposita
under a disjunction, as is plain with ‘Some man runs’. For it follows: ‘Some man runs; therefore,
Socrates runs, or Plato runs, and so on’.”