Abstract
An investigation of Proclus' logic of the syllogistic and of negations in the Elements of Theology, On the Parmenides, and Platonic Theology. It is shown that Proclus employs interpretations over a linear semantic structure with operators for scalar negations (hypernegation/alpha-intensivum and privative negation). A natural deduction system for scalar negations and the classical syllogistic (as reconstructed by Corcoran and Smiley) is shown to be sound and complete for the non-Boolean linear structures. It is explained how Proclus' syllogistic presupposes converting the tree of genera and species from Plato's diairesis into the Neoplatonic linear hierarchy of Being by use of scalar hyper and privative negations.
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REFERENCES
Ammonius, Commentarie sur le Peri hermeneias d'Aristote, Trans. Guillaume de Moerbeke, Corpus latinum commentariorum in aristotelem graecorum, G. Verbeke (ed.) (Louvain: P. Universitaires de Louvain, 1961).
Ammonius, In aristotelis de interpretatione commentarius, Ed. Adolfus Busse, in Commentaria in aristotelem graeca, Vol. IV (Berlin: Gregorius Reimerus, 1895).
Åqvist, Lennart, Predicate Calculi with Adjectives and Nouns, J. Philos. Logic 10 (1981), 1–26.
Bäck, Allan, Aristotle on Predication (Leiden: Brill, 2000 (forthcoming)).
Bochenski, I. M., A History of Formal Logic, 2nd edn (Notre Dame, Indiana: University of Notre Dame, 1961).
Corcoran, John, Completeness of an Ancient Logic, J. Symbolic Logic 37 (1972), 696–702.
Saffery, H. D. and Westerink, L. G., Introduction, Ed. and Trans., Proclus: Théologie Platonicienne, Vol. I (Paris: Les Belles Lettres, 1968), pp. ix–lxxxix.
Hadot, Paul, L'Harmonie des philosophies de Plotin et d'Aristote selon Porphyre dans le commentaire de Dexippe sur les Catégories, Atti del convegno internazionale sul tema 'Platino e il Neoplatonismo in Oriente e in Occidente', Vol. 198/371, Problemi attuali di scienza e di cultura (Rome: Accademia nazionale dei Lincei, 1974), pp. 31–47.
Henry, D. Paul, Mediaeval Logic and Metaphysics (London: Hutchinson, 1972).
Hicks, R. D. (ed.), Diogenes Laertius, Lives of Eminent Philosophers, Vol. II (Cambridge, MA: Harvard University Press, 1970).
Horn, Laurence R., A Natural History of Negation (Chicago: University of Chicago Press, 1989).
Jespersen, Otto, The Philosophy of Grammar (London: Allen and Unwin, 1924).
Kleene, S. C., On a Notation for Ordinal Numbers, J. Symbolic Logic 3 (1938), 15–155.
Lloyd, A. C., Procession and Division in Proclus, Soul and the Structure of Being in Late Neoplatonism: Syrianus, Proclus, and Simplicius, H. J. Blumenthal and A. C. Lloyd (eds) (Liverpool: Liverpool University Press, 1982), pp. 18–45.
£ukasiewicz, Jan, Aristotle's Syllogistic, 2nd edn (Oxford: Clarendon Press, 1957).
£ukasiewicz, Jan, On 3-Valued Logic, in Jan Lukasiewicz, Selected Works, I.M. Bochenski (ed.) (Amsterdam: North-Holland, 1970).
Marinos, The Extant Works or the Life of Proclus and the Commentary on the Dedomena of Euclid, Trans. Al. N. Oikonomides (Chicago: Ares, 1977).
Martin, John N., Aristotle's Natural Deduction Reconsidered, History and Philosophy of Logic 18 (1997), 1–15.
Martin, John N., Elements of Formal Semantics (Orlando, FL: Academic Press, 1987).
Martin, John N., Proclus the Logician, Studies in Neoplatonism, R. Baine Harris (ed.) (S.U.N.Y., forthcoming).
Martin, John N., Existence, Negation, and Abstraction in the Neoplatonic Hierarchy, History and Philosophy of Logic 16 (1995), 169–196.
Martin, John N., A Syntactic Characterization of Kleene's Strong Connectives, Z. Math. Logik Grundlag. Math. 21 (1975), 181–184.
Plotinus, Enneads, Trans. A. H. Armstrong, Loeb Classical Library, 6 vols (Cambridge, MA: Harvard University Press, 1966–88).
Porphyre, Isagoge: Texte grec, Translatio Boethii, Trans. Alain de Libera, Alain-Philippe Segonds, Sic et Non, Alain de Libera (ed.) (Paris: Librairie Philosophique J. Vrin, 1998).
Porphyry, Isagoge, Ed. and Trans. Paul Vincent Spade, Five Texts on the Mediaeval Problem of Universals (Indianapolis, IN: Hackett Publishing Company, 1994), pp. 1–19.
Proclus, Procli commentarium In platonis parmenidem, Ed. and Trans. Victor Cousin, Procli philosophi platonici opera inedita (Paris: Augustus Durand, 1864), pp. 603–1313.
Proclus, Proclus' Commentary on Plato's Parmenides, Trans. Glenn R. Morrow and John M. Dillon (Princeton, NJ: Princeton University Press, 1987).
Proclus, Proclus: A Commentary on the First Book of Euclid's Elements, Trans. Glenn R. Morrow (Princeton, NJ: Princeton University Press, 1970).
Proclus, Proclus: The Elements of Theology, Trans. E. R. Dodds, 2nd edn (Oxford: Clarendon Press, 1963).
Proclus, Théologie Platonicienne, Trans. H. D. Saffrey and L. G. Westerink, Vols. I–VI (Paris: Les Belles Lettres, 1968–1997).
Siorvanes, Lucan, Proclus: Neo-Platonic Philosophy of Science (New Haven: Yale University Press, 1996).
Smiley, Timothy, What is a Syllogism?, J. Philos. Logic 2 (1973), 136–154.
Strange, Steven K., Porphyry, On Aristotle's Categories (Ithaca, NewYork: Cornell University Press, 1992).
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Martin, J.N. Proclus and the Neoplatonic Syllogistic. Journal of Philosophical Logic 30, 187–240 (2001). https://doi.org/10.1023/A:1017521712962
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DOI: https://doi.org/10.1023/A:1017521712962