Abstract
In the previous chapter we showed that the refined definition has real life scientific examples, viz., by pointing out that the Law of van der Waals provides a perfect case of (refined) potential truth approximation, in particular by (double) concretization. Recall that a sequence of three theories is called a case of potential truth approximation when the second is closer to the third than the first is to the third. Two other scientific examples of such sequences have been studied as well. In (Hettema and Kuipers 1995) it is demonstrated that Sommerfeld’s reconstruction of the sequence consisting of the theories of Rutherford, of Bohr and his own theory, i.e., the successive stages of what now is called ‘the old quantum theory’, is also a case of potential truth approximation. In the previous chapter (Section 10.4.) we explained that the technical definition of basic and refined truth approximation can also be directed at so-called provable interesting truths. In (Cools, Hamminga and Kuipers 1994) it is shown that the theory of the capital structure of firms of Modigliani and Miller is closer to a provable interesting truth than the original theory of Kraus and Litzenberger.
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Notes
Note that our way of speaking of ‘potential truth approximation’ is essentially context-independent. Hence it does not imply that ‘the third theory’ has not yet been discarded and replaced. Not only was the theory of Van der Waals discarded long ago, at least in principle, the crucial theory of this article, i.e.,Sommerfeld’s theory of the atom, has also been discarded and replaced since 1925. In fact, many problems with the ’old’ quantum theory started to accumulate since the early 1920s, notably the persistent failure to furnish an explanation for the helium spectrum. Although these problems eventually caused the downfall and replacement of the old quantum theory, they are not relevant to the discussion given here, which is concerned with one-electron atoms.
Lakatos’ assessment of the degeneration of the old quantum theory between, roughly, 1920 and 1926 has been questioned in (Radder 1982).
Note that the assumptions imply that Y satisfies the boundary condition (with respect to X and Z(Y)). Note also that Y does not satisfy the strong version, except in the extreme case that Z(Y)is a one-one concretization of Y. Precisely this happens to be the case for the concretization of BA by SA: every BA-model has one and only one SA-model, since the velocity of light is supposed to be a unique (finite) value.
A plausible question is how to compare the ‘old’ and the ‘new’ quantum theory. As Gerhard Zoubek has rightly suggested, there is not only the possibility of constructing a rather artificial superset of potential models, including the old and the new ones. The other possibility is to make explicit the so-called ’links’ between the two frameworks. Further truth approximation analysis then essentially requires in the first case the extension of structurelikeness to similarity between conceptually divergent structures, and in the second case the extension of refined truthlikeness to divergent conceptual frameworks.
An explicit definition of this as a defined function would require extension of DETCp with a set of investors, and functions mapping their probability beliefs on state j e J,risk aversions, time preference and utility functions.
To formulate this precisely is quite complicated; it is partly a matter of substituting the value 0 for bankruptcy cost C,partly a matter of just skipping C.
A similar qualification has to be made as in the foregoing note.
his can be strictly proven in the exposition of Kraus and Litzenberger (1973)
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© 2000 Springer Science+Business Media Dordrecht
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Kuipers, T.A.F. (2000). Examples of Potential Truth Approximation. In: From Instrumentalism to Constructive Realism. Synthese Library, vol 287. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1618-5_11
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DOI: https://doi.org/10.1007/978-94-017-1618-5_11
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