Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 527
terminate. 72 In discussing the necessity of the present, Abelard follows Boethius
in stating that what is actual at a certain point of time is necessary in the sense
that it can no longer be avoided, 73 but he also argues that unrealized alternatives
may be possible at the same time in the sense that they could have happened at
that time. 74 The actuality of a contingent state of affairs at a specified future time
does not exclude the non-temporal possibility of simultaneous alternatives and the
truth of a proposition about this state of affairs does not make it necessary. This
seems to be the background of Abelard’s deviation from Boethius’s approach to
the truth and falsity of future contingent propositions.
According to Albert the Great and Thomas Aquinas, Aristotle argues in De
interpretatione 9 that future contingent propositions differ from other assertoric
propositions in not being determinately true or determinately false. Their general
view of the structure of Chapter 9 is similar to that of Boethius. Instead of the
Boethian definite-indefinite distinction, Albert and Aquinas employed the terms
‘determinate’ and ‘indeterminate’, as most medieval commentators did. 75 Assertoric
propositions are related to truth or falsity in the same way as their correlates
are related to being or non-being. When future things are indeterminate with
respect to being and non-being, the contradictory propositions about them must
also be indeterminate with respect to truth and falsity. A future contingent proposition
and its denial form a disjunction which is necessarily true. The members of
this disjunction are disjunctively true or false. The indeterminate truth or falsity
of a member of the disjunction does not imply that it is true or that it is false.
It is merely true-or-false. Because of the prospective indeterminateness of a seabattle,
the propositions pertaining to it ‘must be true or false under disjunction,
being related to either, not to this or that determinately.’ 76 According to Aquinas,
truth is not altogether lacking in a pair of contradictory singular future contingent
propositions. It not true to say that both of these are false, for if one of these is
false, the other is true, and vice versa. 77
Following Boethius, Aquinas thinks that contingency pertains to the future.
Past and present things are necessary. The absence of the idea of synchronic alternatives
in Boethius’s approach makes a true proposition about a future contingent
event determinately and necessarily true. Aquinas describes this assumption as
follows:
72Logica ‘Ingredientibus’ 422. 33-40.
73Logica ‘Ingredientibus’ 437.37-438.17.
74Seenote49above. 75Albert the Great, Comm. in Periherm. I.5.4-5, 418-21; Thomas Aquinas, In Peri herm.
I.13, 170-1.
76Thomas Aquinas, In Peri herm. I.15, 202-3; Albert the Great, Comm. in Periherm. I.5.6,
422; see also Averroes, De interpretatione in Aristotlis Opera cum Averrois commentariis I.T
(Venice, 1562–71), 82va and Peter of Ireland, Expositio et quaestiones in librum Aristotelis
Peryermenias seu De interpretatione, ed. M. Dunne, Philosophes médiévaux 34 (Louvain-la-
Neuve: Éditions de l’Institut Supérieur de Philosophie, Louvain and Paris: Peeters, 1996), I.17,
132.164-133.173; I.19, 143.47-56.
77In Peri herm. I.13, 175.