Handbook of the History of Logic: - Fordham University Faculty

Medieval Modal Theories and Modal Logic 531
This, however, is impossible if mobile objects are considered according
to their determinate natures. (In Phys. VII.2.896) 85
Aquinas’s formulations illustrate the nature of medieval essentialism, also showing
some baroque aspects of the theory.
2 MODAL SEMANTICS AND MODAL LOGIC IN TWELFTH AND
THIRTEENTH CENTURIES
2.1 Equipollences and Oppositions
In the Latin translation of Aristotle’s Peri hermeneias by Marius Victorinus, Aristotle’s
two terms for possible, dunaton and endechomenon, were apparently rendered
by possibile and contingens. 86 Boethius states that these words may be
taken as meaning the same, although they are not used in quite the same way:
while the privation of possibility is expressed by inpossibile, the corresponding word
incontingens is not used. 87 Many twelfth-and thirteenth-century authors thought
that the terms possibile and contingens are used as synonyms or, if not, the term
possibile is used for what is not impossible (possibility proper) and contingens for
what is neither impossible nor necessary (two-edged possibility). 88 Using the term
‘possible’ for the basic modality which includes necessity and contingency became
85 The translation is quoted from Thomas Aquinas, Commentary on Aristotle’s Physics, translated
by R.J. Blackwell, R.J. Spath, and W.E. Thirlkel (London: Routledge and Kegan Paul,
1963).
86 A. Becker-Freysing, Die Vorgeschichte des philosophischen Terminus ‘contingens’: Die
Bedeutungen von ‘contingere’ bei Boethius und ihr Verhältnis zu den Aristotelischen
Möglichkeitsbegriffen, Quellen und Studien zur Geschichte und Kultur des Altertums und des
Mittelalters D 7 (Heidelberg: Bilabel, 1938), 20-4.
87 In Periherm. II, 382.17-22; 384.6-7; 392.17-393.12.
88 For the synonymous use, see Peter Abelard, Dialectica 193.31; Super Periermenias XII-XIV,
8, 37; William of Sherwood, Introductio in logicam, 44-5; trans. Kretzmann (1966), 47, 50; Peter
of Spain, Tractatus, I.24. In an anonymous twelfth-century commentary on Aristotle’s Prior
Analytics (Ms. Orléans BM 283) possibile refers to what is not impossible and contingens to this
or to what is neither impossible nor necessary; f. 181a. (For this work, see S. Ebbesen, ‘Analyzing
Syllogisms or Anonymus Aurelianensis III — The (Pesumably) Earliest Latin Commentary on
the Prior Analytics, and Its Greek Model, Cahiers de l’Institut du Moyen- ÂgeGrecetLatin,
Université de Copenhague 37 (1981), 1-20.) In the Dialectica Monacensis the term possibile
is characterized as expressing something like a genus of two species of modality, namely the
necessity and the contingent (De Rijk II-2, 481.9-13, 20-21). Lambert of Auxerre and Robert
Kilwardby suggest that while the common term may be ‘contingent’ or ‘possible’, ‘contingent’
is used for two-edged possibilities (Lambert of Auxerre, Logica, 40.1-42.2; Robert Kilwardby, In
libros Priorum Analyticorum expositio (Venice, 1516, reprinted Frankfurt am Main: Minerva
1968), 7ra-b); see also Albert the Great, Commentarius in librum I Priorum Analyticorum, ed.
A. Borgnet in Opera omnia I(Paris: Vivès, 1890), IV.4, 546. Roger Bacon and some others
stated that contingens is used of what is true or actual but can be false or un-actual, while
possibile refers to what is false or un-actual but can be true or actual; Roger Bacon, Summulae
dialectices, I: De termino, II: De enuntiatione, ed. A. de Libera, Archives d’histoire doctrinale
et littéraire du moyen âge 61 (1986), II.1.6, 247, 260-1, 395-6, 408-10; de Rijk 1967, II.1, 467;
II-2, 391.19-19.