Handbook of the History of Logic: - Fordham University Faculty

Peter Abelard and His Contemporaries 123
occur in what is proportional to that thing [Boethius, 1990, p. 39 (9-10)]. With
this principle in view one may note that a ship’s pilot is not appointed by lot, and
further that the office of pilot on a ship is proportional to the office of the ruler of
a city. The conclusion follows from the maximal proposition plus the two ensuing
facts.
The maximal proposition is the first basic conception Boethius uses to organize
topical theory; the differentia is the second. This latter is simply the feature
which distinguishes one maximal proposition from another, just as a differentia
in general will distinguish one species from another within a given genus. For (i)
the differentia is “from definition”; for (ii) it is “from efficient cause”; and for
(iii) it is “from proportion.” Just as the maximal proposition helps in locating a
salient point about one of the terms out of which the argument may be developed,
the differentia helps in locating the right maximal proposition. The maximal
proposition is a principle which distills the essence of the argument; the differentia
is a label which distills the essence of the principle. 76
With these two notions Boethius purports to impose some order upon the variety
of topics. These notions represent the point of departure for Abelard in his own
handling of topical theory, but, as ever, he adapts the inheritance to serve his own
purposes. Two points in particular inform his approach.
(i) Topical theory is first and foremost for Abelard an ars iudicandi, a technique
for judging adequacy of reasoning. This is not to say that he rejects the other
orientation of topical theory, as an ars inveniendi; in his initial definitions, indeed,
Abelard covers both conceptions of a topic. He allows that it can be defined as an
“argument source” (argumenti sedes) and as “that from which a suitable argument
is drawn” [Abelard, 1970, p. 253 (22-23)]. 77 But he also identifies this definition
as a narrower one, and adopts what he considers the broader one as his starting
point: a topic is the force of an entailment (vis inferentiae) [Abelard, 1970, p. 253
(16)], or, as we might say, an inferential warrant, a consideration which ensures
that there is entailment. Of course, these narrower and broader definitions are
not in conflict, since what warrants an entailment might very well be helpful for
discovering it in the first place. Nonetheless Abelard’s program here focuses on
the topic taken as an inferential warrant. Topical theory is going to be used chiefly
for the purposes of assessment, not discovery.
(ii) An interpretative tendency evident in writings from as early as the ninth
century is to regard topical theory as having a special association with hypothetical
syllogisms [Green-Pedersen, 1984, pp. 140–145]. 78 Abelard is much influenced
76 As Eleonore Stump notes [Stump, 1978, p. 180, note 5] this use of the term “differentia”
must be distinguished from its use in denoting one of the predicables.
77 Abelard associates this approach to topical material with Cicero and Themistius, and treats
it in a later section of the Dialectica [Abelard, 1970, pp. 414 (4) - 466 (25)]. This is briefer
coverage than is given to the other approach, which runs to 261 pages in the de Rijk edition.
From this fact we may infer the greater value he imputes to the broader definition.
78 Niels Jørgen Green-Pedersen believes that “this idea is both un-Aristotelian and un-Boethian
and un-Ciceronian” [Green-Pedersen, 1987, p. 411]. However we find in [Martin, 1991, p. 290]
an indication of a Boethian source; this lies in the fact that, for Boethius, maximal propositions