Abstract
A theory’s fertility is one of the standard theoretical virtues. But how is it to be construed? In current philosophical discourse, particularly in the realism debate, theoretical fertility is usually understood in terms of novel success: a theory is fertile if it manages to make successful novel predictions. Another, more permissible, notion of fertility can be found in the work of Ernan McMullin. This kind of fertility, McMullin claims, gives us just as strong (or even stronger) grounds for realism. My paper critically assesses McMullin’s notion of fertility and its realist rationale. It concludes that McMullin’s preferred example, namely the fertile development of the Bohr-Sommerfeld model of the atom, does not support McMullin’s argument for realism. Although the implications for the realism debate are as of yet unclear, the case study offers some important methodological lessons.
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Notes
The other four virtues Kuhn identified are empirical accuracy, simplicity, unifying power or scope, external and internal consistency.
There are of course other novel success criteria than the ones I mention above. However, temporal and use-novel success are the standard criteria used in the realism debate (e.g. Psillos 1999). Although Leplin’s A Novel Defense of Realism gets often cited, the novel success criterion developed therein has received severe and adequate criticism by Ladyman (1999). For a more detailed discussion of accounts of novel success see my (Schindler 2013).
McMullin uses the idea of U-fertility mainly to describe and criticize Lakatos’s account. See Section 3.3 for a comparison of the two accounts.
Denoting such sociological aspects of science as “Kuhnian” seems slightly unfair. Contrary to common misinterpretations, Kuhn thought there was much more (cognitive) involved in the pursuit of normal science than just sociological opportunity. There is however some textual evidence that Kuhn, at least in his later work, thought of fertility also in sociological terms (Kuhn 1977, 322 f. 6).
Nolan suggests that the meta-hypotheses may be construed as some kind of “general theory” instead (278 f.). This difference is minor and shall not concern us here.
Another criticism of Nolan’s proposal, to be found in Segall (2008), is that “any detailed examination of the history of a long-standing successful theory is likely to show that it is the specifics of the current theoretical and experimental situation that leads to the next development” (244).
McMullin, on several occasions, attributes a theory’s fertility to the model associated with a theory. McMullin has a peculiar view of models. For him, “[t]he theory is derived from the model […] not the reverse […] the theory is about [a particular] model and about nothing else” (McMullin 1968, 389). At least the latter part of this view seems to come close to Cartwright (1983)’s ‘prepared descriptions’ of real systems, which a theory is about, rather than about the real system itself. At the same time, McMullin (ibid.) is quite adamant in his rejection of some of Cartwright’s (antirealist) conclusions. The differences between models and theories shall not concern us here.
The similarities of McMullin’s and Lakatos’s account are indeed striking. Who was first and who might have been inspired by whom is not subject of this paper though. For an attempt to work out differences beyond the ones emphasized in this paper see McMullin (1976). With regards to the Bohr model, McMullin and Lakatos’s accounts are not equally detailed in all respects. I shall use something like the best reconstruction.
In fact, following Fowler’s negative reaction to Bohr’s suggestion, Bohr proposed a further correction to his model, namely the velocity dependence of the mass of the electron (Bohr’s letter to Fowler on April 15, 1914, in: Hoyer 1981, 504 ff.). This, to my knowledge, is the first occasion at which Bohr considered relativity corrections in writing. See also the next stage discussed in the main text of this paper.
Lakatos writes that the change was “as planned” (ibid. 148).
One might perhaps retort that circular motion is more unlikely than elliptical orbits in so far as in circular motion centripetal forces must precisely counterbalance centripetal acceleration. Circular motion would then be an idealization of elliptic motion in that, normally, conditions are such that centripetal forces and centripetal acceleration would not counterbalance each other in nature.
There were further precursors. The attempt to integrate the hydrogen lines into the lines of other elements has been tracked historically by Robotti (1983). Curiously, neither Curtis nor Sommerfeld play any part in Robotti’s story.
In this formula, n, n’ describe the initial electron orbit and m, m’ the final electron orbits (i.e., before and after a quantum ‘jump’ of the electron).
The Stark effect was accounted for by the introduction of a third quantum number, quantising the “location of the orbit” relative to an external electric field. This was done successfully by Sommerfeld’s student Epstein and by Schwarzschild. See e.g. Kragh (2012, 154) for details.
For a philosophical discussion of this achievement see Vickers (2012).
On 21 May 1916, Friedrich Paschen informed Sommerfeld that he could experimentally confirm the predictions of Sommerfeld’s model about the fine structure to be expected in ionized helium. Paschen reported the results to Annalen der Physik in July 1916 where they, according to the publisher (personal communication), saw print probably in September of the same year.
Both formal and construct idealisations are forms of construct idealisations, where simplification is “worked on” a “conceptual representation of the object”, in contrast to causal idealisations, the “problem situation itself” is simplified, so that “the diversity of causes found in Nature is reduced and made manageable” (McMullin 1985, 255 and 265).
On the basis of this, Pauli formulated the famous exclusion principle. See the abovementioned sources for details.
The first paper which Uhlenbeck and Goudsmit published on electron spin appeared in Naturwissenschaften in 1925. A similar paper in English appeared in 1926 in Nature. See de Regt (2001) for a discussion of the role of visualisability in physics.
Non-relativistic quantum mechanics turned out to be a limit of Dirac’s relativistic equation of the electron.
Lakatos appears to suggest that Bohr himself already had that modification in mind when designing the original model (thanks to Helge Kragh for pointing this out to me). There is no textual evidence that Bohr did, but in any case, this seems to matter not so much for whether or not the original Bohr theory, or programme, bore that suggestion.
Bohr’s conversion happened after he learned from Einstein (through Ehrenfest) that the right application of the theory of special relativity could produce the magnetic field needed for electron spin. See ibid.
According to quantum mechanics, vibrations become significant only at high temperatures (Nyhof 1988, 99).
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Schindler, S. Theoretical fertility McMullin-style. Euro Jnl Phil Sci 7, 151–173 (2017). https://doi.org/10.1007/s13194-016-0150-4
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DOI: https://doi.org/10.1007/s13194-016-0150-4