Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 239
and the mode of supposition — of ‘a man’; in the good example it has merely
confused supposition, and in the bad one it has determinate supposition. So the
rule is formulated in terms of whether you move from many cases of determinate
supposition to determinate supposition, or to merely confused supposition.
Rule IV An argument from determinate supposition to distributive confused
supposition does not follow, but only to merely confused supposition.
Thus this does not follow: ‘a man is not seen by Socrates; therefore
Socrates does not see a man’ — e.g. if Socrates sees one man only. But
this follows correctly: ‘a man is seen by every man; therefore every man
sees a man’. [Ibid] 95
The badness of the first inference and goodness of the second are obvious; the rule
identifies the difference in terms of a principle about modes of supposition.
Rule V An argument from distributive confused supposition to determinate
supposition does follow, but not from merely confused supposition.
Thus this follows: ‘Socrates does not see a man; therefore a man is
not seen by Socrates’. But this does not: ‘every man sees a man (e.g.,
every man sees only himself); therefore a man is seen by every man’.
[Ibid (119)]
In the first inference ‘man’ goes from distributive supposition to determinate supposition,
and in the second it goes from merely confused to determinate. The rule
blames the goodness/badness of these inferences on the pattern of the modes of
supposition.
These rules all seem to have insight behind them, and they look promising as
part of an overall theory of inference in terms of modes of supposition. But there
are some problems with them.
Problem 1: Embedded propositions
The rules are all illustrated by fairly simple categorical propositions, but they are
supposed to hold in general. However, the rules are stated in terms of modes of
supposition, which do not change when a proposition is embedded in something
more complex — yet the goodness of the inferences can be affected by this. A
simple example of an application of Rule IV is this inference:
therefore,
If a man is seen by every man, then a man is seen by every man;
If every man sees a man, then a man is seen by every man.
95The translation quoted here has been altered in conformity with discussion in the Preface to
[Kretzmann, 1968].