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Derivational Robustness and Indirect Confirmation

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Abstract

Derivational robustness may increase the degree to which various pieces of evidence indirectly confirm a robust result. There are two ways in which this increase may come about. First, if one can show that a result is robust, and that the various individual models used to derive it also have other confirmed results, these other results may indirectly confirm the robust result. Confirmation derives from the fact that data not known to bear on a result are shown to be relevant when it is shown to be robust. Second, robustness may increase the degree to which the robust result is indirectly confirmed if it increases the weight with which existing evidence indirectly confirms it. This may happen when it strengthens the connection between the core and the robust result by showing that auxiliaries are not responsible for the result.

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Notes

  1. Knuuttila and Loettgers (2011) present a case study (on the circadian clock) that also involves the interplay of data and robustness. See Guillemot (2010) for an account of the interplay of evidence and models in climate research.

  2. See e.g., the special issue (2010, vol. 41) on climate change in Studies in History and Philosophy of Modern Physics. Räisänen (2007) provides a non-technical introduction by a climatologist.

  3. I discuss the context dependence of confirmation via robustness further in Lehtinen (2016). I show, for example, that robustness may entirely fail to confirm even when there is indirect empirical evidence, but also that it is possible that a given initially non-confirming demonstration of robustness may become confirmatory later if the epistemic situation is modified in the right way.

  4. The ‘┬’ and ‘├’ signs refer to the entailment relation, and the vertical line ‘|’ to a direct model fit.

  5. Niiniluoto and Tuomela (1973, pp. 3–4) present essentially the same argument as Okasha but without using the term ‘indirect confirmation’, and Bangu (2006) re-employs the argument but without mentioning Hempel’s result.

  6. I do not intend to argue for HD as opposed to other accounts of confirmation by applying Gemes’ account, and neither did Gemes by presenting it (see e.g., Gemes 1993).

  7. See Hartmann and Fitelson (2015) for an account in which old evidence confirms even in cases weaker than entailment..

  8. See Hands (2016) for a study of robustness with virtually no empirical evidence.

  9. ‘Future temperature increase’ and ‘increase in greenhouse gases’ may refer to various things but the details are not needed in this paper. There are different scenarios of future CO2 emissions and various ways to conceptualise future temperature increases. Equilibrium Climate Sensitivity (ECS) determines the long-term equilibrium warming response to stable atmospheric composition, but does not account for vegetation or ice-sheet changes. Transient Climate Response (TCR) is a measure of the magnitude of transient warming while the climate system, particularly the deep ocean, is not in equilibrium; and Transient Climate Response to Cumulative CO2 emissions (TCRE) is a measure of the transient warming response to a given mass of CO2 injected into the atmosphere, and combines information on both the carbon cycle and climate response. TCR is estimated with high confidence to be likely between 1 and 2.5 °C and extremely unlikely to be greater than 3 °C (Bindoff and Stott 2013, pp. 6, 59–60).

  10. Climate modellers appear to think that RM is robust, however: 'Models are unanimous in their prediction of substantial climate warming under greenhouse gas increases, and this warming is of a magnitude consistent with independent estimates derived from other sources, such as from observed climate changes and past climate reconstructions' (Randall et al. 2007, p. 601).

  11. The history of climate science involves adding various elements to a model that becomes larger and larger (see Edwards 2010 for an extensive history of climate science). For example, the coupling of models of the sea and the climate was a major break-through. Modules for vegetation and sea ice, for example, were then added. One could thus also interpret (6) as the result of successive models. If M1 had been the first model in time, M2 the second, and so on, reality would have been described by M3⊢ R1, R2, R3 and M2⊢ R1, R2 but M2⊬, and M1⊢ R1 but M1⊬R2, R3.

  12. The Navier–Stokes equations belong to what modellers often refer to as the ‘physical core’ of climate models. In this paper, however, the ‘core’ merely refers to CO2 forcing. Katzav (2013) argues that these equations cannot be confirmed because we know them to be true already (see Yablo 2014, p. 101 for a more general claim to this effect).

  13. See Houkes and Vaesen (2012), Odenbaugh (2011), Odenbaugh and Alexandrova (2011) and Woodward (2006). See Katzav (2013, 2014) for a version of this criticism that is specifically targeted at climate models. Kuorikoski et al. (2012) provide a rejoinder to Odenbaugh and Alexandrova's version of this argument.

  14. As I have shown (see fn. 9), there are slightly different estimates of the sensibility of the climate to different forms of forcing..

  15. See e.g., Bindoff and Stott (2013, FAQ 10.1). The report uses these terms to discuss the possibility that another alternative account might explain the observed global warming, the idea that internal variability alone is sufficient: ‘…we conclude that it is virtually certain that internal variability alone cannot account for the observed global warming since 1951’ (p. 22). See Parker (2010a) for a philosophical analysis of fingerprint results from attribution studies that derive results like (5″).

  16. Despite such results, the attribution to greenhouse gases is not perfect because climate-simulation models have hundreds of thousands of lines of computer code, and some parts of it have remained the same for decades. Insofar as all the code is not checked, it is still possible in principle that errors in it could generate the confirmed results.

  17. They thus argue that variety of evidence allocates the confirmation to C.

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Acknowledgements

For their comments on earlier drafts of this paper and discussions about these issues, I would like to thank Till Grüne-Yanoff, Jaakko Kuorikoski, Chiara Lisciandra, Caterina Marchionni, Ilkka Niiniluoto, Jani Raerinne, Jouni Räisänen, Jonah Schupbach, Jacob Stegenga, the anonymous reviewers, and participants in the following conference series: PSA, Models and Simulations, INEM, NNPS, and a workshop on Robustness in Helsinki 2014. Given the complexity of the issues, the present account may still suffer from various weaknesses for which they could not be held responsible.

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    Aki Lehtinen

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Lehtinen, A. Derivational Robustness and Indirect Confirmation. Erkenn 83, 539–576 (2018). https://doi.org/10.1007/s10670-017-9902-6

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