Handbook of the History of Logic: - Fordham University Faculty

128 Ian Wilks
between the antecedent, “It is a man,” and the consequent, “It is not a stone.” 87
A similar analysis applies to “If there is paternity then there is filiation.” Being
a father is a relation of having a child but not a relation of being a child, so we
do not direct attention to the state of being a child by considering the state of
being a father. The state of being a child is not internal to the state of being a
father, and so in that sense the latter does not contain the former. 88 In both of
the above conditionals there is enough linkage to meet the necessity condition, but
not enough to meet the containment one.
This is certainly an uncompromising result. Normally moving in the direction
of relevance implication makes an account of conditionals more intuitive (even
if at the cost of making it also formally more intractable); but Abelard moves
so far in this direction, and is so restrictive in his tolerance for what will count
as an acceptable conditional, that he risks loss of intuitiveness through being
too relevantist. One must, however, remember the program: to find rules for
conditional entailments that are the equal for certitude with the rules for the
syllogistic entailments. In the context of this program Abelard’s restrictions make
sense. The visible result of these restrictions is that his examples of successful
conditional entailments are typically characterized by a shared subject term in
antecedent and consequent, as in “If it is a man it is an animal,” or schematically,
“If x is A then x is B.” 89 Whether a conditional of this form turns out to be
an entailment will depend on whether A and B are in the requisite relation of
containment. If they are, the fact will be established through appeal to the relevant
topic.
We can say generally, then, that topics do for incomplete entailments what
logical form does for complete ones. But the fact that maximal propositions are
indexed to things, and the relationships in which they stand, makes it evident that
they are decidedly not formal argument schemata, but semantic principles which
themselves require knowledge of natures in order to be grasped. The logician does
not study physics (i.e., the philosophy of nature) in order to verify the stated
claims of logic, but needs to have some grasp of it nonetheless to understand
what is meant by particular words. For this program to be successfully carried
out “the property of things must first be investigated” [Abelard, 1970, p. 286
(37)]. Maximal propositions represent the final fruit of this investigation. They
are fundamental principles expressive of how natures are. Our knowledge of them
is without further basis, and no other such principles are to be discovered which
are better known [Abelard, 1970, p. 309 (30–36)].
The many entailments which a maximal proposition yields are themselves expressive
of basic relationships of natures, and in fact hold true even in the absence
87 See [Martin, 2004a, p. 184].
88 This analysis is further affected by the way in which Abelard understands the category of
relation, which, we may say very generally, tends to follow Aristotelian tradition by analysing
it more along the lines of a one-place predicate than we are apt to do in modern times. See
[Brower, 1998]. See also [Marenbon, 1997a, pp. 143–146] and [King, 2004, pp. 96–98].
89 It is possible, however, for antecedent and consequent to share the predicate term instead.
Seenote92belowforanexample.