Abstract
Ockham has a very particular definition of modality: every term that is predicable of a whole sentence is a modal term. His definition reaches well beyond “necessary,” “possible,” “contingent” and “impossible,” including predicates such as “known” and “believed,” but also “written” and “spoken.” He provides a general framework for inferences including every term covered by his definition of modality. However, there is a proper modal syllogistic in Ockham only for the Aristotelian modalities, that combines two distinct semantic apparatus, constituted by Ockhamist modal predicates, on the one hand, and by modal and modally modified copulae, on the other. For the development of a syllogistic for the Aristotelian modalities, both are needed. There is no similar apparatus for other modalities in Ockham.
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Notes
- 1.
All references are to Ockham, unless otherwise specified.
- 2.
- 3.
SL III-1, c. 20, OPh I, 412–413: “[…] quando praemissae de necessario sunt acceptae in sensu compositionis, vel accipiuntur aliquae aequivalentes talibus propositionibus in sensu compositionis, semper est bonus syllogismus, inferens conclusionem consimilem quantum ad sensum compositionis vel aequivalentem. […] Et tenet talis discursus per istam regulam ‘praemissae in syllogismo regulato per dici de omni vel de nullo sunt necessariae, igitur conclusio est necessaria’.”
- 4.
SL III-1, c. 23, OPh I, 419: “[…] in omni figura, si accipiantur omnes propositiones de possibili in sensu compositionis vel accipiantur eis aequivalentes, non valet syllogismus, quia tunc argueretur per istam regulam ‘praemissae sunt possibiles, ergo conclusio est possibilis’, quae regula est falsa. […] sed ista regula vera est ‘si praemissae sunt possibiles et compossibiles, conclusio est possibilis’.”
- 5.
SL III-1, c. 30, OPh I, 435, ll. 10–16: “Et ideo pro sensibus compositionis talium propositionum et aequivalentibus eis est ista regula generalis, quod quando aliquod nomen tale modale potest verificari de praemissis absque hoc verificetur de conclusione, immo potest vere removeri a conclusione, uniformis ex talibus in sensu compositionis non valet nec ex aequivalentibus eis; quando autem de praemissis non potest verificari talis modus nisi etiam verificetur de conclusione, uniformis ex talibus semper tenet.” See also SL III-1, c. 30, OPh I, 437, ll. 59–61.
- 6.
See also SL III-1, c. 21, OPh I, 415, ll. 6–7 and c. 22, 417, l. 4 for the second and the third figures. Cf. ExpElench. II, c. 9, § 4, OPh III, 245, ll. 253–254.
- 7.
See the distinct senses of “contrary” in SL I, c. 43, OPh I, 128–129, ll. 168–180; Quodl. V, q. 24, OTh IX, 111–125.
- 8.
- 9.
SL II, c. 8, OPh I, 273: “Propositio modalis primo modo dicta semper est distinguenda secundum compositionem et divisionem. In sensu compositionis semper denotatur quod talis modus verificetur de propositionis illius dicti, sicut per istam ‘omnem hominem esse animal est necessarium’ denotatur quod iste modus ‘necessarium’ verificetur de ista propositione ‘omnis homo est animal’ […].”
- 10.
SL II, c. 10, OPh I, 276: “Propter quod sciendum quod ad veritatem talium propositionum requiritur quod praedicatum sub forma propria competat illi pro quo subiectum supponit, vel pronomini demonstranti illud pro quo subiectum supponit; ita scilicet quod modus expressus in tali propositione vere praedicatur de propositione de inesse, in qua ipsummet praedicatum praedicatur de pronomine demonstrante illud pro quo subiectum supponit, proportionaliter sicut dictum est de propositionibus de praeterito et de futuro.”
- 11.
This formulation follows the justification for particular modalities; see, e.g. SL III-1, c. 51, OPh I, 485: “[…] quando unus modus est inferior ad necessarium, tunc semper sequitur conclusio de necessario, sicut sequitur ‘omnem hominem esse coloratum est necessarium; Sortem esse hominem est per se; igitur Sortem esse coloratum est necessarium’. Sed quando modus ille non est inferior ad necessarium, tunc non valet mixtio nec respectu conclusionis de necessario nec respectu conclusionis de illo modo. Sicut non sequitur ‘omne album esse coloratum est necessarium; omnem hominem esse album est scitum a me; ergo omnem hominem esse coloratum est scitum a me’, nec sequitur ista conclusio ‘omnem hominem esse coloratum est necessarium’. Tamen aliquando sequitur conclusio de tali modo, sicut sequitur ‘omnem triangulum habere tres est necessarium; isoscelem esse triangulum est scibile; ergo isoscelem habere tres est scibile’. Unde quando aliquis modus non potest competere antecedenti nisi competeat consequenti, tunc in tali mixtione sequitur conclusio de tali modo. Huiusmodi sunt tales modi ‘scibile’, large accipiendo ‘scibile’, ‘credibile’, ‘apprehensibile’, ‘cognoscibile’, ‘proferibile’ et huiusmodi.” See also SL III-1, c. 44, OPh I, 475, ll. 7–17; c. 47, 479, ll. 19–23; c. 57, 490–491, ll. 5–15; c. 61, 494, ll. 16–19; c. 64, 496, ll. 11–17. The general thesis is stated differently, without the implication between modalities: “[…] raro valet mixtio, quia nunquam valet nisi quando tales modi non possunt verificari de praemissis nisi aliquis eorum verificetur de conclusione sequente ex praemissis” (SL III-1, c. 64, 496, ll. 6–8).
- 12.
For the “necessary” see SL III-1, c. 31, OPh I, 441, ll. 56–72; c. 32, 444, ll. 3–5.
- 13.
SL III-1, c. 31, OPh I, 441: “[…] illa minor est de inesse simpliciter in qua non potest preadicatum competere subiecto in uno tempore et negari in alio, sed semper uniformiter se habet, ita quod semper vere praedicatur vel numquam. Illa autem dicitur de inesse ut nunc in qua potest preadicatum uno tempore vere affirmari de subiecto et alio tempore vere negari.”
- 14.
For the contrast between Ockham’s modal theory and nearly everybody else’s see Perini-Santos (2002).
- 15.
See Boh (1982).
- 16.
- 17.
Quodl. VII, q. 9, OTh IX, 731: “[…] actus exercitus est ille qui importatur per hoc verbum ‘est’ vel aliquod consimile verbum, quod non tantum significat aliquid praedicari de alio sed exercet praedicationem, praedicando unum de alio […]. Actus signatus est ille qui importatur per hoc verbum ‘praedicari’ vel ‘subici’ vel ‘verificari’ vel ‘competere’, quae idem significant.” Cf. SL I, c. 66, OPh I, 202–203, ll. 57–94. See Nuchelmans (1987).
- 18.
SL III-1, c. 30, OPh, I, 437: “Sed alii uniformes valent quando uniformes de inesse correspondentes eis valent et ex modalibus sequuntur suae de inesse.” See also SL III-1, c. 51, OPh I, 485, ll. 27–31 and c. 64, 496, ll. 11–13. Ockham offers also a less strict rule: “Si autem praemissae tales sumantur ambae in sensu divisionis in prima figura, semper est syllogismus regulatur per dici de omni vel de nullo quando ex suis de inesse est bonus syllogismus, nisi ratione modi includatur aequivalenter propositio negativa” (SL III-1, c. 30, OPh I, 437). This text can be represented as follows:
(R2*) The sentences in the divided sense p is M and q is M imply r is M in the divided sense iff (i) p and q imply r and (ii) s is M does not imply not-s.
One of Ockham’s examples in SL III-1, c. 30, OPh I, 75–77, “dubitatur,” suggests (R2*), instead of (R2), as the correct rule. This example is not present in every source (see SL III-1, c. 30, OPh I, 437n), and isn’t in a friendly environment, since it follows (R2), not (R2*).
- 19.
SL III-1, c. 64, OPh I, 496: “Si autem praemissae sumantur in alio sensu, tunc si minor inferat suam de inesse in prima figura, semper conclusio sequitur in eadem figura de eodem modo de quo est maior.”
- 20.
For contingent sentences see III-1, c. 47, OPh I, 481, ll. 83–102. In both cases, we should add further conditions concerning the distinct readings of de possibili and de contingenti sentences.
- 21.
See ExpPeri. I, c. 2, §4, OPh II, 389, ll. 11–19; Quodl. VI, q. 29, OTh IX, 695, ll. 38–45.
- 22.
See e.g. SL II, c. 29, 341, ll. 4–5.
- 23.
See Boh (1993, 46–61). In his chapter on Ockham, Boh either makes very general claims that can be assumed under the framework sketched above, or deals with epistemological themes that do not receive a formal treatment in Ockham’s texts. This is also true of Knnuutila on Ockham’s “applied modal logic;” see Knnuutila (1993, 176–179). A particularly interesting case can be found in the obligationes literature; see Dutilh Novaes (2011) and Spade and Yrjönsuuri (2014).
- 24.
I would like to thank Magali Roques and Jenny Pelletier for the invitation to contribute to this volume – Magali should also be thanked for the careful reading of a prior version of the text. Finally, I am very grateful for Claude Panaccio, for his extraordinary work over the years, that has been an inspiration for me since I have started studying Ockham.
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Perini-Santos, E. (2017). The Metatheoretical Framework of William of Ockham’s Modal Logic. In: Pelletier, J., Roques, M. (eds) The Language of Thought in Late Medieval Philosophy. Historical-Analytical Studies on Nature, Mind and Action, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-66634-1_9
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