Newton da Costa on Non-Reflexive Logics and Identity
DOI:
https://doi.org/10.48160/18532330me9.229Keywords:
non-reflexive logics, identity, individuality, quantum mechanicsAbstract
Newton da Costa pioneered first-order systems of so-called non-reflexive logics (NRL). According to those systems of logic, the reflexive law of identity is restricted; it does not apply to every kind of object the system deals with. NRL were later developed into higher-order systems and quasi-set theory by Décio Krause. The main motivation to develop such systems came from non-relativistic quantum mechanics. Intuitively, it is argued that quantum entities somehow “lost their identities”, they are non-individuals. Non-reflexive logics are the systems employed to formally underpin such a metaphysical interpretation of the theory. In this paper we re-access da Costa’s contributions in the light of recent developments on both the metaphysics of quantum mechanics and on the latest developments of the formalism. The result is that even though da Costa had not envisaged any specific metaphysical goals with the first advancement of his system, his discussion may provide for clear insights into the actual debate.
References
Arenhart, J. R. B. (2013), “Weak Discernibility in Quantum Mechanics: Does it Save PII?”, Axiomathes 23: 461-483.
Arenhart, J. R. B. (2017), “The Received View on Quantum Non-Individuality: Formal and Metaphysical Analysis”, Synthese194: 1393-1347.
Bigaj, T. (2015), “Dissecting Weak Discernibility of Quanta”, Studies in History and Philosophy of Modern Physics50: 43-53.
da Costa, N. C. A. (1997), Logiques Classiques et Non Classiques. Essai sur les fondements de la logique, Paris: Masson.
da Costa, N. C. A. (2002), “Logic and Ontology”, Principia6(2): 279-298.
French, S. (2014), The Structure of the World. Metaphysics and Representation, Oxford: Oxford University Press.
French, S. (2015), “Identity and Individuality in Quantum Theory”, in Zalta, E. N. (ed.), The Stanford Encyclopedia of Philosophy (Fall 2015 Edition). URL = http://plato.stanford.edu/archives/fall2015/entries/qt-idind/.
French, S. and D. Krause (2006), Identity in Physics. A Historical, Philosophical and Formal Analysis, Oxford: Oxford University Press.
Lowe, E. J. (1997), “Objects and Criteria of Identity”, in Hale, B. and C. Wright (eds.), A Companion to the Philosophy of Language, Oxford: Blackwell, pp. 613-633.
Muller, F. A. (2011), “Withering Away, Weakly”, Synthese 180(2): 223-233.
Muller, F. A. and S. Saunders (2008), “Discerning Fermions”, British Journal for the Philosophy of Science 59: 499-548.
Muller, F.A. and M.P. Seevinck (2009), “Discerning Elementary Particles”, Philosophy of Science76(2): 179-200.
Saunders, S. (2003), “Physics and Leibniz’s Principles”, in Brading, K. and E. Castellani (eds.), Symmetries in Physics: Philosophical Reflections, Cambridge: Cambridge University Press, pp. 289-307.
Saunders, S. (2006), “Are Quantum Particles Objects?”, Analysis 66: 52-63.
Schrödinger, E. (1996), Nature and the Greeks and Science and Humanism, with a Foreword by Roger Penrose, Cambridge: Cambridge University Press.
Schrödinger, E. (1998), “What Is an Elementary Particle?”, in Castellani, E.(ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics, Princeton: Princeton University Press, pp.197-210.
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