Handbook of the History of Logic: - Fordham University Faculty

Peter Abelard and His Contemporaries 121
in both premises but must have a present tensed conclusion: “Every mortal will
die; every mortal is a living thing; therefore some living thing will die” [Abelard,
1970, p. 248 (26-28)]. 73
While Abelard’s handling of the standard syllogisms is axiomatic in orientation,
his handling of ones with modal and tense variation is taxonomic rather than
axiomatic; he wishes simply to identify a few kinds of non-standard syllogism,
not to systematize them. And nowhere in his treatment of categorical syllogisms,
standard or non-standard, does Abelard follow the deeper purposes of investigating
the very nature of the inferential link itself, and how propositions come to be so
linked. This project is reserved for his treatment of the hypothetical syllogism,
and can indeed be viewed as his chief objective there.
PART 2: ABELARD ON TOPICS, HYPOTHETICAL PROPOSITIONS AND
HYPOTHETICAL SYLLOGISMS
Just as categorical syllogisms are broached in the Dialectica only after prior
ground-laying discussion, so with hypothetical syllogisms. The ground-laying discussion
for these latter, indeed, constitutes the largest single section of that work.
It is important to grasp the procedure Abelard has in mind. The predicative
relation of terms within categorical syllogisms is what makes those syllogisms work,
and so we gain insight into the working of the syllogisms by means of insight into
that predicative relation. But hypothetical syllogisms have terms too; they are the
antecedents and consequents of the conditionals contained in the syllogisms (or the
disjuncts of the corresponding disjunctions). These clause-length terms are in an
implicative relation which needs to be studied as a preliminary for hypothetical
syllogisms, just as the predicative relation needs to be studied as a preliminary for
categorical ones. Abelard attempts to meet this need, and in so doing gives an
extended account of conditionals (and a corresponding account of disjunctions).
This extended account is meant to establish a process for ascertaining when the
antecedents and consequents of conditionals actually do stand in an implicative
relation. The key notion in this confirmatory process is the notion of the topic.
It is here that Abelard’s expository program takes what is, from a contemporary
perspective, a very unfamiliar turn. Clearly one goes nowhere in this explanatory
sequence without a good sense of what a topic is, and so the first step is to explain
it. 74
By far the commonest traditional conception of logic is as a tool for assessing
inferences. To judge whether an inference succeeds or fails requires criteria of adequacy
which the inference may be seen either to meet or fail. Logic is supposed to
73 Abelard’s discussion of syllogistic inference under variation of tense is treated in [Tweedale,
1976, pp. 298–302]. See also [Rosier-Catach, 1999, pp. 150–156], [Jacobi, 2004, pp. 148–49] and
[Wilks, forthcoming].
74 Otto Bird’s groundbreaking work in topical theory is an especially good point of entry into
this material, even if its basic approach is flawed — as argued in [Stump, 1989, pp. 94–95]. See
[Bird, 1959], [Bird, 1960, pp. 141–145] and especially [Bird, 1961].