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.
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.
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Notes
- 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.
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- 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).
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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
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