Handbook of the History of Logic: - Fordham University Faculty

Peter Abelard and His Contemporaries 115
in the designated interval (sitting in the former case, reading in the latter). So
characterized, it becomes a determinate modality.
Abelard considers the inferential relations between determinate and simple
modalities. First, determinate possibility implies simple; “It is possible for Socrates
to read while he reads” implies “It is possible for Socrates to read.” But in general
the converse implication, that simple possibility implies determinate, does not
hold. And second, simple necessity implies determinate; “It is necessary for me to
read” implies “It is necessary for me to read while I read.” But again, the converse
does not in general hold [Abelard, 1958, p. 36 (11–21); Abelard, 2006, 12.73]. The
failure of both converses is instructive.
To say it is necessary for me to read while I read is simply to invoke Aristotle’s
principle and note the historical irrevocability of my reading while I am reading;
for the time period designated by the clause “while I read” my reading is an
irrevocable fact. But this says nothing about me and my nature. It does not
say that reading is inevitable for me (or that not reading is incompatible with
my nature), which is what it would need to say in order to establish the simple
necessity of my reading. From this follows the failure of the converse. Determinate
necessity does not imply simple necessity. 60
More complex is the failure of the other converse. Why does simple possibility
fail to imply determinate possibility? This failure is masked in the case of internal
determination, where the determining verb is the same as the main one; “It is
possible for Socrates to read” may well seem to imply “It is possible for Socrates
to read while he reads.” But certain external determinations make the failure
obvious. “It is possible for Socrates to sit” does not imply “It is possible for
Socrates to sit while he stands” because the determining verb (“stands”) rules
out that the property of sitting, with which the nature of Socrates is admittedly
compatible, can be realized by him at the moment when he is standing. The
lesson here is that simple possibility is temporally indefinite, and the presence of a
simple possibility is no guarantee that it will be realized at a given time. The fact
that Socrates is sitting at a given time implies the determinate necessity of his
doing so then, and also the determinate impossibility of his not doing so then; this
determinate impossibility holds then even though the simple possibility of sitting
holds for Socrates at all times of his life.
Indeed, as Abelard elsewhere suggests, it is still possible for someone with
maimed hands to box, for an amputee to walk and for a blind person to see.
In each case the possibility is understood abstractly in terms of the nature of
“sits,” differs from the main verb, “reads.” In the second the determining and main verb are the
same: “reads.” The former is called an “external” determination, the latter an “internal” one
[Abelard, 1958, p. 34 (9–12); Abelard, 2006, 12.67].
60 Note that there is an assumption about the scope of the temporal determining clause in this
argument, that it is to be read in this way: “Socrates possibly (sits while he stands),” not in
this way: “(Socrates possibly sits) while he stands. ” The former represents a modal reading of
the determining clause, the latter an associated temporal reading [Abelard, 1958, p. 37 (5–23);
Abelard, 2006, 12.76].