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PRIVATIVE NEGATION IN THE PORT ROYAL LOGIC

Published online by Cambridge University Press:  19 September 2016

JOHN N. MARTIN
JOHN N. MARTIN*
Affiliation:
Emeritus Professor of Philosophy, University of Cincinnati
*
*EMERITUS PROFESSOR OF PHILOSOPHY DEPARTMENT OF PHILOSOPHY (210374) UNIVERSITY OF CINCINNATI CINCINNATI, OH, 45208, USA E-mail: [email protected]
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Abstract

In this paper I argue that negation in The Port Royal Logic is not a failed or incoherent approximation of Boolean complementation as maintained by Sylvain Auroux and Marc Dominicy, but is rather a version of privative negation from medieval logic, and that as such it has a perfectly coherent semantics. The discussion reviews the critiques of Auroux and Dominicy as well as the semantics of privative negation as found in Aristotle, Proclus, Ockham, Buridan, Descartes, and Arnauld.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 4 , December 2016 , pp. 664 - 685
Copyright
Copyright © Association for Symbolic Logic 2016 

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References

BIBLIOGRAPHY

Adam, C. & Tannery, P. (editors) (1897–1909). Œuvres de Descartes. Paris: Vrin.Google Scholar
Arnauld, A. (1776). Nouvelle Défense du Nouveau Testament imprimée à Mons contre le Livre de M. Mallet. Œuvres de Messire Antoine Arnauld Docteur de la Maison et Société de Sorbonne. Paris: Sigismond d’Arnay.Google Scholar
Arnauld, A. (1813). Œuvres philosophique d’Antoine Arnauld. Paris: Adolphe Delahays.Google Scholar
Arnauld, A. (1990 [1683]). On True and False Ideas. Manchester: Manchester University Press.Google Scholar
Arnauld, A. & Nicole, P. (1996). Logic or the Art of Thinking. Cambridge: Cambridge University Press. Buroker, J. V. (translator).CrossRefGoogle Scholar
Auroux, S. (1978). Grammaire et logique: une théorie archaïque des relations, Dialogue, 17, 1–19.CrossRefGoogle Scholar
Auroux, S. (1979). La sémiotique des encyclopédistes. Essai d’épistémologie historique des sciences du langage. Paris: Payot.Google Scholar
Auroux, S. (1982). L’Illuminismo Francese e la Tradizione Logica di Port-Royal. Bologna: CLUEB.Google Scholar
Auroux, S. (1992). Port-Royal et l’arbre de Porphyre. Archives et documents de la Sociéte d’historie et d’épistémologie des sciences du langage, 6, 109–122.Google Scholar
Auroux, S. (1993). La Logique des Idées. Montréal, Paris: Bellarmin, Vrin.Google Scholar
Buridan, J. (2001). Summulae de Dialectica. New Haven: Yale University Press.Google Scholar
Conimbricenses. (1617). Commentarii collegii conimbricensis societatis iesu in tres libros de anima, aristotelis stagiritae. Colonia [Cologne], Lazarus Zetznerus.Google Scholar
Cronin, T. J. (1966). Objective Being in Descartes and Suarez. Rome: Gregorian University Press.Google Scholar
Dominicy, M. (1984). La Naissance de la Grammaire moderne. Bruxelles: Pierre Mardaga.Google Scholar
Enriques, F. (1926). L’évolution de la Logique. Paris: Chiron.Google Scholar
Eustachio-De-S.-Paulo (1648). Summa Philosophiae quadripartita, de rebus dialecticis, ethicis, physicis et metaphysicis. Cantabrigia [Cambridge]: Rogerus Danielis.Google Scholar
da Fonseca, P. (1964 [1575]). Instituciões Dialécticas [Institutionum dialecticarum libri octo] . Coimbra: Universidade de Coimbra.Google Scholar
Horn, L. R. (1989). A Natural History of Negation. Chicago: University of Chicago Press.Google Scholar
Martin, J. N. (1987). Elements of Formal Semantics. Orlando: Academic Press.Google Scholar
Martin, J. N. (1995). Existence, negation, and abstraction in the neoplatonic hierarchy. History and Philosophy of Logic, 16, 169–196.CrossRefGoogle Scholar
Martin, J. N. (2001). Proclus and the neoplatonic syllogistic. Journal of Philosophical Logic, 30, 187–240.CrossRefGoogle Scholar
Martin, J. N. (2002). Proclus the logician. Proceedings of the Society for Medieval Logic and Metaphysics, 2, 45–57.Google Scholar
Martin, J. N. (2003). All brutes are subhuman: Aristotle and Ockham on privative negation. Synthese, 134, 429–461.Google Scholar
Martin, J. N. (2011). Existential import in cartesian semantics. History and Philosophy of Logic, 32(2), 1–29.CrossRefGoogle Scholar
Martin, J. N. (2012). Existential commitment and the cartesian semantics of the Port Royal Logic . In Beziau, J-Y., editor. New Perspectives on the Square of Opposition. Bern: Peter Lang.Google Scholar
Pariente, J-C. (1995). Les Termes singuliers dans la Logique de Port-Royal. In Pariente, J-C., editor. Antoine Arnauld (1612–1694): Philosophe, Écrivain, Théologien. Paris: Bibliothèque Mazarine.Google Scholar
Proclus. (1993). The Commentaries of Proclus on the Timaeus of Plato. Reproduction of 1820 edition, Taylor, Thomas (translator). London: Thomas Taylor. Kila: Kessinger.Google Scholar
Proclus. (1864). Procli commentarium in Platonis Parmenidem. Procli Philosophi Platonici Operas Inedita. Paris: Augustus Durand.Google Scholar
Proclus. (1968–1997). Théologie Platonicienne. Paris: Les Belles Lettres. H. D. Saffrey and L. G. Westerink (translator).Google Scholar
d’Abra de Raconis, C. F. (1651). Tertia Pars Philosophiae seu Physicae, Quarta Pars Philosophiae seu Metaphysicae. Totius Philosophiae, hoc est Logicae, Moralis, Physicae et Metaphysicae, brevis et accurata, facilique et clara methodo disposita tractatio. Lugdunum [Lyon]: Irenaeus Barlet.Google Scholar
Toletus, F. (1596). Commentaria una cum quaestionibus in universam Aristotelis logicam. Cologne: Agrippina.Google Scholar
Wahl, R. (2008). Port Royal: The stirrings of modernity. In Gabbay, D. M. and Woods, J., editors. Handbook of the History of Logic: Mediaeval and Renaissance Logic. Amsterdam: Elsevier - North Holland, 667–699.Google Scholar
William_of_Ockham. (1974 [ca. 1323]). Ockham’s Theory of Terms: Part I of the Summa Logicae. Notre Dame: University of Notre Dame.Google Scholar
William_of_Ockham. (1980 [ca. 1323]). Ockham’s Theory of Propositions (Part II of Summa Logicae). Notre Dame: Notre Dame University Press.Google Scholar