Handbook of the History of Logic: - Fordham University Faculty

130 Ian Wilks
(extensionally) “equal definition” [Abelard, p. 333 (21)]. But this definition has
such equality with the thing defined only as a matter of fact (secundum actum rei),
not according to nature (secundum naturam), since although no other rational
and mortal animals are actually to be found except men, “nature does not seem
to require this” [Abelard, p. 333 (32–33)]. In short, the above conditional (“If
Socrates is a rational, mortal animal then he is a man”) lacks the timeless necessity
needed in order for a conditional to be true. This failing is based on the fact that
the requisite containment relation between consequent and antecedent does not
exist; in particular, the meaning of “rational, mortal animal” does not contain
the meaning of “man.” So the above definitional principle fails to have a place in
topical theory as a maximal proposition. By parity of reasoning so do a number
of others: “From whatever the definition is removed, so is the thing defined”;
“Whatever is predicated of the definition is also predicated of the thing defined”
and “Whatever is removed from the definition is removed from the thing defined”
[Abelard, 1970, p. 331 (23-29)]. On the other hand, the nature of the thing defined
will be inclusive of whatever properties are appealed to in its definition; so if we
take the first of the above would-be maximal propositions and put “definition”
for “thing defined,” and vice versa, we will acquire a perfectly good maximal
proposition: “Whatever the thing defined is predicated of, so is the definition”
[Abelard, 1970, p. 338 (4–5)]. 91
Abelard works through a traditional list of maximal propositions and in similar
fashion drops many entries from the list, making decisions in this regard which
are often at the outset non-obvious, even counter-intuitive. I append a few additional
examples, which must suffice to indicate the character of this very extensive
undertaking. (i) Under the topic “from genus,” Abelard accepts “Whatever the
genus is removed from so is the species” and “Whatever does not agree with the
genus does not agree with the species.” He rejects “Whatever is predicated of the
genus in content (de contento) is also predicated of the species” and “Whatever
the genus taken universally is predicated of, any of its species is predicated of”
[Abelard, 1970, p. 340 (5–19)]. 92 (ii) Under the topic “from an integral whole”
Abelard rejects inferences from whole to part. The maximal proposition “When
the whole exists it is necessary that any part of it exist” endorses as true the
conditional “If there is a house there is a wall” [Abelard, 1970, p. 343 (34–36)].
But this conditional is false. It is granted that the house as a whole cannot exist
without roof, wall and foundation. But saying that the house as a whole exists
is simply not the same as saying that any one of those three components exists.
The existence claims for the components are not part of the content of the existence
claim for the whole — which means that “If there is a house there is a
91 The topic “from substance” is discussed in [Martin, 2004a, pp. 186–188].
92 The reasoning behind these results is given in [Stump, 1989, pp. 98–100]. The first (accepted)
maximal proposition is exemplified with this true conditional: “If this rock is not an animal it
is not a man” [Abelard, 1970, p. 340 (11)]. The second (accepted) maximal proposition is
exemplified thus: “If no animal is a stone, no man is a stone” [Abelard, p. 340 (12)]. For the
idea of predicating a genus de contento, see de Rijk’s comment in [Abelard, 1970, p. lxxxiv, note
3].