Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 525
Another interpretation of Boethius and Ammonius holds that future contingents
are not definitely true or false, because their truth-makers are not yet determined,
but are true or false in an indeterminate way. No qualification of the principle
of bivalence is involved. True statements are either determinately true or simply
(indeterminately) true. 65 While Ammonius and Boethius assumed that Aristotle
denied the definite truth of predictions which they took to imply determinism, it
is less clear how they understood the indefinite truth of these. Boethius’s formulations
often suggest that future contingent propositions are true-or-false without
being simply true or false, but perhaps he was not quite sure about this. 66
The past and the present are necessary in Boethius. Prospective contingent alternatives
with respect to a future event remain open until the relevant causes are
settled or the event takes place and the alternative options vanish. Correspondingly
he seems to take the truth of future propositions to mean that things cannot
be otherwise, for the antecedently assumed actuality of future truth-makers implies
that alternative prospective possibilities refer to things which are rendered
temporally impossible by the actualized alternatives.
In his early commentary on De interpretatione, Abelard follows Boethius’s analysis
of future contingent propositions. He understands Boethius’s comments in the
way most contemporary commentators do and accepts the idea that future contingent
propositions are merely true-or-false. Contradictory present tense propositions
are determinately true and determinately false and also disjunctively determinately/necessarily
true or false (etiam sub disjunctione), whereas contradictory
future contingent propositions are merely disjunctively true or false (tantum sub
disjunctione). 67
Abelard changed his view in the Dialectica and his longer commentary on De
interpretatione in Logica ‘Ingredientibus’. The historical order of these two works
is not quite clear. Many scholars have argued that the Dialectica is earlier 68 , but
it is also possible that the texts contain parts written at different times. While the
main structure of Aristotle’s argument in De interpretatione 9 is understood in
the same way in the Dialectica and the early commentary on De interpretatione,
Abelard now argues that future contingent propositions are true or false, although
not determinately or necessarily so, and takes this to be Aristotle’s view as well.
The difference between future contingent propositions and other propositions has
nothing to do with bivalence; it concerns the determinateness or indeterminateness
of the truth of propositions and what is signified by propositions. Misguided
opinions are based on the mistaken idea that the necessity or determinateness of
65 M. Mignucci, ‘Truth and Modality in Late Antiquity: Boethius on Future Contingent Propositions’
in G. Corsi, C. Mangione and M. Mugnai (eds.), Atti del convegno Internazionale di
Storia della Logica. Le Teorie delle Modalità (Bologna: CLUEB, 1989), 47-78, and ‘Ammonius’
Sea Battle’ in Ammonius, On Aristotle: On Interpretation 9, 53-86.
66 See also Sorabji 1998.
67 Editio super Aristotelem De interpretatione, ed. M. Dal Pra in Pietro Abelardo, Scritti di
logica (Florence: La Nuova Italia, 1969), 100.13-19; 112.7-113.3.
68 See Marenbon 1997, 40-8.