Handbook of the History of Logic: - Fordham University Faculty

552 Simo Knuuttila
second is John Buridan’s Treatise on Consequences (BC ). According to the editors,
Ockham’s Summa logicae was written in 1323 and Buridan’s Tractatus in
1335.The third is an anonymous Questions on Prior Analytics (PS). Its anonymous
author is known as Pseudo-Scotus since it was included in the seventeenthcentury
edition of Duns Scotus’s works. I refer to this work as PS. Buridan discussed
modal logic and modal syllogistic also in his Summulae de Dialectica and
in Quaestions on Prior Analytics. Some modal questions are dealt with in his
Questions on Peri hermeneias. 171 I refer mainly to the Treatise on consequences
because it contains a carefully considered summary of his modal theory. It seems
that the treatise by Pseudo-Scotus is later than the works of Ockham and Buridan,
many of the questions being similar to those in Buridan’s Questions on Prior
Analytics. 172
Buridan presents modal logic as part of his general theory of consequences,
which includes sections on the equipollences between various modes in combination
with negations and on the relations of the standard square of opposition
between them, the nature and conversions of compound and divided (de dicto and
de re) modal propositions, the mutual relationship between these two types of
modal propositions and their relations to assertoric propositions, further modal
consequences, and modal syllogisms. 173 The same themes occur in all works mentioned.
Fourteenth-century modal logic strove for generality, which had effects on
the attitudes towards Aristotle’s modal syllogistics. For one thing, it was thought
171 William Ockham, Summa logicae, ed. Ph. Boehner, G. Gál, S. Brown, Guillelmi de Ockham
Opera philosophica, vol. III (St. Bonaventure, N.Y.: St. Bonaventure University, 1974);
John Buridan, Tractatus de consequentiis, ed. H. Hubien, Philosophes médiévaux 16 (Louvain:
Publications Universitaires, Paris: Vander-Oyez, 1976); id., Questiones longe super librum Peri
hermeneias, ed. R. van der Lecq, Artistarium 4 (Nijmegen: Ingenium Publishers, 1983); id.,
Quaestiones in Analytica priora, ed. H. Hubien (not published); idem, Summulae de Dialectica,
an annotated translation with a philosophical introduction by G. Klima (New Haven: Yale
University Press, 2001); Pseudo-Scotus, In librum primum Priorum Analyticorum Aristotelis
quaestiones (John Duns Scotus, Opera omnia, ed. L. Wadding (Lyons, 1640), vol. I, 273-341.
For the date and author of this treatise, see S. Read, ‘Self-Reference and Validity Revisited’ in
Yrjönsuuri (ed., 2001), 184. Buridan’s Treatise on Consequences is translated in King, 1985.
172 For late medieval modal logic and modal theories, see also G.E. Hughes, ‘The Modal Logic in
John Buridan’ in G. Corsi, C. Mangione and M. Mugnai (eds.), Atti del convegno Internazionale
di Storia della Logica. Le Teorie della Modalità (Bologna: CLUEB, 1989), 93-111; Knuuttila
1993, 149-96; Spade 1996, ch. 10; Lagerlund 2000; Thom 2003; Normore 2003; S. Knuuttila,
‘Medieval Theories of Modality’, Stanford Encyclopedia of Philosophy, http://plato.stanford/
edu/entries/modality-medieval/ (2006).
173 In the first half of the fourteenth century, many logicians wrote detailed studies on consequences,
either in comprehensive works on logic, such as Walter Burley’s De puritate artis
logicae or William Ockham’s Summa logicae or in independent treatises, such as Burley’s De
consequentiis and Buridan’s Tractatus de consequentiis. For recent works on late medieval discussions
of consequences, see P. King, ‘Consequences as Inference: Mediaeval Proof Theory’
in M. Yrjönsuuri (ed., 2001), 117-45; I. Boh, ‘Consequence and Rules of Consequences in the
Post-Ockham Period’, in M. Yrjönsuuri (ed., 2001), 147-81; C. Dutilh Novaes, ‘Buridan’s consequentia:
Consequence and Inference within a Token-based Semantics’, History and Philosophy
of Logic 26 (2005), 277-97. While Buridan and Pseudo-Scotus based their discussions on modal
syllogistic on the theory of modal consequences, Ockham did not deal with modal syllogistic in
the section on consequences of the Summa logicae.