Handbook of the History of Logic: - Fordham University Faculty

258 Terence Parsons
The reverse principle also holds for determinate or merely confused supposition: 116
From an inferior to a superior: If a (non-parasitic) term T has
determinate or merely confused supposition in a proposition P , then
from P together with a proposition stating that T ∗ is superior to T ,
the proposition that results by replacing T by T ∗ in P follows.
For example, another of Aristotle’s first figure syllogisms follows by this principle:
Darii
Every M is P
Some S is M
∴ Some S is P
Burley’s version of “from a superior to an inferior” is slightly more comprehensive
than the version stated above: 117
A consequence from a distributed superior to its inferior taken with
distribution and without distribution holds good . . .
I think that what he means by “and without distribution” is that if the quantifier
sign preceding the distributed superior is changed so as to change the term
from having distributive supposition to having determinate or merely confused
supposition, then the inference is still good. For example, not only is this a good
consequence:
Every A is B B is superior to A
Every B is C B is distributed
∴ Every A is C A replaces B in the second premise
so is this:
Every A is B B is superior to A
Every B is C B is distributed
∴ Some A is C A replaces B in the second premise, with ‘every’
changed to ‘some’
Another example would be:
116 Paul of Venice LP III.3 (171): from a lower-level term to its corresponding higher-level term
affirmatively and without a sign of distribution and without any confounding signs impeding
there is a solid inference. E.g., ‘man runs; therefore, animal runs’.” [I don’t know why Paul
does not require a “due mean” here, as he does for the inference from a higher-level term to its
corresponding lower-level term.] Ockham SL III.3-6 (600) cites this rule: “ab inferiori ad superius
sine distributione et affirmative est bona consequentia et simplex.” He then gives a number of
counterexamples to it, such as examples in which terms do not have personal supposition. He
then qualifies the rule (page 601): “ab inferiori ad superius sine distributione et affirmative est
bona consequentia si termini supponant personaliter et significative.” (cited in [Moody, 1965 p.
288, note 1]). “From a superior to an inferior without distribution and affirmative is a good
consequence if the terms supposit personally and significatively.”
117 Burley Consequences in [Kretzmann & Stump, 1988 page 300].