Handbook of the History of Logic: - Fordham University Faculty

538 Simo Knuuttila
‘Socrates necessarily sits when he sits’ is true in the first case but false in the
second case. Perhaps he means that while the modal status of a proposition pertaining
to a temporally definite event is basically independent of temporal changes,
it can be changeable when the modal qualification is evaluated from a temporal
point of view. Things which are not necessary now may be so to-morrow. This is in
agreement with Abelard’s view about unchangeable metaphysical necessities and
possibilities and temporal modalities which are associated with real potencies. 110
After Abelard, an often discussed theory about time and modality was associated
with the distinction between temporal modalities per se and per accidens.
Per se necessary propositions were said to be true whenever they were uttered and
per accidens necessary propositions, true past tense singular propositions referring
to a definite event, were unchangeably true after having begun to be true. The
same analysis was applied to impossible propositions as well. 111
2.4 Modal Conversion
While the conversion of assertoric propositions was frequently discussed in early
medieval logic, the modal conversions were not often dealt with before the Prior
Analytics began to be used in logic teaching in the thirteenth century. One earlier
example is Peter Abelard’s remark that modal propositions in the divided
sense are only convertible into assertoric propositions, not into modal propositions;
for example, ‘For every man it is possible to run’ converts into ‘Something
for which it is possible to run is a man’. 112 This was found problematic when
it was realized that conversion of modals into modals played an important role
in Aristotle’s modal syllogistics which seemed to concentrate on modalities in the
divided sense. 113 According to Aristotle (An. pr. I.3), necessity propositions are
converted in the same way as the corresponding assertoric propositions: a universal
affirmative predication (AaB) implies a converted particular predication (BiA),
a particular affirmative predication (AiB) is equivalent with a converted predication
(BiA), and a universal negative predication (AeB) is converted into universal
negative predication (BeA). The first conversion was called accidental and the
others simple. While these rules are not problematic with respect to modals in
the compound sense, Aristotle employed them in proving modal syllogisms some
of which seem to be acceptable only when the premises are modal propositions in
110 Abelard often thinks of possibility in terms of potency attaching to things of a particular
species; see J. Marenbon, ‘Abelard’s Concept of Possibility’ in B. Mojsisch and O. Pluta (eds.),
Historia philosophiae medii aevi: Studien zur Geschichte der Philosophie des Mittelalters (Amsterdam
and Philadelphia: Gruener, 1991), 595-609, reprinted in Marenbon 2000; for the idea of
metaphysical alternatives, see C.J. Martin, ‘Abelard on Modality: Some Posibilities and Some
Puzzles’, T. Buchheim et al. (eds. 2001), 97-124; Martin 2003.
111 See de Rijk II-1, 371; II-2; 429.1-10; 481.22-482.14; Roger Bacon, Summulae dialectices 2.1.6,
366-72; William of Sherwood, Introductiones in logicam 41.8-16, trans. Kretzmann 1966, 41, and
note 16 above.
112 Super Perihermenias 11.17-12.20.
113 For this view of modal syllogistics, see Summe Metenses in de Rijk 1967, II-1, 468; Dialectica
Monacensis, de Rijk 1967, II-2, 480.10-16; Lambert of Auxerre, Logica 30.17-23.