Abstract
As is well known, there are two crucial arguments in the realism debate. According to the no-miracles argument, it would be a miracle if our best scientific theories – namely, those which successfully predict novel phenomena – were not true (or approximately true). So, we should take theories that yield novel predictions as being true or, at least, approximately so. Clearly, considerations of this sort are raised to support realism. On the other hand, according to the pessimist meta-induction, many of our best-confirmed theories have turned out to be false. So, how can we guarantee that current theories are true? Considerations such as these, in turn, are meant to provide support for anti-realism.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
My thanks go to José Chiappin, Steven French, James Ladyman, Stathis Psillos, and Bas van Fraassen for stimulating discussions. My greatest debt is to Steven French, with whom I have discussed structural realism for several years, and who has developed, with James Ladyman, the best articulated version of the proposal. I also wish to thank Andrés Bobenrieth, Katherine Brading, Geoffrey Cantor, Anjan Chakravartty, John Christie, Jon Hodge, Don Howard, Michel Janssen, John Norton, Michael Redhead, Simon Saunders, and Adrian Wilson for helpful comments on earlier versions of this work.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Both Worrall (1989) and Zahar (1996, 1997) claim that Poincaré was a structural realist. Chiappin (1989) argues that Duhem’s work, rather than Poincaré’s, is better understood as a structural realist view. According to Demopoulos and Friedman (1985), at least in 1927, Russell was a structural realist (see also van Fraassen 1997). In French and Ladyman’s view, a similar point can be made about Cassirer (French and Ladyman 2003a, b).
- 2.
- 3.
- 4.
This alternative is mentioned in French and Ladyman (2003a), without necessarily endorsing it.
- 5.
French and Ladyman (2003a) also mention this possibility, but again without exactly endorsing it.
- 6.
According to this principle, if two objects have the same properties, they are the same. In symbols: ∀P(Px ↔Py) → x = y. The converse of this principle, which states that if two objects are the same, they share the same properties (in symbols: x = y → ∀P(Px ↔Py)), is sometimes called Leibniz’s law.
- 7.
Important work by Décio Krause, Steven French, and Newton da Costa has provided a much-needed formal framework for developing this alternative, independently of the issue of scientific realism (see Krause (1992, 1996), Krause and French (1995), French and Krause (1995, 2006), and da Costa and Krause (1994, 1997). As the authors acknowledge, however, one still needs to articulate in detail the metaphysical picture associated with this approach.
- 8.
For a detailed critical discussion, and references, see Muller (1997).
- 9.
Dirac’s (1930) work represents a further attempt to lay out a coherent basis for the theory. However, as von Neumann perceived, neither Weyl’s nor Dirac’s approaches offered a mathematical framework congenial for the introduction of probability at the most fundamental level, and this was one of the major motivations for the introduction of Hilbert spaces.
- 10.
As French points out: “the fundamental relationship underpinning [some applications of group theory to quantum mechanics] is that which holds between the irreducible representations of the group and the subspaces of the Hilbert space representing the states of the system. In particular, if the irreducible representations are multi-dimensional then the appropriate Hamiltonian will have multiple eigenvalues which will split under the effect of the perturbation” (French 2000). In this way, “under the action of the permutation group the Hilbert space of the system decomposes into mutually orthogonal subspaces corresponding to the irreducible representations of this group” (ibid.; see also Mackey 1993, pp. 242–247). As French notes, of these representations, “the most well known are the symmetric and antisymmetric, corresponding to Bose–Einstein and Fermi–Dirac statistics respectively, but others, corresponding to so-called ‘parastatistics’ are also possible” (ibid.).
- 11.
How could the world possibly be the way this representation (in terms of Hilbert spaces and group theory) says it is? This is, of course, the typical foundational question (see van Fraassen 1991). The way to answer this question is by providing an interpretation of quantum mechanics.
- 12.
Furthermore, quantum mechanics is certainly more unified with the introduction of group theory, and some ontological questions (e.g. about quantum particles) can be better addressed group-theoretically. However, Hilbert spaces are also needed (for instance, as noted above, to introduce probability into quantum theory). But the ontological status of these spaces is far less clear. Such spaces certainly provide an important way of representing the states of a quantum system; but why should this be an argument for the existence of anything like a multi-dimensional Hilbert space in reality? Why is the usefulness of a representation an argument for its truth? This clearly conflates pragmatic and epistemic reasons – and even the realist should be careful in not conflating them.
- 13.
- 14.
- 15.
- 16.
These are the five theoretical virtues taken by Quine as providing good epistemic reasons for adopting a theory (see Quine 1976, p. 247).
References
Azzouni, J. (1997): “Thick Epistemic Access: Distinguishing the Mathematical from the Empirical”, Journal of Philosophy 94, pp. 472–484.
Azzouni, J. (1998): “On ‘On What There Is’”, Pacific Philosophical Quarterly 79, pp. 1–18.
Azzouni, J. (2004): Deflating Existential Consequence. New York: Oxford University Press.
Birkhoff, G., and von Neumann, J. (1936): “The Logic of Quantum Mechanics”, Annals of Mathematics 37, pp. 823–843. (Reprinted in von Neumann (1962), pp. 105–125.)
Bueno, O. (1997): “Empirical Adequacy: A Partial Structures Approach”, Studies in History and Philosophy of Science 28, pp. 585–610.
Bueno, O. (1999): “What is Structural Empiricism? Scientific Change in an Empiricist Setting”, Erkenntnis 50, pp. 59–85.
Bueno, O. (2005): “Dirac and the Dispensability of Mathematics”, Studies in History and Philosophy of Modern Physics 36, pp. 465–490.
Butterfield, J., and Pagonis, C. (eds.) (1999): From Physics to Philosophy. Cambridge: Cambridge University Press.
Cassirer, E. (1936): Determinism and Indeterminism in Modern Physics. (Translated by O. Theodor Benfey in 1956.) New Haven: Yale University Press.
Chakravartty, A. (1998): “Semirealism”, Studies in History and Philosophy of Science 29, pp. 391–408.
Chiappin, J.R.N. (1989): Duhem’s Theory of Science: An Interplay Between Philosophy and History of Science. Ph.D. dissertation, University of Pittsburgh.
da Costa, N.C.A., and Krause, D. (1994): “Schrödinger Logics”, Studia Logica 53, pp. 533–550.
da Costa, N.C.A., and Krause, D. (1997): “An Intensional Schrödinger Logic”, Notre Dame Journal of Formal Logic 38, pp. 179–194.
Dalla Chiara, M.L., Doets, K., Mundici, D., and van Bentham, J. (eds.) (1997): Logic and Scientific Methods. Dordrecht: Kluwer Academic Publishers.
Demopoulos, W., and Friedman, M. (1985): “Critical Notice: Bertrand Russell’s The Analysis of Matter: Its Historical Context and Contemporary Interest”, Philosophy of Science 52, pp. 621–693.
Dirac, P.A.M. (1930): The Principles of Quantum Mechanics. Oxford: Clarendon Press.
Duhem, P. (1906): The Aim and Structure of Physical Theory. (An English translation, by P.P. Wiener, was published in 1954.) Princeton: Princeton University Press.
Field, H. (1980): Science Without Numbers: A Defense of Nominalism. Princeton, N.J.: Princeton University Press.
French, S. (1989): “Identity and Individuality in Classical and Quantum Physics”, Australasian Journal of Philosophy 67, pp. 432–446.
French, S. (1999): “Models and Mathematics in Physics: The Role of Group Theory”, in Butterfield and Pagonis (eds.) (1999), pp. 187–207.
French, S. (2000): “The Reasonable Effectiveness of Mathematics: Partial Structures and the Application of Group Theory to Physics”, Synthese 125, pp. 103–120.
French, S. (2006): “Structure as a Weapon of the Realist”, Proceedings of the Aristotelian Society 106, pp. 167–185.
French, S., and Krause, D. (1995): “Vague Identity and Quantum Non-Individuality”, Analysis 55, pp. 20–26.
French, S., and Krause, D. (2006): Identity in Physics. Oxford: Clarendon Press.
French, S., and Ladyman, J. (2003a): “Remodelling Structural Realism: Quantum Physics and the Metaphysics of Structure”, Synthese 136, pp. 31–56.
French, S., and Ladyman, J. (2003b): “The Dissolution of Objects: Between Platonism and Phenomenalism”, Synthese 136, pp. 73–77.
Greffe, J.-L., Heinzmann, G., Lorenz, K. (eds.) (1996): Henri Poincaré: Science and Philosophy. Berlin: Akademie Verlag.
Hellman, G. (1989): Mathematics Without Numbers: Towards a Modal-Structural Interpretation. Oxford: Clarendon Press.
Hilbert, D., Nordheim, L., and von Neumann, J. (1927): “Über die Grundlagen der Quantenmechanik”, Mathematische Annalen 98, pp. 1–30. (Reprinted in von Neumann 1961.)
Kant, I. (1787): Critique of Pure Reason. (Translated in 1929 by Normal Kemp Smith.) London: Macmillan Press.
Krause, D. (1992): “On a Quasi-Set Theory”, Notre Dame Journal of Formal Logic 33, pp. 402–411.
Krause, D. (1996): “Axioms for Collections of Indistinguishable Objects”, Logique et Analyse 153–154, pp. 69–93.
Krause, D., and French, S. (1995): “A Formal Framework for Quantum Non-Individuality”, Synthese 102, pp. 195–214.
Ladyman, J. (1998): “What is Structural Realism?”, Studies in History and Philosophy of Science 29, pp. 409–424.
Laudan, L. (1996): Beyond Positivism and Relativism. Boulder: Westview Press.
Lewis, D. (1980): “Veridical Hallucination and Prosthetic Vision”, Australasian Journal of Philosophy 58, pp. 239–249. (Reprinted, with a postscript, in Lewis (1986), pp. 273–290.)
Lewis, D. (1986): Philosophical Papers, Volume II. Oxford: Oxford University Press.
Mackey, G.W. (1993): “The Mathematical Papers”, in Wigner (1993), pp. 241–290.
Muller, F.A. (1997): “The Equivalence Myth of Quantum Mechanics”, Studies in History and Philosophy of Modern Physics 28, pp. 35–61; 219–247.
Poincaré, H. (1905): Science and Hypothesis. New York: Dover.
Psillos, S. (1995): “Is Structural Realism the Best of Both Worlds?”, Dialectica 49, pp. 15–46.
Putnam, H. (1980): “Models and Reality”, Journal of Symbolic Logic 45, pp. 464–482. (Reprinted in Putnam (1983), pp. 1–25.)
Putnam, H. (1981): Reason, Truth and History. Cambridge: Cambridge University Press.
Putnam, H. (1983): Realism and Reason. Cambridge: Cambridge University Press.
Quine, W.V. (1976): The Ways of Paradox and Other Essays. (Revised and enlarged edition.) Cambridge, Mass.: Harvard University Press.
Rédei, M. (1997): “Why John von Neumann did not Like the Hilbert Space Formalism of Quantum Mechanics (and What He Liked Instead)”, Studies in History and Philosophy of Modern Physics 28, pp. 493–510.
Redhead, M. (1995): From Physics to Metaphysics. Cambridge: Cambridge University Press.
Resnik, M. (1997): Mathematics as a Science of Patterns. Oxford: Clarendon Press.
Russell, B. (1927): The Analysis of Matter. London: Routledge.
Schrödinger, E. (1926): “Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen”, in Schrödinger (1927), pp. 45–61.
Schrödinger, E. (1927): Collected Papers on Wave Mechanics. (Translated by J.F. Shearer.) New York: Chelsea.
Shapiro, S. (1991): Foundations Without Foundationalism: A Case for Second-Order Logic. Oxford: Clarendon Press.
Shapiro, S. (1997): Philosophy of Mathematics: Structure and Ontology. New York: Oxford University Press.
van Fraassen, B.C. (1980): The Scientific Image. Oxford: Clarendon Press.
van Fraassen, B.C. (1991): Quantum Mechanics: An Empiricist View. Oxford: Clarendon Press.
van Fraassen, B.C. (1997): “Structure and Perspective: Philosophical Perplexity and Paradox”, in Dalla Chiara et al. (eds.) (1997), pp. 511–530.
von Neumann, J. (1932): Mathematical Foundations of Quantum Mechanics. (English translation, by Robert T. Beyer, first published in 1955.) Princeton: Princeton University Press.
von Neumann, J. (1961): Collected Works, vol. I. Logic, Theory of Sets and Quantum Mechanics. (Edited by A.H. Taub.) Oxford: Pergamon Press.
von Neumann, J. (1962): Collected Works, vol. IV. Continuous Geometry and Other Topics. (Edited by A.H. Taub.) Oxford: Pergamon Press.
von Neumann, J. (1981): “Continuous Geometries with a Transition Probability”, Memoirs of the American Mathematical Society 34, No. 252, pp. 1–210.
Weyl, H. (1927): “Quantenmechanik und Gruppentheorie”, Zeit. für Phys. 46, pp. 1–46.
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.
Wigner, E.P. (1931): Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra. (English translation 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. Wightman.) Berlin: Springer-Verlag.
Worrall, J. (1989): “Structural Realism: The Best of Both Worlds?”, Dialectica 43, pp. 99–124.
Zahar, E. (1996): “Poincaré’s Structural Realism and his Logic of Discovery”, in Greffe et al. (eds.) (1996), pp. 45–68.
Zahar, E. (1997): “Poincaré’s Philosophy of Geometry, or does Geometric Conventionalism Deserve its Name?”, Studies in History and Philosophy of Modern Physics 28, pp. 183–218.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Bueno, O. (2010). Structural Empiricism, Again. In: Bokulich, A., Bokulich, P. (eds) Scientific Structuralism. Boston Studies in the Philosophy and History of Science, vol 281. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9597-8_5
Download citation
DOI: https://doi.org/10.1007/978-90-481-9597-8_5
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9596-1
Online ISBN: 978-90-481-9597-8
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)