Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 237
2 applied to the whole proposition. Probably the latter is intended, though the
statement of the rule seems to require the former.
About 3: The rules seem to make the predicate term distributive, since both
quantifier signs individually distribute it. This conflicts with the application of
the criteria. 94
About 5 and 6: The same thing can be said for the predicate terms of examples
5and6if‘not’ is taken to be a distributing sign when it occurs within a basic
categorical proposition. If on the other hand the ‘not’ has no effect at all, the
predicate term is clearly distributive because of the ’every’ or‘no’. In either case
the result conflicts with the criteria.
So the parts of the theory do not hang together. If the criteria for modes
of supposition are accurately stated above, then the rules for causes of mode of
supposition do not work for the applications in question. Perhaps that means that
some other criteria are needed, but it is not clear what they might be.
We have been discussing what happens when we look at nonstandard basic
categorical propositions. There are other complications as well. If ‘not’ isnot
a distributing sign when it occurs outside of a minimal categorical proposition,
then it is clear that modes of supposition in the 13th century theory are not
invariant under logical equivalence. In particular, William’s rules of equipollence
change modes of distribution. Since ‘no’ is equipollent to ‘not some’, if neither
‘not’ (used outside a basic categorical) nor ‘some’ can distribute, then ‘donkey’
is not distributed in ‘Not some donkey is a stone’, though it is distributed in
the equipollent proposition ‘No donkey is a stone’. This is not necessarily an
objection — indeed, it seems like a fairly natural consequence of the local nature
of modes in the 13th century theory. This is like saying that the quantifier in
‘¬∀xF x’ is universal, even though the quantifier is not universal in the logically
equivalent ‘∃x¬Px’. So with respect to quantificational phenomena, classifying
a term as distributed in the early theory is much like classifying a quantifier as
universal. Universal-quantifierhood is not preserved under logical equivalence, nor
is distributive-termhood.
Mobility is different, as is the analogue for mobility of quantifiers. The universal
quantifier is mobile in ‘∀x¬Fx’ as is the existential quantifier in ‘¬∃xF x’; in both
cases the quantifier may be instantiated; that is, you get a logical consequence by
erasing the quantifier and replacing the variable it was binding with a name.
(The 14 th century theory, unlike the 13 th century one, makes the modes of
supposition behave logically like mobility.)
94 It was common to handle such cases by giving a rule that states: Whatever immobilizes the
mobile, mobilizes the immobile, and vice versa. In that case, one sign mobilizes the word and
the other reverses this. This would make the predicate immobile — which is clearly the right
result. But the rules we are examining are about modes of supposition, not about mobility, and
William has no “reversal” principles for those.