Abstract
We argue that the robustness analysis of idealized models can have confirmational power. This responds to concerns recently raised in the literature (especially by Odenbaugh & Alexandrova), according to which (a) the robustness analysis of models whose idealizations are not discharged is unable to confirm the causal mechanisms underlying these models, and (b) the robustness analysis of models whose idealizations are discharged is unnecessary. In response, we make clear that, where idealizations sweep out, in a specific way, the space of possibilities— which is sometimes, though not always, the case—they can be holistically discharged. In turn, this can be used to show that the robustness analysis of idealized models can have confirmational force after all.
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Notes
There is some debate as to what exactly the confirmation is about. As Weisberg (2006) notes, the confirmation could be from the core assumptions of the model to a predicted consequence, or it could be the other way around. In what follows, we follow Alexandrova & Odenbaugh (2011) and focus on the latter case; however, the conclusions below can be easily reformulated with a view towards the former account.
Odenbaugh and Alexandrova (2011) distinguish two types of idealizations (see also Kuorikoski et al., 2010): Galilean idealizations—which remove some possible confounding causal factors—and tractability idealizations—which are mathematical “niceties” introduced to ensure the model functions at all. For present purposes, a closer analysis of this is not necessary, though.
It is important to note how this criticism is distinct from concerns about the independence of models. Even if the relevant models are all independent, arguments like those expressed by Alexandrova and Odenbaugh suggest that RA fails to be confirmatory. Since none of the models in question are accurate reflections of the target system, drawing a conclusion about the target system from this set is premature. What we can derive from the RA is that the result can be achieved from many counterfactual, often simplified, situations. What needs to be done, though, is connecting at least one of these counterfactuals to the real world through discharging assumptions. But this would mean that there is no need for the RA. Regardless of how model independence is determined, there remains this further concern.
Weisberg (2006) also responds to Orzack and Sober (1993). However, he does this by noting that “robust theorems” of the above sort are really only a part of RA. The latter is about determining the core, shared structure of a set of models that is responsible for deriving an empirically confirmed result, and then using a variety-of-evidence argument to obtain confirmation for the robust theorem in question. However, our point here is that there is more that can be said on behalf of the confirmational properties of RA. See also Justus (2012).
Levins’s presentation of robustness had a slightly different approach, as his focus was on whether the prediction M- > P—“the robust theorem”—could be considered true. However, as also noted by Odenbaugh (2011, 1179), much of Levins’s discussion can be appropriately tweaked so as to fit the presentation of Alexandrova & Odenbaugh (2011). See also below.
It is debatable how much conformation it provides. However, this can be left open here; for present purposes, it is just important that it provides some confirmation.
See Pincock, 2011 pg. 99 for a discussion of deep-water wave models.
Note also that the set of idealized values cannot be seen as an estimate of the depth of the ocean floor, as that depth varies. This set of idealized values is literally just the range of the depth of the ocean floor, not an estimate of it at any given point.
Note that if we expected the shape, or change in depth of the ocean floor within our range of possibilities to be causally relevant, this would then be included in our set C, and so the model would be different.
Of course, if the variation in the depth of the ocean floor is suspected to be causally relevant, then presenting the ocean floor as a single value would be inappropriate: the above set of models then is not a good partitioning of the space of possibilities, and would need to include the variation as well.
There are other typical assumptions, such as there only being two “kinds” rather than a broader diversity.
A further question that might be raised here concerns whether our response to Alexandrova and Odenbaugh’s argument surreptitiously requires models that lack independence. However, as noted above, we set this question aside here. On the one hand, while, as also noted earlier, the characterization of model independence is far from clear, there is no obvious reason why assuming the ocean floor has consistent depth of x meters and assuming it has a consistent depth of y meters (where x and y are different) are not independent assumptions (for example). On the other hand—and most importantly—we ignore the question of model independence here because, as stated above, the argument presented by Alexandrova and Odenbaugh is meant to show that RA is not confirmatory at all. If the main concern is an issue of model independence, then we can move on from Alexandrova and Odenbaugh’s argument as spurious, and the focus should be on defining model independence.
Note also that Levins (1993, p. 555) responded to the criticisms leveled by Orzack and Sober (and others like them) by arguing that observation is relevant to “the choice of the core model and the selection of plausible variable parts.” Odenbaugh (2011) takes this to mean that we need to have empirical evidence for the set of core causal assumptions of the model—and then rightfully points out that, in that case, the idealizations of the model do not really matter, since we have empirical evidence for the representational parts of the model already. However, here, it is the second part of Levins’s statement that matters: What we need—and may well have—is evidence for the “variable parts of the model.”
It is the latter kind of evidence that can give RA a confirmatory role to play.
As noted in the example of models of waves, this may even be plausible for some models of wave formation in oceans, where an infinite ocean depth may be assumed.
We thank an anonymous referee for useful discussion of this point.
Note also that Schupbach’s account is more general and is intended to apply not just to models.
Incidentally, this is quite in line with Popper’s account of corroboration: see Popper (2002, chap. 10).
Levins, 1993 pg. 554.
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Fuller, G.P., Schulz, A.W. Idealizations and Partitions: A Defense of Robustness Analysis. Euro Jnl Phil Sci 11, 107 (2021). https://doi.org/10.1007/s13194-021-00428-8
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DOI: https://doi.org/10.1007/s13194-021-00428-8