Handbook of the History of Logic: - Fordham University Faculty

126 Ian Wilks
firm as genuine entailments all of those conditionals which arise from substitution
in its open places — except that the substituting terms must be further delimited
as standing in the topical relation of species to genus. 81 The topical rule is
more qualified than the syllogistic, but just as confirmatory. To understand this
is to understand why Abelard regards topical theory as such an important area
of research. Given that the basic rules of form for syllogistic entailments already
appear to be discovered and fully expressed, it is natural to seek next the discovery
and full expression of rules for conditional entailments.
In support of this program, Abelard tightens the analogy between syllogistic
and conditional entailments in two ways.
(i) He distinguishes these entailments as perfectae and imperfectae respectively.
Imperfectae means “imperfect” in the sense of “incomplete,” not in the sense of
“defective.” 82 A Barbara syllogism gives us a complete entailment, while “If it is a
man then it is an animal” gives us an incomplete one. The point of the distinction
is not to mark the quality of the entailments, because both involve the closest
possible inferential links. The point is to mark the quality of guarantee for that
link. The explicitness of a syllogism is such that we do not even have to pay
particular attention to the content of its propositions in order to grasp the fact
that the inference succeeds. We need only note the pattern of the terms. We can,
indeed, make arbitrary substitutions for the terms, but still be assured that that
the resulting entailment succeeds, as in: “If every man is a stone and every stone is
wood then every man is wood” [Abelard, 1970, p. 255 (35)]. “If it is a man then it is
an animal” cannot be so simply confirmed as this, even though, as we have seen, it
can be confirmed. Hence it is an entailment properly speaking, just an incomplete
one. Note that the compete/incomplete distinction is traditionally applied within
the domain of syllogisms themselves [Abelard, 1970, pp. 233 (35)–234 ((8)]. First
figure syllogisms corresponding to the first four moods are complete, in that they
are self-evidently valid; all other moods are incomplete in that, while valid, they
are not self-evidently so. They require reduction to first-figure ones in order to
be shown to be so. This is the sort of distinction being made between syllogistic
and conditional entailments. The latter fail in obviousness, not in strength, and
need additional means to have obviousness conferred upon them. These means are
supplied by topical theory. Calling conditional entailments “incomplete” presents
their difference from complete ones as a difference of presentation, not content,
and the label thus suggests the underlying likeness of the two. 83
(ii) Further to this suggestion is Abelard’s account of the inferential link itself,
which he applies indifferently to both kinds of entailment. He identifies necessity as
81 As Christopher Martin notes [Martin, 1986, p. 566], topical entailments generally will hold for
“uniform substitution of terms standing in an appropriate topical relationship.” These contrast
with syllogistic (i.e., complete) entailments, which hold for “any uniform substitution of terms.”
See also [Martin, 1992, p. 116].
82 I will translate perfecta as “complete” consistently with my earlier rendering of oratio perfecta
as “complete phrase.” Imperfecta is accordingly rendered as “incomplete.”
83 On this distinction see the discussion in [Martin, 2004a, pp. 169–171], under the heading
“Perfect and Imperfect Entailment.”