Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 507
In Section (1) I shall deal with some influential medieval interpretations of
modal concepts from Boethius to Aquinas. I do not mean that these were shared
by everybody before Aquinas and by nobody after him. Since the eleventh century
recovery of philosophical modal theories, Boethian formulations of central ancient
conceptions had often been considered congenial, but were also qualified by theological
considerations. These discussions were accompanied by some attempts to
redefine modal concepts using the idea of alternativeness. While all these trends
influenced mid-thirteenth century discussions, many thinkers were particularly interested
in interpreting modal terms in the light of Aristotelian essentialism. This
approach is also found in Robert Kilwardby’s commentary on Aristotle’s Prior
Analytics (c. 1240) which became the standard thirteenth-century textbook for
modal syllogistics. Many thirteenth-century paradigms lost their significance in
early fourteenth-century discussions of modal theory, as will be shown in section
(3). Before this, however, I shall discuss the details of earlier logical modal theories
including modal syllogistics in section (2). Section (3) is about fourteenth-century
developments and section (4) about medieval theories of applied modalities.
1 GENERAL SEMANTIC PARADIGMS FROM BOETHIUS TO THOMAS
AQUINAS
1.1 Extensional Interpretation of Modality
In the introductory remarks of his commentary on Chapter 9 of Aristotle’s Peri
hermeneias, Thomas Aquinas classifies various types of propositions on the basis
of their ‘matter’:
In necessary matter all affirmative propositions are determinately true;
this holds for propositions in the future tense as well as in the past
and present tenses; and negative ones are false. In impossible matter
the contrary is the case. In contingent matter, however, universal
propositions are false and particular propositions are true. This is
the case in future tense propositions as well as those in the past and
present tenses. In indefinite ones, both are at once true in the future
tense propositions as well as those in the past and present tenses. (In
Peri herm. I.13, 168 [5], trans. Oesterle, with changes) 6
The matter of a proposition is associated with the habitude of a predicate to a
subject and is explained as follows:
If the predicate is per se in the subject, it will be said to be a proposition
in necessary or natural matter, for example ‘Man is an animal’
6 In Aristotelis libros Peri Hermeneias et Posteriorum analyticorum expositio, ed. R. Spiazzi
(Turin: Marietti, 1964); Aristotle: On Interpretation. Commentary by St. Thomas and Cajetan,
J.T. Oesterle, Mediaeval Philosophical Texts in Translation 11 (Milwaukee, Wisc.: Marquette
University Press, 1962).