Handbook of the History of Logic: - Fordham University Faculty

Peter Abelard and His Contemporaries 113
the notion of possibility involved here is understood, it is clear that the de re
reading of the example proposition allows it to be true, and the de sensu reading
does not.
This is not an argument for the superiority of de re readings of modal propositions,
since, as Abelard notes, the opposite result holds for “It is necessary for
the standing man not to sit.” This is true taken de sensu (since “The standing
man does not sit” is necessarily true) and false taken de re (since it is false that
the standing man necessarily does not sit) [Abelard, 1958, p. 14 (8–13); Abelard,
2006, 12.19]. Both this example and the previous one simply convey how very different
the two readings are. Nevertheless, Abelard does prefer the de re approach.
The problem with the de sensu approach is that it makes modal propositions into
impersonal propositions; these, as we have seen, lack a referring subject term and
as such lack features like universality, particularity, and ability to convert, and
therefore fit poorly into the forms and figures of syllogistic logic. We can compare
the standing of impersonals in this regard to the standing of relational propositions.
These likewise fit poorly into the forms and figures, and need to be re-cast
somehow into conventional subject-predicate syntax. As they stand, prior to this
change, they are perfectly coherent propositions, capable of being true or false;
but from a syllogistic perspective, their limitation is that they are not perspicuous
expressions of their content. This would seem to be Abelard’s view about
impersonals generally and, more specifically, about de sensu modals.
But there is a more technical limitation to be observed in de sensu modals.
The infinitival propositions in which they are expressed offer two different points
at which negations may be inserted. “It is possible for Socrates to run” can be
negated as a whole: “It is not possible for Socrates to run.” But the infinitival
portion, since it involves a verb, can be negated as well: “It is possible for Socrates
not to run.” Abelard notes that this second negation in fact makes sense only on
a de re reading. On a de sensu reading the infinitival phrase “for Socrates to run”
is of course the subject of the proposition. Now one does not negate a proposition
by negating its subject term; for example, one does not regard “Non-Socrates is
running” as being a negated form of “Socrates is running.” So one must likewise
not regard “It is possible for Socrates not to run,” taken de sensu, as being a
negated form of “It is possible for Socrates to run”; again, the subject term on
this de sensu reading is “for Socrates to run,” and that is what the sign of negation
has just been applied to. The conclusion is that the de re reading engenders a
class of negated forms which vanish when the reading is de sensu. In fact there
are three forms of de re negation: the two just mentioned (“It is not possible for
Socrates to run”; “It is possible for Socrates not to run”) and their combination:
“It is not possible for Socrates not to run.” In being able to capture only one of
these three, the de sensu reading must be taken as comparatively less expressive
[Abelard, 1958, p. 21 (22)–22 (15); Abelard, 2006, 12.38–39].
When quantifiers are attached and varied, these four de re forms (the origi-
played some role in his thought.” Marenbon argues that neither approach captures Abelard’s
understanding of the modal operators [Marenbon, 1991; Marenbon, 1997a, pp. 221–223].