Positio impossibilis and concept formation: Duns Scotus on the Concept of infinite Being
Abstract
The purpose of this study is to investigate Duns Scotus's uses of the technique of positio impossibilis for elaborating his concept of ens infinitum or ontological infinitas in Quodlibet q. 5. Although there are several studies about Scotus's account of infinite being as a proper concept of God and of infinitum as the fundamental intrinsic mode of being, there is no targeted investigation of his conscious application of that logical tool for the purpose of concept formation. In order to acquire a complex concept like “infinite being”, Scotus is concerned first of all with the compatibility of its contents and with conceivability. He starts the technique exploring mathematical potential infinity according to Aristotle and arrives secundum imaginationem at ontological actual infinity through the analysis of the notions of “whole” (totum) and “perfection” (perfectum).Downloads
References
Alluntis, F. & Wolter, A. B. (1975). Glossary: virtually. In John Duns Scotus, God and the Creatures - The Quodlibetal Questions, Translated., Intros., Notes, and Glossary by F. Alluntis and A. B. Wolter. Princeton/London: Princeton University Press.
Ashworth, J. (1993). Ralph Strode on Inconsistency in Obligational Disputations. In Jacobi, K. (Hrsg.). Argumentationstheorie. Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns. Leiden: Brill, 363-386.
Catania, F. J. S. (1993). John Duns Scotus on Ens Infinitum. The American Catholic Philosophical Quarterly, 68, 37-54.
Charlton, W. (1991). Aristotle’s Potential Infinites. In Judson, L. (ed.). Aristotle’s Physics - A Collection of Essays. Oxford: Clarendon Press, 129-149.
Counet, J. M. (1994). L’univocité de l’étant et la problématique de l’infini chez Jean Duns Scot. In Follon, J. & Mcevoy, J. (eds.). Actualité de la pensée médiévale. Louvain-la-Neueve/Louvain/Paris: Éditions de l’Institut Supérieur de Philosophie - Éditions Peeters, 287-328.
Cross, R. (2005). Duns Scotus on God. Aldershot: Ashgate.
De Tudela, J. P. & Velasco (1981). Identidad, forma y diferencia en la obra de Juan Duns Scoto. Una aproximación matemática al problema de su interpretación. Madrid: Editorial de la Universidad Complutense.
Dutilh Novaes, C. (2005). Medieval Obligationes as Logical Games of Consistency Maintenance. Synthese, 145(3), 371–395.
Dutilh Novaes, c. (2006). Roger Swyneshed’s Obligaciones: a Logical Game of Inference Recognition?. Synthese, 151(1), 125-153.
Heath, Th. 1998). Mathematics in Aristotle. Bristol: Thoemmes Press (reprinted from the 1949 edition).
Hofmeister Pich, R. (2007). Infinity and Intrinsic Mode. In Hofmeister Pich, R. (ed.). New Essays on Metaphysics as Scientia Transcendens. Loivain-la-Neuve: FIDEM, 159-214.
Honnefelder, L. (1990). Scienti transcendente. Hamburg: Felix Meiner Verlag.
Honnefelder, L. (2005). Duns Scotus. München: Beck Verlag.
Houdebine, J. L. (1984). Excès de langages (Hölderlin, Joyce, Duns Scot, Hopkins, Cantor, Sollers). Paris: Editions Denoël.
King, P. (2003). Scotus on Metaphysics. In Williams, Th. (ed.). The Cambridge Companion to Duns Scotus. Cambridge: Cambridge University Press, 15-68.
Knuutila, S. (1997). Positio impossibilis in Medieval Discussions of the Trinity. In: Marmo, C. (ed.). Vestigia, imagines, verba. Semiotics and Logic in Medieval Theological Texts (Xllth-XIVth Century). Turnhout: Brepols, 277-288.
Knuutila, S. (2006). How Theological Problems Influenced the Development of Medieval Logic? In Caroti, S., Imbach, R., Kaluza, Z., Stabile, G. & Sturlese, L. (eds.). “Ad ingenue acuitionem”, Studies in Honour of Alfonso Maierù. Louvain-la-Neuve. Turnhout: Brepols, 183-198.
Knuutila, S. (2007). Modality as Alternativeness in John Duns Scotus. In Hofmeister Pich, R. (ed.). New Essays on Metpahysics as scientia transcendens. Lovain-la-Neuve: FIDEM, 145-157.
Martin, Ch. J. (1997). Impossible positio as the Foundation of Metaphysics or, Logic on the Scotist Plan? In: Marmo, C. (ed.). Vestigia, imagines, verba. Semiotics and Logic in Medieval Theological Texts (Xllth-XIVth Century). Turnhout: Brepols, 255-276.
Martin, Ch. J. (1992). Obligations and Liars. In Read, S. (ed.). Sophisms in Medieval Logic and Grammar. Dordrecht: Kluwer, 357-381.
Koch, A. F. (2005). Apeiron/ unendlich. In Höffe, O. (Hrsg.). Aristoteles-Lexikon, Redaktion: Rolf Geiger und Philipp Brüllmann. Stuttgart: Alfred Kröner Verlag, 55-58.
Körner, S. (1986). The Philosophy of Mathematics. New York: Dover Publications (republication of the second edition, 1968).
Kouremenos, Th. (1995). Aristotle on Mathematical Infinity. Stuttgart: Franz Steiner Verlag.
Leslie, J. (1995). Finite/infinite. In Kim, J. & Sosa, E. (eds.). A Companion to Metaphysics. Oxford: Blackwell Publishers (reprinted 1998).
Lewis, D. (1973). Counterfactuals. Oxford: Blackwell.
Mondolfo, R. (1968). O infinito no pensamento da Antiguidade Clássica. Sao Paulo: Mestre Jou, 429-461.
Moore, A. W. (1998). Infinity. In Craig, E. (ed.). The Routledge Encyclopedia of Philosophy, vol. 4. London/New York: Routledge, 772-778.
Murdoch, J. E. (1982). Infinity and Continuity. In: Kretzmann, N., Kenny, A. & Pinborg, J. (eds.). The Cambridge History of Later Medieval Philosophy. From the Rediscovery of Aristotle to the Disintegration of Scholasticism 1100-1600. Cambridge: Cambridge University Press, 564-591.
Pütz, Ch. (1997). Die Obligationenlehre in der scholastischen Logik, Untersuchungen zum Einfluss der stoischen Logik auf die Lehre von den Verpflichtungen (De obligationibus). Düsseldorf: Universitat Düsseldorf.
Ross, W. D. (1936). Commentary. In: Aristotle,Aristotle's Physics, a revised text with introduction and commentary by W. D. Ross. Oxford: Clarendon Press (reprinted 1979).
Seifert, J. (2005). A Vontade como perfeição pura e a nova concepção nao-eudaimonística do amor segundo Duns Scotus. Veritas, 50(3), 51-78.
Sondag, G. (2005). Duns Scot. La métaphysique de la singularité. Paris: Vrin.
Sondag, G. (2005). Jean Duns Scot sur l’infini extensif et l’infini intensif. Revue Thomiste, 105, 11-122.
Sondag, G. (2005-2006). Jean de Damas et Jean Duns Scot sur l’infinité de l’essence divine. Chora - Révue d’Études Anciennes et Médiévales, 3-4, 285-325.
Spade, P. V. (1982). Three Theories of Obligationes: Burley, Kilvington and Swydeshed on Counterfactual Reasoning. History and Philosophy of Logic, 3, 1-32.
Spruyt, J. (1993). Thirteenth-Century Positions on the Rule ‘ex impossibili sequitur quodlibet’. In Jacobi, K. (Hrsg.) Argumentationstheorie. Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns. Leiden: Brill, 161-193.
Sweeney, L. (1992). Divine Infinity in Greek and Medieval Thought. New York: Peter Lang Verlag.
Vos, A. (2006). The Philosophy of John Duns Scotus. Edinburgh: Edinburgh University Press.
Wolf, S. (1983). Das potentiell Unendliche - Die aristotelische Konzeption und ihre modernen Derivate. Frankfurt am Main: Verlag Peter Lang.
Yrjönsuuri, M. (1996). Obligations as Thought Experiments. In Angelelli, I. & Cerezo, M. (eds.). Studies on the History of Logic. Berlin: Walter de Gruyter, 79-96.
Yrjönsuuri, M. (ed.) (2001). Medieval Formal Logic. Dordrecht: Kluwer.
Yrjönsuuri, M. (ed.) (1993). The Role of Casus in Some Fourteenth Century Treatises on Sophismata and Obligations. In Jacobi, K. (Hrsg.). Argumentationstheorie. Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns. Leiden: Brill, 301-322.
Yrjönsuuri, M. (1998). The Compossibility of Impossibilities and Ars Obligatoria. History and Philosophy of Logic, 19(4), 235-248.
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