Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 267
I have argued above that whether one descends to a disjunctive or conjunctive
term is a matter of grammar, not of logic. That may be why the addition of a
fourth mode in terms of descent to a conjunctive term has not yielded an interesting
theory. However, there is a way to add a fourth mode that yields an improved
account. This is achieved not by adding a new mode that classifies terms which
satisfy none of the conditions for the traditional modes, but rather by subdividing
the category of distributive supposition. For reasons to be given later, I will call the
one sort of distribution “wide distribution” and the other “narrow distribution”.
Wide distributive supposition is traditional distributive supposition in cases in
which one can ascend back to the original proposition from the whole conjunction
of propositional instances under the term. (Not from a single instance, but from
the whole conjunction.) Narrow distributive supposition is distribution where one
cannot make this ascent. The four modes would then be:
Determinate:
Descent to a disjunction of propositions, and ascent back
from the whole disjunction.
Merely confused:
No descent to a disjunction of propositions but ascent back
from the disjunction.
Wide distributive:
Descent to a conjunction of propositions and ascent back
from the conjunction.
Narrow Distributive
Descent to a conjunction of propositions and no ascent back
from the conjunction.
There is precedent for the category of wide distribution; it is what Paul of Venice
[LM:TS 3.11a (95)] 140 proposes for mobile distribution. So far as I know, narrow
distribution has not been proposed. (Immobile distribution generally refers to
cases in which no descent is possible.)
If we think of denoting phrases as restricted quantifiers, then this is equivalent
to saying: 141
140 “Distributive general reference is twofold because some is mobile, some immobile. Distributive
mobile general reference is the meaning of a common term beneath which one can infer to
all of its singulars conjunctively on the condition of a proper middle and, conversely, with the
same middle. Thus this follows: ‘This animal runs and this animal runs and thus of each individual
and these are all animals; therefore, every animal runs’.” He correctly includes subjects
of universal affirmatives, and both subjects and predicates of universal negatives as having this
mode of supposition.
141 I am speaking loosely here when I refer to quantifier rules such as “Existential Instantiation”.
Such rules can indeed be invoked, but only if the syntax of the language is enhanced with
variables, etc.