Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 245
Every donkey is this mammal
you may infer the original proposition:
Every donkey is a mammal.
In illustrating the definitions above we showed that the subjects of affirmative
propositions and the predicate of the universal affirmative have the modes that
they were assigned throughout the tradition. All of the other terms in the standard
categorical propositions are like this. For example, we can show that by these
definitions the predicate term of a particular negative proposition has distributive
supposition:
The term ‘donkey’ has distributive supposition in ‘Some stone is not a donkey’
because
Descent: You may descend under ‘donkey’ to a conjunction of instances
of all donkeys. That is, from:
Some stone is not a donkey
you may infer:
Some stone is not this donkey and some stone is not that
donkey and ...and so on for all the donkeys.
Ascent: You may not ascend back to the original proposition; from
an instance of the form:
Some stone is not this donkey
you may not infer the original proposition:
Some stone is not a donkey.
The earlier and later theories agree on the terms of the standard Aristotelian
categorical propositions, but they disagree in many other cases. Consider the
proposition
Not every man is running
The subject of this proposition was taken to have distributive supposition by
Sherwood. This is presumably because the proposition is got by putting ‘not’ in
front of a universal affirmative proposition, in which ‘man’ is already distributed.
But on the later theory the mode of supposition changes when the ‘not’ is put
on. It is easy to check that according to the later theory of ascent and descent
the term ‘man’ in‘not every man is running’ has determinate supposition. This
is because from
Not every man is running