Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 551
modal explication of being and the disjunctive transcendental notions of necessity
and contingency. 169
God’s omniscience involves all possibilities and as objects of God’s knowledge
they receive an intelligible or objective being. Some of these are included in God’s
providential plan of creation and will receive an actual being. The description of a
possible world at a certain moment consists of compossible possibilities. Though
possibilities necessarily are what they are, the actualizations of non-necessary possibilities
are not necessary but contingent. All things which are contingently actual
at a certain moment could be not actual at that very moment. Since all finite beings
are contingently actual, the contingent alternative possibilities are possible
with respect to the same time, though they are not compossible with what is actual.
According to Scotus, impossibilities are incompossibilities between possible
ingredients, such as Socrates’s sitting at a certain time and Socrates’s not sitting
at that same time. God could have chosen a world in which the first happens
by Socrates’s free will or a world in which the second happens by Socrates’s free
will. Since these possibilities are real possibilities, though not compossible, they
are Socrates’s possibilities in alternative histories. 170
Scotus’s new modal metaphysics influenced early fourteenth-century philosophy
and theology in many ways. From the point if view of logic and its applications
to natural philosophy, the most significant ideas were the distinction between
logical and real modalities and the association of logical modalities with alternative
imaginative domains. Thirteenth-century essentialist assumptions were largely
dropped from modal logic based on new modal semantics.
3.2 Early Fourteenth-Century Modal Logic
I shall sketch the main lines of early fourteenth-century modal logic by concentrating
on three works. The first is William Ockham’s Summa logicae (OSL). In
respect to the variety of the combinations of types of premises in modal syllogisms,
this includes the most extensive fourteenth-century discussion of the topic. The
169 For modalities in Scotus’s metaphysics, see L. Honnefelder, Scientia transcendens. Die
formale Bestimmung der Seiendheit und Realität in der Metaphysik des Mittelalters und der
Neuzeit (Duns Scotus – Suarez – Wolff – Kant – Peirce) (Hamburg: Meiner, 1990), 3-108.
170 Ord. I.43, 14; Lect. I.39.1-5, 62-5; Ord. I.35, 32, 49-51; I.38, 10. For Scotus’ modal theory,
see also Knuuttila 1993, 139-46; C. Normore, ‘Scotus, Modality, Instants of Nature, and the
Contingency of the Present’ in Honnefelder, Wood and Dreyer (eds., 1996), 161-74; Normore,
‘Duns Scotus’s Modal Theory’ in T. Williams (ed.), The Cambridge Companion to Duns Scotus
(Cambridge: Cambridge University Press, 2003), 129-60; S.P. Marrone, ‘Revisiting Duns Scotus
and Henry of Ghent on Modality’ in Honnefelder, Wood and Dreyer (eds., 1996), 175-89. Many
scholars have paid attention to similarities between Scotus and Leibniz and regarded both as
predecessors of the ideas codified in possible worlds semantics. Scotus, as distinct from Leibniz,
did not use the term ‘possible world’, but it received a theoretical role in modal discussions
before Leibniz; see S.K. Knebel, ‘Necessitas moralis ad optimum. Zum historischen Hintergrund
der Wahl der Besten aller möglichen Welten’, Studia Leibnitiana 23 (1991), 3-24; J. Schmutz,
‘Qui a inventé les mondes possibles’ in J.-C. Bardout and V. Jullien (eds.), Les mondes possibles,
Cahiers de philosophie de l’Universite de Caen (Caen: Presses universitaires de Caen, 2006),
9-45.