Handbook of the History of Logic: - Fordham University Faculty

Peter Abelard and His Contemporaries 129
of things which manifest those natures. Abelard distinguishes between the import
of a universal affirmative categorical like “All men are mortal” and the corresponding
conditional, “If it is a man then it is mortal.” The key linking word in
the former is the copula “is” (est), which “proposes only an act of inherence of
things” [Abelard, 1970, p. 279 (9-10)]; but the key linking word in the latter is
the connective “if” (si), which “proposes necessity of entailment” [Abelard, 1970,
p. 279 (13)]. The categorical asserts inherence, and fails to be true if there is no
inherence — which is what happens if the terms fail to denote any existing thing.
So it is false that all men are mortal if it turns out that there are no men. But
the conditional asserts entailment, not inherence, and this entailment will hold
whether the terms succeed in denoting or not. “All true conditionals are true
from eternity” [Abelard, 1970, p. 279 (18)], Abelard says. Their truth depends
only upon facts about natures, not facts about the things which instantiate them.
For understanding Abelard’s program in constructing a theory of incomplete entailment,
the point is clarifying. Incomplete entailment, as we have seen, is as
grounded in necessity as complete entailment; what confers that necessity is not
a specific argument form but timeless relationships that hold between natures. In
defining the domain of incomplete entailments, and attempting to provide maximal
propositions as the foundational principles of this domain, Abelard is therefore
undertaking a program of considerable philosophical import. 90
In this program he naturally proposes to whittle down the received list of topics
to ones which yield maximal propositions of this sort — ones which imply families
of timelessly true conditionals, marked as such by the fact that in each case the
sense of the consequent is contained in the sense of its antecedent. The strategy for
proceeding with the program is to identify and reject those maximal propositions
which in fact give rise to conditionals lacking the requisite properties. This suffices
to demonstrate their inadequacy.
The first set of topics he subjects to this scrutiny are the ones listed as topics
“from substance,” under which heading are grouped various principles relating
definitions to the things they define. Here is the first: “Whatever the definition
is predicated of, the thing defined is predicated of as well” [Abelard, 1970, p. 331
(23)]. One of the conditionals contained under this would-be maximal proposition
is “If Socrates is a rational, mortal animal then he is a man” [Abelard, 1970, p. 331
(31)]. This conditional seems unobjectionable at first sight, but Abelard argues
that it is not necessarily true. More is involved in being a man, he argues, than
simply being rational and mortal; what qualifies as a man is also able to walk, is
two-footed, and shares in learning (perceptibile discipline), and there are, indeed,
many other such properties involved in being a man “for which we do not have
names” [Abelard, 1970, p. 332 (12–13)]. We do not need more than “rational”
and “mortal” for the purposes of definition because these suffice to provide an
90 This program is the interpretative key for grasping the considerable material on topical theory
in the Dialectica — material which otherwise can seem disjoint and directionless. Christopher
Martin has been chiefly responsible for our knowledge of this interpretative key. See especially
[Martin 1987a], [Martin 1987b], [Martin 1992] and [Martin 2004a].