Ontology and the Mathematization of the Scientific Enterprise
Abstract
In this basically expository paper we discuss the role of logic and mathematics in researches concerning the ontology of scientific theories, and we consider the particular case of quantum mechanics. We argue that systems of logic in general, and classical logic in particular, may contribute substantially with the ontology of any theory that has this logic in its base. In the case of quantum mechanics, however, from the point of view of philosophical discussions concerning identity and individuality, those contributions may not be welcome for a specific interpretation, and an alternative system of logic perhaps could be used instead of a classical system. In this sense, we argue that the logic and ontology of a scientific theory may be seen as mutually influencing each other. On the one hand, logic contributes to shape the general features of the ontology of a theory; on the other hand, the theory also puts constraints on the possible understanding of ontology and, respectively, on possible systems of logic that may be the underlying logic of the theory.
Keywords: Logic; Classical ontology; Quantum ontology; Quantum mechanics; Identity
References
BUB, J. (2014). Quantum Entanglement and Information. In: The Stanford Encyclopedia of Philosophy (http://plato.stanford.edu/archives/fall2014/entries/
qt-entangle/).
CANTOR, G. (1955). Contribution to the Founding of the Theory of Transfinite Numbers. New York: Dover.
DA COSTA, N. C. A. (2002). Logic and ontology. In: Principia 6 (2): 279-98.
DA COSTA, N. C. A. (1980). Ensaio sobre os Fundamentos da Lógica. São Paulo: Hucitec.
DEWEY, J. (1938). Experience and Education. Toronto: Collier-MacMillan
D’ESPAGNAT, B. (1983). In Search of Reality. New York: Springer.
DOMENECH, G., HOLIK, F. and KRAUSE, D. (2008). Q-spaces and the Foundations of Quantum Mechanics. In: Foundations of Physics 38 (11): 969-994
FRENCH, S. and KRAUSE, D., (2006). Identity in Physics: a Historical, Philosophical and Formal Analysis. Oxford: Oxford Un. Press.
GALILEI, G. (1967). Dialogue Concerning the Two Chief World Systems: Ptolemaic and Copernican. New York: The Modern Library.
GRIFFITHS, D. J. (2005). Introduction to Quantum Mechanics, 2nd.ed. New Jersey: Pearson Prentice Hall.
KETTERLE, W. (2001). Nobel Lecture. The Official Website of the Nobel Prize: http://www.nobelprize.org/nobel prizes/physics/ laureates/2001 /ketterle-lecture. htm1
HUSSERL, E. (1970). The Crisis of European Sciences and Transcendental Phenomenology. Trans. David Carr. Evanston: Northwestern Univ. Press.
KOSSO, P. (1998). Appearance and Reality: An Introduction to the Philosophy of Physics. New York: Oxford Univ. Press.
KRAUSE, D. and ARENHART, J. R. B. (2014). Logical reflections on the semantic approach. [Forthcoming]
KRAUSE, D.; ARENHART, J. R. B.; MORAES, F. T. F. (2011). Axiomatization and Models of Scientific Theories. In: Foundations of Science, 16: 363-382.
LORENZEN, P. (1971). Differential and integral: a constructive introduction to classical analysis. Texas: Univ. Texas Press.
LOUX, M. J. (1998). Metaphysics: a contemporary introduction. London/New York: Routledge.
MAGALHÃES, J. C. and KRAUSE, D. (2001). Suppes predicate for genetics and natural selection. In: Journal of Theoretical Biology, 209 (2): 141-53.
MAITLAND RIGHT, J. D. (1973). All operators on a Hilbert space are bound. In: Bull. Am. Math. Soc. 71(6): 1247-1250.
MITTELSTAEDT, P., (2005). Quantum Physics and Classical Physics - In the Light of Quantum Logic. In: International Journal of Theoretical Physics, 44(7): 771-781.
NAGEL, E., SUPPES, P. and TARSKI, A. (eds.) (1962). Logic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congress. Stanford: Stanford Univ. Press.
PENROSE, R. (2004). The Road to Reality. New York: Vintage Books.
POST, H. (1963). Individuality in Physics. In: The listener, 10 October 1963: 534-537. Reprinted in (1973) Vedanta for East and West, 14-22.
REDHEAD, M. (1987). Incompleteness, Non-Locality and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics. Oxford: Clarendon Press.
REDHEAD, M. and TELLER, P. (1991). Particles, Particle Labels, and Quanta: The Toll of Unacknowledged Metaphysics. In: Foundations of Physics, 21: 43-62.
ROVELLI, C. (2013). Aristotle's physics.
SAUNDERS, S. (2003). Physics and Leibniz’s Principies. In: Brading, K., and Castellani, E. (eds). Symmetries in Physics: Philosophical Reflections, Cambridge: Cambridge Univ. Press, 289-307.
SCHRODINGER, E. (1952). Science and Humanism. Cambridge: Cambridge Univ. Press.
STACHEL, J. (2005). Structural realism and contextual individuality. In: Ben- Menahem, Y. (ed.). Hilary Putnam. Cambridge: Cambridge Univ. Press, 203-219.
SUPPES, P. (2002). Representation and Invariance of Scientific Structures. Stanford: CLSI.
WEYL, H. (1949). Philosophy of Mathematics and Natural Science. Princeton: Princeton Univ. Press.