Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 569
ing impossible follows, but he had in mind actualization in the history of the
actual world. The denial of an omnitemporally actual state of affairs is said to
be impossible. In the thirteenth century, some thinkers qualified Aristotle’s characterization
of possibility as something which can be assumed as actual without
contradiction by explaining that possibilities referring to the same moment of time
are not necessarily compossible in the sense that they could be actual at the same
time. In Scotus’s theory, actualizability as a criterion of possibility does not refer
to the already existing actual world, nor is it explained by referring to prospective
options of which the unrealized will disappear, as in the theories of diachronic
modalities. Temporally definite possibilities are primarily treated as referring to
alternatives, as is shown by the definition of a contingent state of affairs: ‘I do
not call something contingent because it is not always or necessarily the case, but
because its opposite could be actual at the very moment when it occurs’.
In the fourteenth century, many authors followed Scotus in explicating the
meaning of modal terms by referring to simultaneous alternatives as the basic
model. This is also reflected in the reformulation of modal logic with the systematic
distinction between modalities de dicto and de re and the division of
de re modalities into those with actual subject terms and those with non-actual
subject terms. The basic notion was that of logical possibility which was distinguished
from the more restricted notion of natural possibility. John Buridan’s
theory of modal consequences is considered as one of the greatest achievements
of medieval logic. Aristotle’s modal syllogistics was regarded as a fragmentary
theory in which the different types of the fine structure of modal statements were
not distinguished. Contrary to thirteenth-century approaches, Ockham, Buridan
and their followers did not try to reconstruct Aristotle’s theory as such into a
uniform system. The new modal paradigms which show some similarities to the
background ideas of possible worlds semantics also influenced fourteenth century
logic of discourse (obligations logic) and the treatments of applied modal logic,
the logic of knowledge and belief and the logic of norms.
Primary Literature
BIBLIOGRAPHY
[Alan of Lille, 1981] Alan of Lille. Regulae caelestis iuris, ed. N.M. Häring, Archives d’histoire
doctrinale et littéraire du moyen âge 78 (1981), 97-226.
[Albert of Saxony, 1502] Albert of Saxony. Sophismata (Paris, 1502).
[Albert the Great, 1890a] Albert the Great. Commentarius in Perihermenias, inOpera omnia,
ed. A. Borgnet, vol. I (Paris: Vivès, 1890).
[Albert the Great, 1890b] Albert the Great. Commentarius in Librum I Priorum Analyticorum,
in Opera omnia, ed. A. Borgnet, vol. I (Paris: Vivès, 1890).
[Alexander of Aphrodisias, 1883] Alexander of Aphrodisias. In Aristotelis Analyticorum priorum
librum I commentarium, ed. M. Wallies, Commentaria in Aristotelem Graeca 2.1 (Berlin:
Reimer, 1883).
[Ammonius, 1961] Ammonius. Commentaire sur le Peri hermeneias d’Aristote. Traduction de
Guillaume de Moerbeke, ed. G. Verbeke, Corpus Latinum Commentariorum in Aristotelem
Graecorum (Louvain: Publications Universitaires, Paris: Béatrice-Nauwelaerts, 1961); the
Greek text is edited by A. Busse in Commentaria in Aristotelem Graeca 4.5 (Berlin, 1897).