Handbook of the History of Logic: - Fordham University Faculty

482 Catarina Dutilh Novaes
this is not necessary, as the enumeration of the valid rules is supposed to be
exhaustive, and all patterns not falling within the patters of these valid rules are
immediately false. The medievals, however, did not have the ambition of presenting
exhaustive lists of valid rules, and therefore it was also useful for them to know
how to identify when a consequence did not hold. 51
‘Whatever does not follow from the antecedent, does not follow from the consequent.’
A ⇒ B C ⇒ B
C ⇒ A
‘Of that from which the consequent does not follow, the antecedent does not
follow from it either’
A ⇒ B C ⇒ B
C ⇒ A
They also discussed rules involving modalities, such as ‘from the necessary the
contingent does not follow’ or ‘from the possible does not follow the impossible’. 52
The rules presented here are those that can be easily formulated within a purely
propositional framework. However, as already noted, treatises on consequences
contained many more rules which, by contrast, were based on properties of terms;
these rules were just as significant, and the only reason why they are not treated
here is because their formulation presupposes concepts from elsewhere (such as
supposition theory — for reasons of space, it is not possible to go into such details
here). But just to illustrate the point, here is an example, Burley’s Rule 7
in the shorter version of De Puritate: ‘an inference holds from a distributed superior
to an inferior taken either with distribution or without distribution. But
an inference does not hold from an inferior to a superior with distribution. For
it follows: ‘Every animal runs, therefore, every man runs, and a man runs’, but
not conversely.’ [Burley, 2000, 16] ‘Animal’ is the superior of ‘man’, and from
a proposition where ‘animal’ is distributed follow both the proposition where its
inferior ‘man’ is distributed and the one where it is not.
3.5 Dissident voices
So far I have treated medieval theories of consequences as if they were homogeneous
with respect to the rules of consequence accepted by their authors. While not all
authors stated all these rules explicitly, they are in any case all compatible with
one another. However, a small minority rejected two of the very basic rules of
the notion of consequence presented so far, namely the ex impossibili and the
ad necessarium rules. These rules follow naturally from the modal definition of
51 In the same manner that theories of fallacies — that is, theories of apparently sound but in
fact unsound reasoning — were crucial for medieval logicians.
52 More on modal inferences can be found in the chapter on modalities in the present volume.