Handbook of the History of Logic: - Fordham University Faculty

Peter Abelard and His Contemporaries 101
talk of shared forms. So he has no preference as between the two interpretations,
and in fact regularly invokes both. That is what he is doing in the above passage.
Predicating “white” of “Socrates” actually invokes both of the semantic roles that
“white” is able to play: both its ability to name a white thing, and its ability to
signify whiteness. The predication “conjoins” both to Socrates, as Abelard says
above; that is, it construes Socrates as being in a relation to whiteness and as
being in a relation to a white thing. The first relation is inherence, the second
identity. The predication expresses both.
On the other hand, it is only the inherence relation that is explicitly expressed,
thus becoming the relation which is explicitly conveyed by the terms of the predication.
The identity relation is only implicitly expressed, and remains in the
background. So only one of the items Socrates is conjoined with is meant to be
appealed to in the predication. But why is the other unintentionally conveyed?
Abelard explains this result as in effect forced on the speaker by the peculiar characteristics
of the copula verb “is.” This word also serves as our way of predicating
existence (as in “Socrates is”), and this alternate, existential meaning is not normally
divorced from the word, even in its usage as a copula. In this he diverges
from the view of the Dialectica, where, as we have seen, he is only too willing
to construe words as losing their received signification. But the post-Dialectica
approach requires some notion of existence to be melded with the signification of
the predicate name. Accordingly, “white” cannot be used with “is” without some
implication, albeit in the background, that what “white” is being used to signify is
not just a white thing, but an existing white thing. In other words, the predicate
“is white” attributes whiteness, but at the same time unavoidably identifies what
is said to be white with a white thing. Even though one only intends to attribute
the form to what is named by the subject, one cannot help do something else as
well: identify what is implicitly named by the predicate with what is named by the
subject. One act is intended, two completed; Abelard refers to both of the two as
“conjoining.” His account of the copula verb phrase may therefore be summarized
thus: each act of predication involves both kinds of conjunction. 36
This grasp of the semantics of verb function gives us entry into the next level of
semantic theory: the proposition. 37 One can group words in all sorts of ways that
36 Abelard’s treatment of predication and the copula verb remains one of the most extensively
studied aspects of his logical theory. In addition to the works already cited on this issue, the
following should be noted: [Nuchelmans, 1973, pp. 140–141], [de Rijk, 1981b, pp. 33–40], [Jolivet,
1982, pp. 56–62], [Jacobi, 1986], [Mews, 1987, pp. 21–25], [Marenbon, 1999], [Rosier-Catach,
1999, pp. 141–162], [Rosier-Catach, 2003b] and [Jacobi, 2004, pp. 147–150].
37 “Proposition” is not an ideal translation for propositio. For the medievals the propositio
always means a propositional sign, not propositional content [Kretzmann, 1970, p. 767]; for
Abelard in particular it always denotes a sentence-token [Marenbon, 1997a, p. 203, note 2]. Current
usage tends to associate “proposition” more with content and less with tokens. Accordingly,
John Marenbon has more recently rendered the term as “propositional sentence” [Marenbon,
2004, p. 59, note 2]. One sometimes finds the phrase “statement-making utterance” [Nuchelmans,
1973, p. 146; de Rijk, 1986, p. 95]. Christopher Martin describes the propositio as
“propositional token” [Martin, 2004a, p. 193, note 4]. I nonetheless use “proposition” in translation
to maintain continuity with the standard translation for maxima propositio in topical