Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 231
Some A is every B A is determinate B is distributive
Every A is every B A is distributive B is distributive
No A is every B A is distributive B is merely confused
Some A is no B A is determinate B is distributive
Some A is not every B A is determinate B is determinate
Some A is not no B A is determinate B is determinate
7.3 Mobility
Some terms in a proposition are mobile and some are immobile. A mobile term is
one that can be instantiated; that is, the proposition containing it entails the result
of replacing the term (along with its quantifier sign, if any) 88 with any discrete term
that stands for a suppositum of the original term. For example, ‘donkey’ is mobile
in the proposition ‘Every donkey is running’ because that proposition, together
with the information that Brownie is a donkey, entails ‘Brownie is running’. This
inference is also called a descent, since one moves from a term such as ‘donkey’
toaterm‘Brownie’ that stands for something that falls under ‘donkey’. Terms
that are not mobile are immobile. An example is ‘donkey’ in‘Every running thing
is a donkey’; from this and that fact that Brownie is a donkey one may not infer
(descend to) ‘Every running thing is Brownie’.
Sherwood, and most others see mobility as limited to distributive terms. Sherwood’s
definition of mobility is:
[Distributive confused supposition is] mobile when a descent can be
made, as in the term ‘man’in[‘every man is an animal’]. It is immobile
when a descent cannot be made, as here: ‘only every man is running’
(for one cannot infer ‘therefore only Socrates is running’) [IL V.2 (108-
09)]
Lambert’s definition is practically the same (he even illustrates it with the same
examples). [PT 3g(v) (113)] 89 The identical examples suggest an identical source
for both passages.
Mobility interacts in complicated ways with other notions, as we will see.
88 If the quantifier sign is negative, such as ‘no’, then you need to preserve the negation by
inserting ‘not’ in its place. For example, from ‘No donkey is running’ and‘Brownie is a donkey’
you infer ‘Not Brownie is running’. Since discrete terms commute with ‘not’ youcanwrite
instead ‘Brownie is not running’.
89 Lambert “Notice that confused supposition is strong (= distributive) whenever it is mobile,
but not conversely — mobile whenever it is strong (= distributive) — for it can indeed be strong
(= distributive) and immobile. When one says ‘Only every man is running’, ‘man’ hasstrong
(= distributive) but immobile confused supposition; for the exclusive word [‘only’] added to the
distributed term impedes it so that a descent cannot be made under it.” Lambert uses ‘strong’
where others use ‘distributed’.