Handbook of the History of Logic: - Fordham University Faculty

114 Ian Wilks
nal plus the three negations) proliferate. When parallel listings are compiled for
impossibility and necessity the forms proliferate further. (Note that there is no
separate treatment of contingency, since Abelard erroneously takes this mode as
identical with possibility [Abelard, 1958, p. 24 (2); Abelard, 2006, 12.41]). So,
starting with the simple de re statement “All men can possibly run,” varying it
by quantification, negation, and substitution of other modes, we end up with a
twenty-four-entry list which is essentially an expanded square of opposition for
quantified modal statements [Abelard, 1958, pp. 25 (19) — 26 (7); Abelard, 2006,
12.44]. 58 Modal statements de dicto do not proliferate quite so generously, given
the restriction just noted, but likwise generate a series of forms. Abelard is content
simply to present these relationships, and has no further theory to build
upon them. This absence of theoretical enhancement is also the case — and more
surprisingly so — for the further relations he observes between the de re and de
sensu modalities themselves. An affirmative possibility de sensu is said to imply
the corresponding affirmative possibility de re, but not vice versa [Abelard, 1958,
p. 29 (14–16); Abelard, 2006, 12.55]. By contrast, an affirmative impossibility
(= a negative possibility) de re is said to imply the corresponding affirmative
impossibility de sensu [Abelard, 1958, pp. 29 (25)–30 (3); Abelard, 2006, 12.56],
presumably again not vice versa. But for necessity the implication goes both ways.
An affirmative necessity de sensu both implies and is implied by the corresponding
affirmative necessity de re [Abelard, 1958, pp. 32 (30)–33 (2); Abelard, 2006,
12.64]. These suggestive principles are tested against various examples, but are
not pursued for the fundamental insights they might yield into the nature of the
central modal concepts themselves.
These remarks concern Abelard’s account of simple modality. He also has an
account of determinate modality, which arises from this much-controverted Aristotelian
principle: “What is necessarily is when it is, and what is not necessarily
is not when it is not” [Aristotle, 1963, p. 52 (19a23)]. Something which was or is
the case can be viewed as an irrevocable historical fact, and in this sense gains a
necessity just by virtue of the passage of time. This is determinate necessity. The
corresponding notion of possibility will be similarly distinct from simple possibility
as defined purely in terms of compatibility with nature.
The phrasing of Aristotle’s principle exhibits the standard way of expressing determinate
modal statements: apply an adverbial while-clause (i.e., a dum-clause)
to the modal proposition so as to specify its modal content. The purpose of the
specification is to indicate an interval of time, and the modal content of the proposition
is then understood with reference to this interval. So Abelard works with
examples like “It is possible for Socrates to read while he sits” and “It is possible
for Socrates to read while he reads” [Abelard, 1958, p. 36 (14–15); Abelard, 2006,
12.73]. 59 The possibility in question (reading) is thus characterized as applying
58 There is some question as to whether Abelard fully grasped the relationships inherent in a
square of opposition for quantified modals. See [Knuuttila, 1998, p. 88], [Lagerlund, 2000, p. 37],
and [Thom, 2003, p. 55]. On this point, Martin defends Abelard in [Martin, 2001, pp. 122–123].
59 Notice the structural difference between the two forms. In the first the determining verb,