Handbook of the History of Logic: - Fordham University Faculty

568 Simo Knuuttila
Peter Lombard wrote in his influential Sentences that ‘Things cannot be other than
as God foreknows them’ is true in the compound sense and false in the divided
sense. The truth of the compound sense saves God’s infallibility, while the falsity
of the divided sense expresses God’s freedom and the metaphysical contingency
of the future. It is assumed that when something is, it is possible that it is not
at that very instant of time at which it is actual. These theological formulations
exemplify twelfth-century deviations from the Aristotelian thesis ‘What is necessarily
is when it is’. This was traditionally understood as implying the principle of
the necessity of the present, which was not questioned in ancient modal theories.
Since temporally definite propositions about contingent things were regarded as
unchangingly true in God’s knowledge, the contingency of these propositions also
implied the denial of the Aristotelian equation of immutability with necessity. The
new modal idea could be characterized as the model of simultaneous alternatives.
Its theological foundation was Augustine’s idea of God, who as the creator and
providence of the world, acts by free choice between alternatives.
In accordance with the new modal conception, possibilities as the objects of
divine power were regarded as much more numerous than possibilities associated
with natural powers. While exemplification in the actual world was often regarded
as a criterion of the genuineness of the types of natural possibility, it was
not relevant for divine possibilities. In twelfth-century theology, natural possibilities
secundum inferiorem causam were said to be possibilities secundum cursum
naturae and possibilities secundum superiorem causam meant divine possibilities.
There were similar discussions in medieval Arabic philosophy.
In twelfth-century logical treatises, which were influenced by Boethius’s works,
one can find ideas not discussed in ancient sources in Abelard’s analysis of the
types of modal propositions, future contingents and the logic of conditionals and
late twefth-century and early thirteenth-century works on the logic of terms, time
and modality, some of these being associated with the idea of modality as referential
plurality. The increasing reception of Aristotle’s philosophy in the thirteenth
century gave support to traditional modal paradigms, as is seen in the discussions
of modal conversion and Robert Kilwardby’s very influential commentary on
Aristotle’s Prior Analytics, in which modal syllogistic is treated as an essentialist
theory of the structures of being.
While twelfth-century modal innovations were used to some extent in thirteenthcentury
theology, they were not extensively discussed in philosophical contexts.
Things became different when John Duns Scotus combined the various elements
of the conception of modality as alternativeness into a detailed theory. Scotus
describes the simultaneous alternatives as the domains with respect to which God
chooses the actual world, but the structure of the theory is taken to pertain to
logical modalities which are what they are independently of whether anything
exists. A possible state of affairs is characterized as expressing something to which
to be is not repugnant. What is impossible is a combination of elements which are
incompossible.
Even Aristotle said that when a possibility is assumed to be actualized, noth-