John Buridan’s Theory of Consequence and His Octagons of Opposition

Part of the Studies in Universal Logic book series (SUL)

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.

Keywords

Octagons of opposition Assertoric syllogism Modal syllogism Oblique syllogism Signification Buridan 

Mathematics Subject Classification

01A35 03-03 03A05 

References

  1. 1.
    Adams, M.M.: William Ockham, vol. 2. University of Notre Dame Press, Notre Dame (1987) Google Scholar
  2. 2.
    Anonymous: Ars Burana. In: De Rijk, L.M. (ed.) Logica Modernorum, vol. II 2, pp. 175–213. Van Gorcum, Assen (1967) Google Scholar
  3. 3.
    Bochenski, I.M.: A History of Formal Logic. Thomas, I. (trans., ed.). Chelsea, New York (1962) Google Scholar
  4. 4.
    Boethius, A.M.S.: Commentarii in librum Aristotelis Peri Hermeneias, editio prima. Meiser, C. (ed.). Teubner, Leipzig (1877) Google Scholar
  5. 5.
    Boethius, A.M.S.: Commentarii in librum Aristotelis Peri Hermeneias, editio secunda. Meiser, C. (ed.). Teubner, Leipzig (1880) Google Scholar
  6. 6.
    Buridan, J.: Summulae de Dialectica. Klima, G. (Eng. trans.). Yale University Press, New Haven (2001) Google Scholar
  7. 7.
    De Morgan, A.: On the Syllogism and Other Logical Writings. Heath, P. (ed.). Routledge & Kegan Paul, London (1966) MATHGoogle Scholar
  8. 8.
    De Rijk, L.M.: Peter of Spain: Tractatus. Van Gorcum, Assen (1972) Google Scholar
  9. 9.
    Hubien, H.: Iohanni Buridani: Tractatus de Consequentiis. Publications Universitaires, Louvain (1976) Google Scholar
  10. 10.
    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) Google Scholar
  11. 11.
    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) Google Scholar
  12. 12.
    Keele, R.: Applied logic and mediaeval reasoning: iteration and infinite regress in Walter Chatton. Proc. Soc. Mediev. Log. Metaphys. 6, 23–37 (2006) Google Scholar
  13. 13.
    Keynes, N.J.: Studies and Exercises in Formal Logic. Macmillan, London (1884) Google Scholar
  14. 14.
    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) Google Scholar
  15. 15.
    Lagerlund, H.: Medieval theories of the syllogism. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2010) Google Scholar
  16. 16.
    Londey, D., Johanson, C.: The Logic of Apuleius. Brill, Leiden (1987) Google Scholar
  17. 17.
    Priest, G., Read, S.: The formalization of Ockham’s theory of supposition. Mind 86, 109–113 (1977) MathSciNetCrossRefGoogle Scholar
  18. 18.
    Thom, P.: Medieval Modal Systems. Ashgate, Farnham (2003) Google Scholar
  19. 19.
    Thomsen Thörnqvist, C.: Anicii Manlii Severini Boethii De Syllogismo Categorico. Acta Universitatis Gothoburgensis, Gothenburg (2008) Google Scholar
  20. 20.
    Wengert, R.G.: Schematizing De Morgan’s argument. Notre Dame J. Form. Log. 15, 165–166 (1974) MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    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) Google Scholar

Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of St AndrewsSt AndrewsUK

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