Handbook of the History of Logic: - Fordham University Faculty

524 Simo Knuuttila
the distinction between definite and indefinite division of truth and falsity in the
contradictory pairs of propositions. This terminology was also used in Ammonius’s
commentary. Since this work was not known to Boethius, both authors
apparently based their commentaries on earlier Greek discussions in which these
qualifications were introduced. 59 According to Boethius, Aristotle argues that if
all pairs of contradictory propositions definitely divide truth and falsity and all
propositions are definitely true or definitely false, then everything necessarily occursasitdoes.
60 The fact that contingent future things, events and states of
affairs are not determined refutes the thesis that all affirmations or negations are
definitely true or definitely false. 61 The disjunctive pairs of contradictory future
contingent propositions can be said to divide truth and falsity only in a very special
sense; ‘the whole body of the contradiction does indeed separate into truth
and falsity, but this truth and falsity is undifferentiated and alterable.’ 62 Boethius
interprets Aristotle’s final solution as follows:
For it is necessary as regards future and contingent contradictions that
the whole contradiction have one part true and the other false. For
example, if someone affirms that there is going to be a sea battle tomorrow
. . . and if someone denies it . . . the whole contradiction will
indeed have one part true, the other false; but there will not be one
of them definitely true and the other definitely false. (In Periherm. I,
122.26-123.10, trans. Kretzmann) 63
The majority interpretation of contemporary commentators is that Ammonius and
Boethius ascribe to Aristotle the view that the predictions of future contingent
things and their denials differ from other contradictory pairs, because truth and
falsity are not definitely distributed between these propositions, which are consequently
neither definitely true nor definitely false. This is taken to mean that they
are not true or false. In answering the Stoic criticism, Boethius might have thought
that future contingent propositions have the disjunctive property of being trueor-false,
which would mean something other than simply lacking a truth value. 64
59 Sorabji 1998. Ammonius’s commentary was translated by William of Moerbeke in 1268 and
was used by Thomas Aquinas. See note 8.
60 Boethius thinks that the term ‘definitely’ can be added to Aristotle’s argument as part of
what Aristotle means (In Periherm. I, 108.18-26; 125.20; II, 204.8-25; see also I, 109.9-17;
110.28-112.4; 114.8-24; II, 208.7-23; 211.26-213.4).
61 In Periherm. II, 219.5-17.
62 In Periherm. I, 108.2-5; cf. I, 106.30-107.6; II, 208.7-18.
63 This contradiction is said to be indefinitely both true and false (I, 124.28); according to the
longer commentary, ‘one part of the contradiction is true and the other false only indefinitely’
(II, 246.12-13).
64 Craig 1988, 79-98; R. Gaskin, The Sea Battle and the Master Argument, Quellen und Studien
zur Philosophie 40 (Berlin: de Gruyter, 1995), 146-84; N. Kretzmann, ‘Boethius and the Truth
about Tomorrow’s Sea Battle’ in Ammonius, On Aristotle: On Interpretation 9, 24-52. D. Frede
argues argues that Boethius gives up the principle of bivalence and does not extend it to include
the disjunctive formulation; see ‘The Sea-Battle Reconsidered : A Defense of the Traditional
Interpretation, Oxford Studies in Ancient Philosophy, vol. III (Oxford: Clarendon Press, 1985),
44-5.