Abstract
At the origin of our approach lay two encounters between Greek thought and Quantum Mechanics, one of them deliberately conceived by its author, the other being a meeting between new QM-concepts and one of the oldest problems of human thinking about the world. The first encounter has been presented in a short lecture by C. Piron [74, p. 169] in which he attempted to develop a realistic QM-interpretation based on two concepts fundamental to Aristotelian metaphysics, viz. potentiality and actuality. The second one is the doctoral dissertation of D. Aerts [3]. It both by content and title dealt with the problem of the One and the Many, the central theme Plato inherited from fifth century philosopher Parmenides of Elea. In what follows we will attempt to make clear that these encounters are not of a purely coincidential nature. We intend to develop in this paper an analysis and re-evaluation of these old questions and their solutions. Our contention is that this analysis might amount into new perspectives on the interpretation of QM, since the enigmas and paradoxes of early Greek thought, and the solutions presented to them in the “classical period” are, more than we realize, bound to mark our way of looking at and reasoning about the world1. The thought instruments developed by Plato and Aristotle, in order to solve the riddles following out of so called “pre-Socratic” thought, which are epitomized in the, according to both classical thinkers apparent, contradiction between the “world views” of Heraclitus of Ephesus and Parmenides of Elea, are in use up to the present, be it in slightly modified forms2.
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References
Adâmek, J., Herrlich, H. and Strecker, G. E., Abstract and Concrete Categories, J. Wiley & Sons, 1990.
Aerts, D. and Daubechies, I., Helv. Phys. Acta,51, 1978, p. 661.
Aerts, D., The One and the Many, PhD-thesis, Free University of Brussels, 1981; Found. Phys., 12, 1982, p. 1131.
Aerts, D., J., Math. Phys., 27, 1986, p. 202.
Aerts, D., Found. Phys., 24,1994, p. 1227.
Aerts, D., Coecke, B. and Smets, S., “On the Origin of Probabilities in Quantum Mechanics: Creative and Contextual Aspects”, in: Cornelis, G. and Van Bendegem, J. P. (eds. ), Einstein Meets Magritte: Metadebates,Kluwer Academic Publishers, 1998.
Aerts, D., Broekaert, J., Smets, S., “A Quantum Mechanical Description of the Liar Paradox”, submitted for the proceedings of the 20th Int. conf. on Philosophy, Boston, 1998.
Aerts, D., “The Entity in Modern Physics: the Creation-DiscoveryView of Reality”, in: Peruzzi, E. (ed. ), Identity and Individuality of Physical Objects, Springer Verlag, Berlin, 1998.
Amira, H., Coecke, B. and Stubbe, I., “How Quantales Emerge by Introducing Induced State Transition in Operational Theories”, Heiv. Phys. Acta,1998, to appear.
Arendt, H., The life of the mind. One/Thinking, one-volume edition, Harcourt Brace Jovanovich Publishers, London, 1978.
Aspect, A. et al., Phys. Rev. Lett., 49, 1982, p. 1804.
Barr, M. and Wells, C., Toposes, Triples and Theories, Springer, 1995.
Bell, J., Physics, 1 , 1965, p. 195.
Beltrametti, E. G. and van Fraassen, B. C. (eds. ), Current Issues in Quantum Logic, Plenum, 1981.
Birkhoff, G. and von Neumann, J., Ann. Math., 37, 1936, p. 823.
Bloch, O. R., La philosophie de Gassendi. Nominalisme, Matérialisme et Métaphysique, Martinus Nijhoff, La Haye, 1971.
Bohm, D., Phys. Rev., 85 , 1952, p. 166.
Campbell, J., The Masks of God, volume I, Primitive Mythology, Arkana, Penguin Books, N. Y., 1991.
Carnap, R., “Empiricism, Semantics, and Ontology”, in: Boyd, R., Gasper, P. and Trout, J. D. (eds. ), The Philosophy of Science, MIT press, Massachusetts, 1992.
Castaneda, H. N., “Plato’s theory of relations”, in: Bunge, M. (ed. ), Exact Philosophy, D. Reidel Publishing Comp., Dordrecht, 1973.
Coecke, B., Hidden Measurement Systems,Doctoral Dissertation, Free University of Brussels, 1995; Hell). Phys. Acta,70, 1997, p. 442; Hell). Phys. Acta,70, 1997, p. 462.
Coecke, B., “A Representation for Compound Quantum Systems as Individual Entities: Hard Acts of Creation and Hidden Correlations” and “A Representation for Spin-S Quantum Entities as 2S Individual Spin-1/2 Quantum Entities”, Found. Phys., to appear, 1998.
Coecke, B. and Valckenborgh, F., Int. J. Theor. Phys., 37, 1998, p. 311.
Coecke, B. and Moore, D. J., “Decompositions of Probability Measures on Complete Ortholattices in Join Preserving Maps”, Preprint, FUND-DWIS, Free University of Brussels, 1998.
Coecke, B. and Stubbe, I., “On a Creation-Based Extension of Operational Theories”, Internal Report VUB. FUND. 1998. 3, 1998.
Coecke, B. and Stubbe, I., “Quantum Mechanics as a Theory of Induction”, Preprint, FUND-DWIS, Free University of Brussels, 1998.
Coecke, B., “Compoundness as Diagrams in Quasi-Categories”, notes of a lecture given at IQSA-Atlanta, August 1997; Coecke, B. and Stubbe, I., “On a Duality of Quantales emerging from an Operational Resolution”, Int. J. Theor. Phys., to appear, 1998; Coecke, B. and Stubbe, I., “The Category of Mutual Inductions for Entities Described by Pseudo States”, In preparation, 1998.
Cohen, B. I., “Newton’s third law and universal gravity”, in: Scheurer, P. B. and Debrock, G. (eds. ), Newton’s scientific and philosophical legacy, Kluwer Academic Publishers, Dordrecht, 1988.
Conché, M., Epicure. Lettres et maximes, texte établi par Marcel Conché, PUF, Paris (1987).
De Cusa, N., “De Docta Ignorantia”, in: Hoffmann, E. and Klibansky, R. (eds. ), Lipsiae, In Aedibus Felicis Meiner, 1932.
Daniel, W., “Bohr, Einstein and Realism”, Dialectica, 43, 1989.
Dellian, E., “Inertia, the innate force of matter”, in: Scheurer, P. B. and Debrock, G. (eds. ), Newton’s scientific and philosophical legacy, Kluwer academic publishers, Dordrecht, 1988.
Diels, H. and Kranz, W., Fragmente der Vorsokratiker, erster Band, Weidmann, Dublin, Zürich, 1971.
Dijksterhuis, E. J., De mechanisering van het wereldbeeld,7th ed., Meulenhof, Amsterdam, 1950-1996.
Dobbs, B. J. T., “Newton’s alchemy and his `active principle’ of gravitation”, in: Scheurer, P. B. and Debrock, G. (eds. ), Newton’s scientific and philosophical legacy, Kluwer academic publishers, Dordrecht, 1988.
Einstein, A., Podolski, E. and Rosen, N., Phys. Rev., 47, 1935, p. 777.
Einstein, A., “On the electrodynamics of moving bodies”, in: The principle of relativity. A collection of original papers on the special and general theory of relativity. Notes by A. Sommerfeld., Dover publicatons, New York, 1952.
Einstein, A., “Can quantum-mechanical description of physical reality be considered complete?”, in: Wheeler, J. A., and Wojciech, H. Z. (eds. ), Quantum Theory and Measurement, Princeton University Press, Princeton, 1983.
Eilenberg, S., and Mac Lane, S.,Trans. Am. Math. Soc., 58, 1945, p. 231.
Epstein, R. L., The semantic foundations of Logic, Vol. I, Kluwer academic publishers, Dordrecht, 1990.
d’Espagnat, B., Conceptual Foundations of Quantum Mechanics, W. A. Benjamin, 1976.
Foulis, D. J., and Randall, C. H., “Manuals, Morphisms and Quantum Mechanics”, in: Marlow, H. (ed. ), Mathematical Foundations of Quantum Theory, Academic Press, 1978.
Foulis, D. J., Piron, C. and Randall, C. H.,Found. Phys., 13, 1983, p. 813.
Foulis, D. J., and Randall, C. H.,Found. phys., 13, 1983, p. 843.
Fowler, H. N., Plato in twelve volumes, Loeb Classical Library, Heinemann, London, 1967.
Von Fritz, K., “Nous, noein, and their derivatives in pre-Socratic philosophy”, in: Mourelatos, A. P. D. (ed. ), The Pre-Socratics, a collection of critical essays, Princeton University Press, Princeton, 1974 - 1993.
Gisin, N., and Piron, C.,Lett. Math. Phys., 5, 1981, p. 379.
Harré, R., “The redundancy of Spacetime: Relativity from Cusa to Einstein”, in: Aerts, D. (ed. ), Einstein Meets Magritte: White Book, Kluwer Academic Publishers, 1998.
Hersh, R.,in: Tymoczko, T.(ed. ), New Directions in the Philosophy of Mathematics,Birkhäuser, 1986, p. 9.
Jammer, M.,Concepts of Space. The history of theories of space in physics,3rd. ed., Dover Publications, N. Y., 1954-1993.
Jauch, J. M., and Piron, C.,Helv. Phys. Acta,36, 1963, p. 827.
Jauch, J. M., Foundations of Quantum Mechanics, Addison-Wesley, 1968.
Jauch, J. M., and Piron, C., “On the structure of quantal proposition systems”, Helv. Phys. Acta, 42, 1969.
Jaynes, J., The origin of consciousness in the breakdown of the bicameral mind, Houghton Mifflin Company, Boston, 1976.
Kaufman, L., “Virtual Logic”, talk delivered at the Einstein Meets Magritte Conference, June 1995.
Kirk, G. S., Heraclitus. The Cosmic Fragments, Cambridge University Press, Cambridge, 1975.
Kirk, G. S., Raven, J. E., and Schofield, M.,The Presocratic Philosophers. A critical history with a selection of texts,Cambridge University Press, Cambridge, 1983.
Lanczos, C., The variational principles of mechanics, fourth ed., Dover publications, New York, 1970.
Luck, G., Arcana Mundi. Magic and the Occult in the Greek and Roman Worlds. A collection of Ancient Texts,The Johns Hopkins University Press, Baltimore and London, 1985.
Ludwig, G., “An Axiomatic Basis of Quantum Mechanics”, in: Neumann, H. (ed. ), Interpretations and Foundations of Quantum theory,B. I. -Wissenschaftsverlag, 1981.
Ludwig, G., and Neumann, H., “Connections between Different Approaches to the Foundations of Quantum Mechanics”, in: Neumann, H. (ed. ), Interpretations and Foundations of Quantum theory, B. I. -Wissenschaftsverlag, 1981.
Mac Lane, S., Categories for the working Mathematician, Springer, 1971.
McGuire, J. E., and Rattansi, P. M., “Newton and the `Pipes of Pan”’, Notes and records of the Royal Society of London, 21, 1966.
McLarty, C., Elementary Categories, Elementary Toposes, Oxford Sci. Publ., 1995.
Mittelstaedt, P., “Classification of Different Areas of Work Afferent to Quantum Logic”, in: Beltrametti, E. G. and van Fraassen, B. C. (eds. ), Current Issues in Quantum Logic, Plenum, 1981.
Moore, D. J.,Helv. Phys. Acta, 66 , 1993, p. 471.
Moore,D. J.,Helv. Phys. Acta, 68 , 1995, p. 658.
Moore, D. J., Int. J. Theor. Phys., 36, 1997, p. 2211.
Moore, D. J., “On State Spaces and Property Lattices”, British J. Phil. Sc., to appear, 1998.
Mourelatos, A. P. D., The Pre-Socratics, a collection of critical essays,Princeton University Press, Princeton, 1974-1993.
Newton, I., Isaaci Newtoni, Opera quae extant omnia, Commentariis illustrabat Samuel Horsley, Londini: exc. Joannes Nichols, 1889.
Owen, G. E. L., “Plato on Non-Being”, in: Vlastos, G. (ed. ), Plato: a collection of Critical Essays, vol I, Doubleday, 1971.
Piron, C., Foundations of Quantum Physics, W. A. Benjamin, 1976.
Piron, C., “Le réalisme en physique quantique: une approche selon Aristote”, in: The concept of physical reality. Proceedings of a conference organized by the Interdisciplinary Research Group, Univ. of Athens, 1983.
Piron, C., Erkenntnis,16, 1981, p. 398.
Piron, C., “Quantum Mechanics Fifty Years After”, in: Lahti, P., and Mittelstaedt, P. (eds. ), Symposium on the Foundations of Modern physics, World scientific, 1985.
Piron, C., Mécanique Quantique Bases et Applications, Presses Polytechniques et Universitaires Romandes, Lausanne, 1990.
Piron, C., “Un nouveau regard sur le monde physique”, preprint, Université de Genève, 1996.
Piron, C., “Quantum Mechanics and Relativity: two failed revolutions”, in: Aerts, D., (ed. ), Einstein Meets Magritte: White Book, Kluwer Academic Publishers, 1998.
Quinton, A., The Nature of Things, Routledge & Kegan Paul, London and Boston, 1973.
Rauch, H.,Hely. Phys. Acta,61, 1988, p. 589.
Redondi, P., Galilei, eretico, Einaudi, Turino, 1983.
Rescher, N., and Brandom, R., The logic of inconsistency. A study in Non-Standard Possible-World Semantics and Ontology, Basil Blackwell, Oxford, 1980.
Riezler, K., Parmenides, Text, Übersetzung, Einführung und Interpretation, Vittorio Klostermann, Frankfurt a. M., 1970.
Rosen, R., “The Roles of Necessity in Biology”, in: Newton to Aristotle. Toward a Theory of Models for Living Systems, Birkhäuser, Boston, Basel and Berlin, 1989.
Schrödinger, E., Space-Time Structure,Cambridge University Press, Cambridge, 1950-1985.
Schrödinger, E., Nature and the Greeks and Science and Humanism, Canto,Cambridge University Press, 1954-1996.
Spencer Brown, G., Laws of Form, George Allen and Unwin, ltd., London, 1969.
Toulmin, S., Cosmopolis, the hidden agenda of modernity, University of Chicago Press, Chicago, 1984.
Tredennick, H., Aristotle. Metaphysics, books I-IX, Loeb XVII, Loeb Classical Library, Harvard University Press, Cambridge, Massachusetts, 1996.
van Fraassen, B. C., Quantum Mechanics, Clarendon Press, Oxford, 1991.
Vlastos, G., “Reasons and causes in the Phaedo”, in: Vlastos, G. (ed. ), Plato: a collection of Critical Essays, vol I,Doubleday, 1971.
Vlastos, G.,Studies in Greek Philosophy, volume I: The Presocratics,Princeton University Press, Princeton, 1993.
von Neumann, J.,The Mathematical Foundations of Quantum Mechanics,Princeton University Press, 1955.
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Verelst, K., Coecke, B. (1999). Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach. In: Cornelis, G.C., Smets, S., Van Bendegem, J.P. (eds) Metadebates on Science. EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2245-2_12
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