Abstract
One of the manuscripts of Buridan’s Summulae contains three figures, each in the form of an octagon. At each node of each octagon there are nine propositions. Buridan uses the figures to illustrate his doctrine of the syllogism, revising Aristotle’s theory of the modal syllogism and adding theories of syllogisms with propositions containing oblique terms (such as ‘man’s donkey’) and with propositions of “non-normal construction” (where the predicate precedes the copula). O-propositions of non-normal construction (i.e., ‘Some S (some) P is not’) allow Buridan to extend and systematize the theory of the assertoric (i.e., non-modal) syllogism. Buridan points to a revealing analogy between the three octagons. To understand their importance we need to rehearse the medieval theories of signification, supposition, truth and consequence.
This work is supported by Research Grant AH/F018398/1 (Foundations of Logical Consequence) from the Arts and Humanities Research Council, UK.
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Notes
- 1.
The images come from Vatican ms. Pal.Lat. 994, ff. 6ra, 11[10]v, 7r and 1v, respectively. Reproduced by permission of the Biblioteca Apostolica Vaticana.
- 2.
The names of the moods in the medieval mnemonic record the reduction procedure (see, e.g., [8, p. 52]):
- 3.
We can also convert AeB per accidens to BoA, although Aristotle does not call this a conversion (since AeB converts to BeA). For BeA implies its subaltern BoA, for Aristotle writes at 26b15: “‘P does not belong to some S’ is … true whether P applies to no S or does not belong to every S.”
- 4.
See, e.g., [1, p. 1008].
- 5.
See, e.g., [12, p. 25].
- 6.
See [21].
- 7.
Cited in [21, p. 221].
- 8.
Buridan, Commentary on Aristotle’s Metaphysics, cited in [21, p. 224].
- 9.
Simple supposition, of a term for a universal or concept, was subsumed by Buridan under material supposition.
- 10.
See [17].
- 11.
As Aristotle noted: Prior Analytics I 13, 32b25-28.
- 12.
[9, I 1, p. 17].
- 13.
[6, Sophismata 2, sophism 5, pp. 847–848].
- 14.
[6, Sophismata 2, conclusion 14, p. 858].
- 15.
[9, I 3, p. 21].
- 16.
- 17.
- 18.
- 19.
Aristotle identified four direct and two indirect moods in the first figure, four in the second figure and six in the third figure.
- 20.
The octagon has ‘Of no human is [some] donkey …’ and ‘Of every human no donkey …’
- 21.
- 22.
- 23.
Buridan’s modal octagon was described in detail in [10].
References
Adams, M.M.: William Ockham, vol. 2. University of Notre Dame Press, Notre Dame (1987)
Anonymous: Ars Burana. In: De Rijk, L.M. (ed.) Logica Modernorum, vol. II 2, pp. 175–213. Van Gorcum, Assen (1967)
Bochenski, I.M.: A History of Formal Logic. Thomas, I. (trans., ed.). Chelsea, New York (1962)
Boethius, A.M.S.: Commentarii in librum Aristotelis Peri Hermeneias, editio prima. Meiser, C. (ed.). Teubner, Leipzig (1877)
Boethius, A.M.S.: Commentarii in librum Aristotelis Peri Hermeneias, editio secunda. Meiser, C. (ed.). Teubner, Leipzig (1880)
Buridan, J.: Summulae de Dialectica. Klima, G. (Eng. trans.). Yale University Press, New Haven (2001)
De Morgan, A.: On the Syllogism and Other Logical Writings. Heath, P. (ed.). Routledge & Kegan Paul, London (1966)
De Rijk, L.M.: Peter of Spain: Tractatus. Van Gorcum, Assen (1972)
Hubien, H.: Iohanni Buridani: Tractatus de Consequentiis. Publications Universitaires, Louvain (1976)
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)
Karger, E.: John Buridan’s theory of the logical relations between general modal formulae. In: Braakhuis, H.A.G., Kneepkens, C.H. (eds.) Aristotle’s Peri Hermeneias in the Latin Middle Ages, pp. 429–444. Ingenium, Groningen (2003)
Keele, R.: Applied logic and mediaeval reasoning: iteration and infinite regress in Walter Chatton. Proc. Soc. Mediev. Log. Metaphys. 6, 23–37 (2006)
Keynes, N.J.: Studies and Exercises in Formal Logic. Macmillan, London (1884)
King, P.: Jean Buridan’s Logic: The Treatise on Supposition and the Treatise on Consequences. King, P. (trans., with a Philosophical Introduction). Reidel, Dordrecht (1985)
Lagerlund, H.: Medieval theories of the syllogism. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2010)
Londey, D., Johanson, C.: The Logic of Apuleius. Brill, Leiden (1987)
Priest, G., Read, S.: The formalization of Ockham’s theory of supposition. Mind 86, 109–113 (1977)
Thom, P.: Medieval Modal Systems. Ashgate, Farnham (2003)
Thomsen Thörnqvist, C.: Anicii Manlii Severini Boethii De Syllogismo Categorico. Acta Universitatis Gothoburgensis, Gothenburg (2008)
Wengert, R.G.: Schematizing De Morgan’s argument. Notre Dame J. Form. Log. 15, 165–166 (1974)
Zupko, J.: How it played in the rue Fouarre: the reception of Adam Wodeham’s theory of the complexe significabile in the Arts Faculty at Paris in the mid-fourteenth century. Francisc. Stud. 54, 211–225 (1997)
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Read, S. (2012). John Buridan’s Theory of Consequence and His Octagons of Opposition. In: Béziau, JY., Jacquette, D. (eds) Around and Beyond the Square of Opposition. Studies in Universal Logic. Springer, Basel. https://doi.org/10.1007/978-3-0348-0379-3_6
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