Abstract
Whereas most of his predecessors attempted to make sense of, and if necessary correct, Aristotle’s theory of the modal syllogism, John Buridan starts afresh in his Treatise on Consequences, treating separately of composite and divided modals, then of syllogisms of necessity, possibility, and with mixed premises. Finally, he comes in the penultimate chapter of the treatise, Book IV Chap. 3, to present a concise treatment of syllogisms with premises of contingency, that is, two-sided possibility. The previous modal syllogisms had all been taken with an affirmed mode only, since modal conversion equates negated necessity and possibility with affirmed possibility and necessity, respectively. But in his Conclusions concerning syllogisms of contingency, he also treats those with negated mode. These are the non-contingency syllogisms.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Barbara is a mnemonic for the AAA syllogism in the first figure. See, e.g., Aristotle [1, pp. 67–71], Buridan [2, §5.2.2, pp. 320–1]. L, M, X and Q stand respectively for the modalities necessity, possibility, assertoric and contingency. For the full mnemonic, and discussion of the problem of the two Barbaras, see, e.g., Thom [8].
- 2.
See Sophistici Elenchi 4, 166a24–26. “Amphiboly and ambiguity depend on these modes of speech. Upon the combination of words there depend instances such as the following: ‘A man can walk while sitting, and can write while not writing’. For the meaning is not the same if one divides the words and if one combines them in saying that ‘it is possible to walk-while-sitting’.”
- 3.
See, e.g., Thom [9, p. 169].
- 4.
Buridan, Summulae de Dialectica [2, §1.8.5, p. 76]: “But as far as ‘contingent’ is concerned, we should realise that sometimes ‘contingent’ is taken broadly, and then it is synonymous with ‘possible’, and sometimes it is taken strictly, and this we call ‘contingent both ways’, and then it is a species of ‘possible’ distinguished from ‘necessary’.”.
- 5.
So-called by George Hughes [6]; Buridan himself calls them ‘great figures’—magnae figurae.
- 6.
Buridan expands the universal affirmative to contain an explicit I-proposition in the 14th Conclusion of Book I of the Treatise on Consequences [5, p. 52] : “ ‘homo est animal et nullus homo est aliud ab animali’ … haec copulatiua aequiualent isti universali affirmatiuae ‘omnis homo est animal’.” So it is false if the subject is empty, just as its contradictory, the particular negative, is true in the same circumstances: “non sequitur ‘chimaera non est homo; ergo non homo non est non chimaera’, quia prima est uera et secunda falsa.” Hubien [5, p. 53].
- 7.
Note that, where \(\underline{b}\to a\) adds to b→a the requirement that b is non-empty, \(b\not\to a\) not only denies b→a but disjoins the possibility of emptiness of b, as shown by axiom 1.5 below.
- 8.
I’ve amended axioms 1.5 and 1.6 somewhat from Thom’s formulation.
- 9.
Thom [9, p. 17] writes, e.g., “for some ‘d’, b←d∣a”.
- 10.
Note that \(\underline{b}\to a\) does not say that every existing B is A, but that every B is A and there are Bs.
- 11.
The word Aristotle uses here is endechesthai.
- 12.
Hubien [5, II 5, p. 62].
- 13.
Cf. Summulae de Dialectica [2, §1.8.3, p. 73]: “But a proposition about contingency with a negated mode can be said to be about necessity and impossibility disjunctively, for ‘B is not contingently A’ is equipollent to ‘B has to be A or B cannot be A’. (Buridan [3, pp. 87–8]: Sed illa de contingenti modo negato potest dici de necessario et impossibili disiunctive; nam istae aequipollent ‘B non contingit esse A’ et ‘B necesse est esse A vel impossibile est esse A’.) See also §1.8.10, [2, p. 99].
- 14.
Thom [9, p. 183 ff.] seems to miss the fact that these four conclusions concern non-contingency rather than contingency.
- 15.
The fourth Conclusion of I 8 reads: “In any good consequence whatever follows from the consequent follows from the antecedent, and the consequent follows from whatever the antecedent follows from, and similarly, put in the negative, whatever does not follow from the antecedent does not follow from the consequent, and the antecedent does not follow from whatever the consequent does not follow from.” (Omnis bonae consequentiae quidquid sequitur ad consequens sequitur ad antecedens et ad quodcumque sequitur antecedens ad illud sequitur consequens; et similiter, negatiue, quidquid non sequitur ad antecedens non sequitur ad consequens et ad quodcumque non sequitur consequens ad illud non sequitur antecedens [5, pp. 33–4].)
- 16.
Hubien [5, p. 131]: Ad quascumque praemissas sequitur conclusio de necessario de modo affirmato ad easdem sequitur conclusio de contingenti de modo negato.
Haec conclusio probatur per quartam conclusionem primi libri, sicut praecedens. Quia tales de necessario antecedunt talibus de contingenti.
- 17.
Hubien [5, p. 131]: In prima figura et in tertia ex maiore de contingenti, siue de modo affirmato siue de modo negato, sequitur conclusio similiter de contingenti si minor sit de necessario uel de possibili uel de contingenti.
Haec conclusio, quantum ad primam figuram, manifesta est per dici de omni uel de nullo, sicut manifesta erat quarta conclusio huius libri.
Sed quantum ad tertiam figuram manifestari potest per syllogismos expositorios et per impossibile, sicut manifestabatur sexta conclusio huius libri.
- 18.
Hubien [5, p. 131]: Ex maiore de contingenti et minore de inesse ualet prima figura ad conclusionem de contingenti particularem, non ad uniuersalem.
Haec conclusio declaratur sicut declarabatur secunda pars decimae conclusionis huius libri. Quod enim non sequatur conclusio uniuersalis patet. Quia omnem hominem contingit ridere et omne currens est homo (ponatur ita esse), tunc conclusio uniuersalis esset falsa. Et si maior sit de modo negato instantia est. Quia nullum equum contingit ridere, omne currens est equus (ponatur ita esse), conclusio etiam uniuersalis esset falsa.
- 19.
Hubien [5, p. 132]: Ex maiore uniuersali de contingenti in tertia figura et minore de inesse sequitur conclusio similiter de contingenti, sed si maior sit particularis non sequitur conclusio de contingenti.
Prima pars conclusionis probatur. Quia in omnibus modis tertiae figurae habentibus maiorem uniuersalem si minor quae ponitur de inesse conuertatur fiet prima figura, quae ualebat, ut dictum est in conclusione praecedente.
Secunda pars patet. Quia quamuis quendam currentem contingat ridere et omne currens sit equus, tamen nullum equum contingit ridere. Similiter est si maior ponatur negatiua, quia aequiualet affirmatiuae.
Si autem loquamur de modo negato adhuc instatur. Quia quendam intelligentem non contingit creare et omnis intelligens est deus (ponatur hoc), non sequitur “ergo deum non contingit creare”.
- 20.
Hubien [5, p. 130]: Quoniam deum contingit creare, et tamen nihil quod contingit esse deum et contingit creare, quia nihil contingit esse deum, immo omne necesse est esse deum uel necesse est non esse deum.
References
Aristotle: Prior Analytics Book I. Clarendon Aristotle Series. Clarendon Press, Oxford (2009). Translated with an Introduction and Commentary by Gisela Striker
Buridan, J.: Summulae de Dialectica Yale U.P., New Haven (2001). An annotated translation, with a philosophical introduction by Gyula Klima
Buridan, J.: Summulae de Propositionibus. Brépols, Turnhout (2005). Ria van der Lecq, ed.
Buridan, J.: Treatise on Consequences. Fordham University Press, New York (2014). S. Read, Eng. Tr.
Hubien, H.: Iohanni Buridani: Tractatus de Consequentiis. Publications Universitaires, Louvain (1976). English translation in [4]
Hughes, G.: The modal logic of John Buridan. In: Atti del Congresso Internazionale di Storia della Logica: La Teorie delle Modalità, pp. 93–111. CLUEB, Bologna (1989)
Lagerlund, H.: Modal Syllogistics in the Middle Ages. Brill, Leiden (2000)
Thom, P.: The two Barbaras. Hist. Philos. Logic 12(2), 135–149 (1991)
Thom, P.: Medieval Modal Systems. Ashgate, Farnham (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
I am very happy to dedicate this paper to Jean-Yves Béziau.
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Read, S. (2015). John Buridan on Non-contingency Syllogisms. In: Koslow, A., Buchsbaum, A. (eds) The Road to Universal Logic. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-10193-4_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-10193-4_21
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-10192-7
Online ISBN: 978-3-319-10193-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)