Abstract
In this paper I investigate the relation between physics and metaphysics in Plato’s participation theory. I show that the logic shoring up Plato’s metaphysics in paraconsistent, as had been suggested already by Graham Priest. The transformation of the paradoxical One-and-Many of the pre-Socratics into a paraconsistent Great-and-Small bridges the abyss between archaic rationality and the world of classical logic based ultimately on the principle of contradiction.
Indeed, language is an organ of perception, not simply a means of communication.
J. Jaynes, Origin of Consciousness
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References
Abraham W.E. (1972) The nature of Zeno’s argument against plurality in [DK 29B 1]. Phronesis 17: 40–52
Balme D.M. (1962) Aristotles biology. Classical Quartely 12(1): 81–98
Barnsley M. (1988) Fractals everywhere. Academic Press, Boston
Belnap N. (1977) A useful four-valued logic. In: Dunn J.M., Epstein G. (eds) Modern uses of multiple-valued logic.. D. Reidel, Dordrecht-Boston, pp 8–37
Benveniste E. (1966) Problèmes de linguistique générale I & II. Gallimard, Paris
Bollack J., Wismann H. (1972) Héraclite ou la séparation. Ed. de Minuit, Paris
Cantor, G. (1962). Grundlagen einer allgemeinen Mannigfaltigkeitslehre. In Gesammelte Abhandlungen. Hildesheim: Georg Olms Verlag.
Castañneda H.N. (1973) Plato’s theory of relations. In: Bunge M. (eds) Exact Philosophy.. Reidel Publishing Company, Dordrecht
Cherniss, H. (1962) [1945]. The Riddle of the academy. New York: Russell & Russell.
Conche, M. (1998) [1986]. Héraclite. Fragments. Presses Universitaires de France.
Conche, M. (1999). Parménide. Le Poème: Fragments. PUF.
Cordero, N.-L. (1984). Les deux chemins de Parménide. Paris.
Couloubaritsis L. (1997) La Physique d’Aristote. Bruxelles, Ousia
Crombie M. (1963) An examination of Plato’s doctrines Plato on knowledge and reality (VolII). Routledge, London
De Win X. (1980) Plato. Verzameld Werk (3rd Ed.). Boek III De Nederlandsche Boekhandel, Antwerpen
Deleuze G. (1969) Logique du sens. Minuit, Paris
Dixsaut M. (2001) Métamorphoses de la dialectique dans les dialogues de Platon. Vrin, Paris
Falcon A. (2000) Aristotle, Speusippus, and the method of division. Classical Quartely 50(2): 402–414
P. Geach’s influential article (1966). Plato’s Euthyphro: An analysis and commentary. The Monist, 50, 369–382.
Gredt J. (1961) Elementa Philosophiae Aristotelico-Thomisticae. Sumptibus Herder, Barcinone
Günther G. (1962) Cybernetic ontology and transjunctional operations. BCL publication 68. In: Yovits, Jacobi &Goldstein (eds) Photomechanically reproduced from Self-organizing Systems. Spartan Books, Washington D.C., pp 313–392
Jaynes J. (1976) The origin of consciousness in the breakdown of the bicameral mind. Houghton Mifflin Company, Boston
Johnson, W.E. (1921). Logic, Part I, Chapter IX: “the determinable”. Cambridge.
Kripke S. (1963) Semantic analysis of model logic I, normal propositional calculi. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9: 67–96
Krizan M.K. (2006) A defense of Diairesis in Plato’s Gorgias, 463e5-466a3. Philosophical Inquiry XII(1–2): 1–21
Kuratowski K., Mostowski M. (1968) Set theory. N. Holland, Amsterdam
Łukasiewicz J. (1993) Über den Satz des Widerspruchs bei Aristoteles (trans. J.M. Bochenski). Georg Olms Verlag, Hildesheim
Moravcsik J.M. (1973) The anatomy of Plato’s divisions. In: Lee E.N., Mourelatos A.P.D., Rorty R.M. (eds) Exegesis and argument phronesis supplementary Vol. I. Humanities Press, N.Y., pp 324–348
Onians R.B. (1994) [1951]. The origins of European thought. Cambridge, Cambridge University Press
Oosthout H. (2004) Aristoteles. De Getallen en de dingen. De Boeken M en N van de Metafysica. Deel 2: Boek N. Klement, Kampen
Owen G.E.L. (1957) Zeno and the mathematicians. Proceedings of the Aristotelian Society 8: 199–222
Owen G.E.L. (1971) Plato on Non-being. In: Vlastos G. (eds) Plato: A collection of critical essays (Vol. i). Anchor/Doubleday, N.Y.
Pelletier F.J. (1990) Parmenides, Plato, and the semantics of not-being. Univ. of chicago Press, Chicago and London
Pesce D. (1990) Il Platone di Tubinga, E due studi sullo Stoicismo. Brescia, Paideia
Poincaré, H. (1998) [1908]. La Relativité de L’Espace. In Science et Méthode. Paris.
Priest, G. (1987). In contradiction. A study of the transconsistent. Martinus Nijhoff.
Priest G., Routley R. (1989) Paraconsistent logic. Essays on the inconsistent. Philosophia Verlag, München
Priest, G. (2002). Paraconsistent logic. In Handbook of philosophical logic (2nd ed.). Dordrecht etc.: Kluwer.
Riezler K. (1970) Parmenides. Text, Übersetzung, Einführung und Interpretation. Vittorio Klostermann, Frankfurt
Robin, L. (1963). La théorie platonicienne des idées et des nombres d’après Aristote. Étude Historique et Critique. Hildesheim: Georg Olms Verlag [reprint 1908].
Rucker, R. (1995) [1982]. Infinity and the mind. The science and philosophy of the infinite. Princeton: Princeton University Press.
Sayre K.M. (1983) Plato’s late ontology. Princeton University Press, Princeton, New Jersey
Serfati, M. (1998). Quasi-ensembles d’ordre r et approximations de répartitions ordonnées. Mathematiques et Sciences Humaines, 143.
Sheppard, A. D. R. (1997). Phantasia and Inspiration in Neoplatonism. In M. Joyal (Ed.), Studies in Plato and the Platonic tradition (pp. 201–10). Aldershot.
St. Denis P., Grim P. (1997) Fractal images of formal systems. Journal of Philosophical Logic 25: 181–122
Stenzel, J. (1931). Studien zur Entwicklung der Platonischen Dialectik von Sokrates zu Aristoteles. Teubner Leibzig und Berlin.
Stenzel J. (1933) Zahl und Gestalt Bei Platon und Aristoteles 2nd Ed. Leipzig, Teubner
Strang, C. (1971). Plato and the Third Man. In G. Vlastos (Ed.), Plato: A collection of critical essays (pp. 184–200). Doubleday.
Tannery P. (1885) Le concept scientifique du continu. Zenon d’Elee et Georg Cantor. Revue philosophique de la France et de l’étranger 20: 385–416
Tarán L. (1981) A critical edition with a collection of the related texts and commentary. Brill, Leiden
Verelst K. (2006a). De Ontologie van den Paradox. Doctoral Dissertation, Vrije Universiteit Brussel
Verelst, K. (2006b). Zenos Paradoxes. A Cardinal Problem. I. On Zenonian Plurality. In Paradox: Logical, Cognitive and Communicative Aspects. Proceedings of the First International Symposium of Cognition, Logic and Communication, Series: The Baltic International Yearbook of Cognition, Logic and Communication (Vol. 1). University of Latvia Press, Riga, 2006b.
Vickers, S. (1996) [1989]. Topology via logic. Cambridge: Cambridge University Press.
Vlastos G. (1993) Studies in greek philosophy The Presocratics (Vol I). Princeton University Press, Princeton
von Fritz, K. (1978). Schriften zur griechischen Logik. Fromann-Holzboog, Stuttgart-Bad Cannstatt, band 2.
von Fritz, K. (1992). Nous, noein and their derivatives in pre-Socratic philosophy. Reprinted in: A. P. D. Mourelatos, The pre-Socratics. A collection of critical essays. Princeton: Princeton University Press.
Watson, G. (1982). Fantasia in Aristotle, De Anima 3. 3. The Classical Quarterly, New Series, 32, 1, pp. 100–113.
Weyl, H. (1926). Philosophie der Mathematik und Naturwissenschaft. München.
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Verelst, K. On What Ontology is and Not-is. Found Sci 13, 347–370 (2008). https://doi.org/10.1007/s10699-008-9130-2
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DOI: https://doi.org/10.1007/s10699-008-9130-2