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BUENO, Otávio; FRENCH, Steven. Infestation or pest control: the introduction of group theory into quantum mechanics. Manuscrito: Revista Internacional de Filosofia, Campinas, SP, v. 22, n. 2, p. 37–68, 1999. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8666147. Acesso em: 8 out. 2024.

Resumo

The applicability of mathematics to science is a fundamental issue in both the philosophy of mathematics and the philosophy of science. In this paper we offer a structuralist approach to this issue which acknowledges the often complex moves which have to be made to bring mathematical and physical structures into na appropriate relationship. Our overall representational framework is that of the partial structure approach of Newton da Costa and we presente as a case study the application of group theory to atomic and nuclear physics. We conclude with some remarks on the implications of our work for realism in both the philosophy of mathematics and the philosophy of science.

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Referências

Butterfield, J. & Pagonis, C. (eds.) (1999). From Physics to Philosophy (Cambridge, Cambridge University Press).

Bueno, O. (1997). Empirical Adequacy: A Partial Structures Approach, Studies in History and Philosophy of Science 28, pp. 585-610.

Bueno, O. (1990a). Empirism, Conservativenes and Quase-Truth. Philosophy of Scince66(Proceeedings), pp. S474-S485.

Bueno, O. (1999b). What is Structural Empiriscism? Scientific Change in an Empiricist Setting, Erkenntnis 50, pp. 59-85.

Bueno, O. (1999c). Empiricism, Mathematical Change and Science Change, forthcoming in Studies in History and Philosophy of Science, 1999.

Bueno, O. (s.d). What is (Really) Wrong with Structural Realism?, unpublished manuscript (California State University and University of Leeds).

Bueno, O. & French, S. (s.d). From Weyl to von Neumann: An Analysis of the Application of Mathematics to Quantum Mechanics, unpublished manuscript (California State University of Leeds).

Bueno, O., Freench, S. & Ladyman, J. (s.d). Partial Structures and the Relationship between the Mathematical and the Physical, unpublished manuscript (California State University, University of Leeds, and Bristol University).

Castellani. E. (1998). Galilean Particles: An Example of Constituion of Objects, in Castellani, E. (ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics, (Princeton University Press), pp. 181-194.

Coleman, A.J. (1997). “Groups and Physics: Dogmatic Opinions of a Senior Citizen”, Notices of the American Mathematical Society 44, pp. 8-17.

Costa, N.C.A. da (1986). Pragmatic Probability , Erkenntnis 25, pp 141-162.

Costa, N.C.A. da & French, S. (1989). Pragmatic Truth and the Logic of Indution, British Journal for the Philosophy of Science 40, pp. 333-356.

Costa, N.C.A. da & French, S. (1990). The Model-Theoretic Approach in the Philosophy of Science. Philosophy of Science 57, pp. 248-265.

Costa, N.C.A. da & French, S. (1993a). Towards na Acceptable Theory of Acceptance: Partial Structure and the General Correspondence Principle, in French & Kamminga (eds.) (1993), pp. 137-158.

Costa, N.C.A. da & French, S. (s.d). Partial Truth and Partial Structures: A Unitary Account of Models in Scientific and Natural Reasoning, unpublished book (University of São Paulo and University Leeds).

Dalla Chiara, M.L., Doets, K., Mundici, D. & van Benthan, J. (eds.) (1997). Structures and Norms in Science (Dordrecht, Kluwer Academic Publishers).

Doncel, M.A. et al. (eds.) (1987). Symmetries in Physics (1600-1980) Proceedings of the 1st International Meeting of the History of Scientific Ideas (Bellaterra).

Eckart, C. (1930). The aplication of Group Theory to the Quantum Dynamics of Monoatomic Systems, Reviews of Modern Physics 2, pp. 305-360.

French, S. (1989). Identity and individuality in classical and quantum Physics, Australasian Journal of philosophy 67, pp. 432-446.

French, S. (1997). Partiality, Pursuit and Pratice, in Dalla Chiara et al. (eds.) (1997), pp. 35-52.

French, S. (1999). Models and Mathematics in Physics: The Role of Group Theory, in Butterfield and Pagonis (eds.) (1999).

French, S. (s.d). The Reasonable Effectiveness of Mathematics: Partial Structure and the Application of Group Theory to Physics, in Synthese.

French, S. & Kamminga, H. (eds.) (1993). Correspondence, Invariance and Heuristics: Essays in Honour of Heinz Post (Dordrecht, Reidel).

French, S. & Ladyman, J. (1999). Reinflating the Semantic Approach, International Studies in the Philosophy of Science 13, pp. 103-121.

French, S. & Ladyman, J. (s.d). Remodeling Structural realism, unpublished manuscript.

French, S. & Redhead, M. (1988). Quantum Physics and the Identity of Indiscernibles, British Journal for the Philosophy of Science 39 pp. 233-246.

Gavroglu, K. (1995). Fritz London: A Scientfic Biography (Cambridge University Press).

Glymour, C. (1980). Theory and evidence (Princeton, N. J., Princeton University Press).

Grattan-Guinness, I. (1992). Structure-similarity as a Cornestone of the Philosophy of Mathematics, in Echeverria, J. Ibarra, A. & Mormann, T. (eds.), The Space of Mathematics (de Gruyter): 91-111.

Hellman, G. (1989). Mathematics without Numbers: Towards a Modal-Structural Interpretation (Oxford, Clarendon Press).

Hesse, M. (1963). Models and Analogies in Science (Oxford, Oxford University Press).

Heitler, W. (1963). Man and Science (Edinburg, Oliver and Boyd).

Judd, B.R. (1993). Applied Group Theory (1926-1935), in A.S. Wightman (ed.), The Collected Works of Eugene Paul Wigner, Part A, The Scientific Papers, Vol 1, pp. 17-33 (Springer Verlag).

Kattaus, S. (s.d). Review of M. Stiener, the Applicability of Mathematics as a Philosophy Problem, in Metascience.

Ladyman, J. (1998). What is Structural Realism?, Studies in history and Philosophy of Science 29, pp. 409-424.

Mackey, G.W. (1993). The Mathematical Papers, in Wingner (1993), pp. 241-290.

Mehra, J. (1971). The Solvay Conferences in Physics (Dordrecht, Reidel).

Mikenberg, I., Costa, N.C.A. da & Chuaqui, R. (1986). Pragmatic Turth and Aproximation to Turth, Journal of Symbolic Logic 51, pp. 201-221.

Miller, A. (1987). Symmetry and Imagery in the Physics of Bohr, Einstein and Heisenberg, in Doncel et. Al. (1987), pp. 299-325.

Peressini, A. (1997) Troubles with Indispensability: Applying Pure Mathematics in Physical Theory, Philosophia Mathematica 3, pp. 210-227.

Redhead, M. (1975). Symmetry in Intertheory Relations, Synthese 32, pp. 77-112.

Shapiro, S. (1997). Philosophy of Mathematics: Struture and Ontology (New York, Oxford University Press).

Steiner, M. (1998). The Applicability of Mathematics as a Philosophical problem (Cambridge, Mass., Havard University Press.)

Van Fraassen, B.C. (1991). Quantum Mechanics: An Empiricist View (Oxford, Clarendon Press).

Van Fraassen, B.C. (s.d a). Structure, Reality, and realism: Structuralism versus Realism about Science, paper delivered at the University of Leiden in June 99.

Van Fraassen, B.C. (s.d b). The Theory of Tragedy ando f Science: Does Nature have Narrative Structure?, in Proceedings of the Conference Aristotle and Modern Science (Thessaloniki, Sept 1997), Peter Lang Publishers.

Weyl, H. (1927). Quantenmechanik und Gruppentheorie, Zeit. Für Phys. 46 pp. 1-46. (This pape ris reprinted in Weyl’s Collected Works, Vol. III, (1968), pp. 90-135).

Weyl, H. (1931). The theory of Groups and Quantum Mechanics. (Translated from the second, revised German edition by H.p. Robertson. The first edition was published in 1928.) (New York, Dover).

Weyl, H. (1968). Gesammelte Abhandlungen Vol. III (Berlin, Springer-Verlag).

Wigner, E.P. (1931). Group Theory and Its application to the Quatum Mechanics of Atomic Spectra. (The English translation was published in 1959.) (New York, Academic Press).

Wigner, E.P. (1993). The Collected Works of Eugene Paul Wigner. The Scientific Papers, volume 1. (Edited by Arthur S. Wghtman.) (Berlin Springer-Verlag).

Wilson, M. (s.d). The Unreasonable Uncooperativeness of Mathematics in Natural Science, in The Monista.

Worrall, J. (1989). Structural Realism: The Best of Both Worlds?, Dialectica 43, 99-124.

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Copyright (c) 1999 Manuscrito: Revista Internacional de Filosofia

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