Handbook of the History of Logic: - Fordham University Faculty

474 Catarina Dutilh Novaes
more so, the formal vs. material distinction that are crucial for the understanding
of 14 th century theories of consequence. Besides these, there is also a distinction
that is sometimes found explicitly stated but sometimes not, and which sometimes
overlaps with the formal vs. material distinction but sometimes does not, namely
the distinction bona de forma vs. bona de materia.
It is important to understand that these divisions are not necessarily meant to
be sub-divisions of each another; they are also often understood as alternative,
overlapping ways of dividing consequences. Ockham, for example, presents several
such distinctions but does not present them as sub-divisions of one another
(Summa III-3, Chapter 1). So let us now take a closer look at each of them.
Formal vs. material consequences. This distinction first appears in Ockham
(cf. [Green-Pedersen, 1984, 287]), but afterwards it is to be found in virtually all
treatises on consequence in the 14 th century. However, what distinguished formal
from material consequences varies per author.
For Ockham, this distinction is related to his doctrine of intrinsic and extrinsic
middles. Ockham says that a consequence is formal when there is such middle,
intrinsic or extrinsic, validating the consequence; otherwise, when there isn’t such
middle and the consequence holds only in virtue of its very terms (Summa Logicae,
p. 589), it is a material consequence. As already mentioned, Ockham’s extrinsic
and intrinsic middles are reminiscent of the topical framework, but they are extremely
modified versions of topical concepts, as shown by Green-Pedersen [1984,
chapter E].
But what are intrinsic and extrinsic middles? An extrinsic middle is a proposition
not containing the terms that form the antecedent and the consequent of the
putative consequence, but which is a general rule describing the fact (ontological,
logical or other) that warrants the passage from the antecedent to the consequent.
An intrinsic middle, by contrast, is formed by the very terms that form the antecedent
and the consequent of the putative consequence. Ockham says that some
formal consequences hold only in virtue of an extrinsic middle, while others need
an intrinsic as well as an extrinsic middle to hold. Syllogisms, for example, hold
only in virtue of extrinsic middles; a consequence such as ‘Only a man is a donkey,
therefore every donkey is a man’ holds in virtue of the following extrinsic middle:
‘an exclusive and a universal with transposed terms signify the same and are
convertible’. But a consequence such as ‘Socrates is not running, therefore a man
is not running’ requires that the intrinsic middle ‘Socrates is a man’ be true in
order to hold (and it still requires an extrinsic middle to validate it mediately).
(Ockham, Summa Logicae, p. 588).
What exactly a material consequence is for Ockham is still a matter of controversy
among scholars, as the passage where this notion is explained is known to
be corrupted (Summa Logicae, p. 589). 45 Ockham gives two examples of material
consequences, one of the ex impossibili kind (from an impossible proposition anything
follows) and one of the ad necessarium kind (a necessary proposition follows
45 See [Schupp, 1993] on the corruption of the text.