Handbook of the History of Logic: - Fordham University Faculty

Peter Abelard and His Contemporaries 111
are modes. The modes of modal logic are adverbs too, just very specialized ones.
So “necessarily” just qualifies the assertion that something is thus by the addition
that it cannot be otherwise [Abelard, 1970, p. 194 (7)]. But note that what
are grammatically adverbs do not always, strictly speaking, modify the verb; the
adverb “falsely,” for example, does not say how a verb applies, but in fact says
that the verb does not apply. “Possibly” invokes a similar point. If we say “S is
possibly P ” we do not deny the truth of “S is P ,” but we definitely do not affirm
it as a truth either. So “possibly” does not operate in typical adverbial fashion
to indicate mode of inherence [Abelard, 1958, p. 4 (7–10); Abelard, 2006, 12.4].
Is it even an adverb? Abelard still wants to say it is. His view is that “possible”
functions as an adverb syntactically (secundum positionem constructionis) evenif
not semantically (secundum sensum); that is, syntax assigns it a modifying role,
even if this role is not forthcoming just from its semantic properties plus those of
the accompanying verb.
So claims of possibility are still explained as claims about the nature of the
subject (i.e., that S is possibly P ). These claims, however, are not about what the
nature is, but rather about what it is not repugnant (repugnet) to [Abelard, 1970,
p. 193 (36)]. Something is possible for Socrates when it is not repugnant to his
nature. To use Abelard’s example, the possibility that Socrates is a bishop lies in
the fact that being a bishop is not repugnant to Socrates’ nature [Abelard, 1970,
p. 193 (35–36)]. 55 This fact alone suffices to establish the possibility of Socrates’
being a bishop, even if he has never been one and never will be one. In this way,
“Socrates is possibly a bishop” is construed as being of subject/predicate form,
where a subject is named and a predicate is said of it — with “possibly” modally
qualifying the latter.
Besides this adverbial presentation of modes there is another. Modes can also
be nominal, and can be indicated by names, not adverbs. When indicated by
names they function as predicates of whole propositions, as in “It is necessary
that Socrates runs.” Here the subject is not a thing but a dictum (“that Socrates
runs”), and the point of the predication is to impute necessity to this dictum:
that Socrates runs is necessary. In other words, what is said by “Socrates runs” is
necessary. Here we have an impersonal construction, where the subject term fails
to denote a thing; this sort of construction characterizes nominal modes generally.
The greater complexity of impersonal propositions, as opposed to personal ones,
has already been noted, and Abelard always sees nominal modes as posing special
problems that adverbial ones do not. The common syntactic form of modal
propositions in Abelard’s time involves a nominal mode placed with an infinitival
construction, as in “It is necessary for Socrates to run.” This literally involves
a nominal mode — “necessary,” as opposed to “necessarily” — which literally
functions as predicate term. Nonetheless, Abelard claims, a non-literal, adver-
55 While Abelard defines possibility in terms of natures, he elects not to define necessity in
terms of natures as well (as he could have done by saying that necessity is the incompatibility
of the absence of a form with a nature). Instead he speaks of the necessary as the “inevitable”
(inevitabilis) [Abelard, 1970, p. 194 (8); Abelard, 1958, p. 21 (2); Abelard, 2006, 12.35].