Abstract
The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation.
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References
Adams M. (1987) William Ockham (Vol. 2). University of Notre Dame Press, Notre Dame
Albert of Saxony: (1988) Insolubles. In: Kretzmann N., Stump E. (eds) Cambridge translations of medieval philosophical texts, volume I: Logic and philosophy of language. Cambridge University Press, Cambridge, MA, pp 337–368
Anon. (1967). Ars Burana. In L. De Rijk (Ed.), Logica modernorum, Vol. II 2 (pp. 175–213). Assen: Van Gorcum.
Buridan, J. (2001). Summulae de dialectica. New Haven, CT: Yale University Press. G. Klima, Eng. Tr.
Cesalli L. (2001) Le réalisme propositionnel de Walter Burley. Archives d’histoire doctrinale et littéraire du moyen âge 68: 155–221
De Morgan, A. (1966). In P. Heath (Ed.), On the syllogism and other logical writings. London: Routledge and Kegan Paul.
de Ockham, G. (1974). In P. Boehner et al. (Eds.), Summa logicae. St. Bonaventure: Franciscan Institute Publications.
De Rijk L. (1967) Logica modernorum. Van Gorcum, Assen
Hubien H. (1976) Iohannis Buridani: Tractatus de consequentiis. Publications Universitaires, Louvain
Hughes, G. (1989). The modal logic of John Buridan. In Atti del Congresso Internazionale di Storia della Logica: La teorie delle modalità (pp. 93–111). Bologna: CLUEB.
Keele R. (2006) Applied logic and mediaeval reasoning: Iteration and infinite regress in Walter Chatton. Proceedings of the Society for Medieval Logic and Metaphysics 6: 23–37
Löb M. (1955) On a solution of a problem of Leon Henkin. Journal of Symbolic Logic 20: 115–117
Potter M. (2009) Wittgenstein’s notes on logic. Oxford University Press, Oxford
Priest G., Read S. (1981) Ockham’s rejection of ampliation. Mind 90: 274–279
Spade P. (1974) Five logical tracts by Richard Lavenham. In: ODonnell J. (eds) Essays in honour of Anton Charles Pegis. Pontifical Institute of Mediaeval Studies, Toronto, ON, pp 70–124
Spade P. (1976) Robert Fland’s consequentiae: An edition. Mediaeval Studies 38: 54–84
Thom P. (2003) Medieval modal systems. Ashgate, Farnham
Wengert R. (1974) Schematizing De Morgan’s argument. Notre Dame Journal of Formal Logic 15: 165–166
Yrjönsuuri, M. (Ed.). (2001). Medieval formal logic. Dordrecht: Kluwer.
Zupko, J. (1994–1997). 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. Franciscan Studies, 54, 211–225.
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Paper presented at the Workshop on The Philosophy of Logical Consequence at Uppsala, 31 October–2 November 2008.