Abstract
The underdetermination thesis poses a threat to rational choice of scientific theories. We discuss two arguments for the thesis. One draws its strength from deductivism together with the existence thesis, and the other is defended on the basis of the failure of a reliable inductive method. We adopt a partially subjective/objective pragmatic Bayesian epistemology of science framework, and reject both arguments for the thesis. Thus, in science we are able to reinstate rational choice called into question by the underdetermination thesis.
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Notes
For a nice survey of the literature contending why the underdetermination thesis is wrong see (Norton 2008). This notion of underdetermination is different from the way Kelly has construed the term in his writings. Kelly (1996) writes, “Underdetermination occurs, roughly, when the same data may arise regardless which of the two competing hypotheses is correct. This is just a special way to argue that no logically reliable inductive method exists relative to scientist’s background assumptions. \(\ldots \)I propose to define underdetermination as the impossibility of reliability (in a given sense) relative to the assumptions at hand. \(\ldots \)We may then hope to map out the structure of degrees of underdetermination in a systematic manner.” In his article (Kelly 2000), he distinguishes two kinds of underdetermination, global underdetermination and local underdetermination. He has also discussed different degrees of local underdetermination. Although we will consider an argument for underdetermination from a failure of a reliable method, unlike Kelly we don’t construe underdetermination in terms of its hierarchies corresponding to different notions of reliability.
These two arguments are relatively new and there is not much discussion of them in recent literature on the topic. Representative examples are Kukla (1998), and especially Mayo (1996). Although Mayo discusses and ultimately rejects different versions of the underdetermination thesis, she has not addressed these arguments.
For several recent papers on the debate between Bayesian and non-Bayesian approaches to inference, decision, prediction, simplicity, and automated reasoning see (Bandyopadhyay and Forster 2011a). See also the “Introduction” to the same edited volume (Bandyopadhyay and Forster 2011b) for a review of these approaches.
The term “deductivism” is a misleading term if it is not properly defined. In their jointly edited book, Grunbam and Salmon (1988) use the term in two different ways. Grunbam while reconstructing Coffa’s view on “deductive chauvinism,” writes, “Coffa applied the term ’deductive chauvinism’ to the view that the higher the probability assigned to an explanandum event, the better the explanation yielding it (private communication).” Salmon, on the other hand, says “Deductivism read: deductive chauvinism) is the view that the only logical devices required in the empirical sciences are deductive.” Salmon in his joint article with Earman (1992) uses deductivism in the same sense when he brands Popper as a deductivist. These two notions of deductivism seem to be misleading unless an attempt is made to relate one notion to the other. If we are to be charitable to them, we should accept Salmon’s construal of deductivism, because it is the standard characterization. Salmon’s sense of deductivism has to do with taking deductive method as used in mathematics, logic and geometry as the paradigm method of understanding science. We, however, are not working with this sense of deductivism.
Earman has attributed this example to Laudan and Leplin. (See Laudan and Leplin 1991).
We follow Boyd (1996) in distinguishing the underdetermination thesis from empirical indistinguishability thesis.
Our claim that “evidence” could include observable consequence is consistent with our previous argument that observable consequence is neither necessary nor sufficient for being supporting evidence. When we say that evidence is not necessarily observable consequences, this merely says that some evidence may be something that is not an observable consequence. In our case, it was something that was not a consequence at all. That, of course, leaves it open that some (or even most) evidence may be observable consequences. Similarly, in denying that being an observable consequence is sufficient for being evidence, we simply asserted that some observable consequences may not be evidence. The claims we make are very week, but suffice to dispose of the view that evidence = logical consequences.
We are three Bayesians who are worried about the subjective nature of prior probability. Several non-Bayesians also find it to be problematic with Bayesianism. For example, one of Mayo’s main criticisms (1996) against the Bayesian is that the latter’s notion of prior smacks of subjectivism. For a defense of Bayesian position, see Howson and Urbach (1993), chapter 15, pp. 417–419. In the following pages especially in Sect. 6, we find fault with her criticism because it is over-simplicistic.
Hawking and Mlodinow (2010), p. 141. They discuss only the probability of the Pope being a Chinese without addressing Bayesianism or a priori probability.
For a different perspective on the notion of simplicity see Sober (1974, 1995, and also Sober in Forster and Sober 1994). In fact, Sober has subscribed to two accounts of simplicity. (1) A theory is simpler than the other with regard to substantive background assumptions. His first notion of simplicity is influenced by Jack Good’s views on confirmation. See Good (1983) (2) According to Sober’s second notion, a theory is simpler than the other just in case the former contains fewer numbers of adjustable parameters than the latter with respect to some background assumptions of the contending mathematical theories. Sober’s second notion draws its strength from his joint work with Forster. We thank Sober for helping us understand his position better. Our view of simplicity overlaps with Swinburne’s view of simplicity. For the latter view see Swinburne (2001).
There are several objective measures of “complexity” in a variety of contexts such as computational, logical (syntactic, semantic, and descriptive), information-theoretic, and statistical. One important notion known as Kolmogorov complexity (see, Li and Vitanyi 2008) actually straddles several of the above contexts, and is also closely related to randomness (see Dasgupta 2011, where further references may be found). See footnote 24 for measures of simplicity from the statistical perspective, which is the one most relevant for our purposes.
One of the referees provided further information about some some automated regression-methods that although do not explicitly involve prior probability, do take into account the degree of simplicity in statistical models. For more on this point, see footnote 24. For evaluation of the use of AIC, see Bandyopadhyay et al. (2013).
Several papers are already written on non-informative priors. Objective or robust Bayesian accounts for less subjective or even objective ways to assign priors are cases in point (see Berger 1994). This point is due to one of the referees of the paper.
Empirical indistinguishability is sometimes defined in terms of theories entailing (perhaps with background assumptions) the same evidence. Our definition is more general, since it does not specify the relation between evidence and the theory it confirms.
He requires the set to include all but a set of measure 0 of possible worlds from a larger set of possible worlds including all possible values of evidence statements.
The problem related to reliability of scientific methods is Earman’s one live research problem. For his recent position on reliability, see Earman and Roberts [forthcoming]. In this paper, they offer two arguments, epistemological and semantic arguments for the Humean supervenience (HS) thesis. According to HS thesis, there do not exist any two possible worlds that agree with respect to Humean base, but disagree on what the laws are. The central theme of their arguments is that if laws matter to science, then the only way to make sense of that is to assume HS thesis. Their epistemological argument rests heavily on assuming the reliability of scientific methods. This line of defense of HS thesis on the basis of reliability of methods goes against the spirit of Earman’s argument for underdetermination. However, we won’t address this yet to be published Earman’s paper.
Earman’s views on Bayesian subjectivism have undergone changes over the years. In Earman’s Bayes or Bust?, he was prone to Bayesian personalism (subjectivism). However, he made an observation that gave the impression that he also cared for objectivity of scientific inference. To quote, “This [i.e., the value of the crucial factor prob(E/not T & K)] may be acceptable to the thorough going Bayesian personalists, but it is unacceptable to anyone who wants to find a modicum of objectivity in scientific inference.” (p. 168). In 92, he was yet to be a through going personalist. He didn’t seem to endorse full-scale personalism in that context. In 93 during the time Earman wrote (1993), he became converted to personalism. One possible way out of the inconsistent triad (that consists of semantic realism, epistemic realism and the underdetermination thesis together) was to invoke subjective priors. He, however, didn’t adopt that move in that paper. He opted for antirealism instead. In this paper, however, he didn’t consider one possibility, that is, there could be some constraints on priors which need not lead to subjectivism. In his recent book, Hume’s Abject Failure, he has considered both constraints, subjective and objective, on priors. It is clear that he is a full-blown subjectivist (personalist) in this book. According to Earman, satisfying probability calculus provides the only constraint on the structure of an agent’s belief within Bayesianism. He holds further that this rationality constraint of Bayesianism fails to deliver the truth or the objectivity of the agent’s beliefs. We thank Earman for clarifying his position to us through e-mails.
One needs to be careful that a priori probabilities are not the same as prior probabilities although the latter are acquired from the former by conditionalizing prior probabilities on a priori probabilities together with all the evidence and background information an agent has before the prior has been fixed. Those priors in question are found with the help an agent’s a priori probabilities, background information and evidence so far gathered till the prior has been determined.
Some Bayesians might think that our approach to inferential problems, whether one employs estimation technique, or hypothesis testing technique, is completely misguided. According to our Bayesian critics, after all, the purpose of most inferential studies is to provide the statistician or the client with decisions. Hence, for them, it is much more relevant to provide evaluation criteria of decision (for such a position, see Robert (1994, p. 39) However, we disagree with them, because we are primarily interested in non-decision theoretical approach to theory choice.
Various statistical methods, such as the Least Absolute Shrinkage and Selection Operator (lasso), adjusted \(R^{2}\), and ridge regression, penalize for number of parameters (complexity) through regularization, or shrinkage. Shrinkage methods are a more continuous alternative to simply retaining or discarding variables and can be used to decrease prediction error. They typically involve penalize the absolute size of the regression coefficient and can be convenient when we want some automatic feature/variable selection or when dealing with highly correlated variables. Lasso uses a data-dependent penalty term (beyond just dependence on sample size), as opposed to model selection criteria such as BIC, BTC, and AIC. (See, Park and Cassella 2008; Kyung et al. 2010) One of the referees of this paper has called out attention to these recent statistical papers on the relevant issue.
We owe this point to one of the referees.
We wish to thank J. Allard, R. Boik, G. Brittan, C. Howson, J. Earman, J. Good, K. Intemann, K. Kelly, J. Leplin, S. Levy, E. McIyntre, P. Mukhopadhyay, J. Roberts, S. Roy, E. Sober, S. Vineberg, John Welch, G. Wheeler and several referees of various journals for their suggestions regarding the contents of the paper. We are especially thankful to three referees of this journal for their detailed suggestions and insightful comments on the previous draft of this manuscript. Some versions of the paper were presented at the Society for the Exact Philosophy meetings in Montreal, the Methodology Conference in Santinekatan, and the American Philosophical Association meetings in Chicago. The paper has been financially supported by the NASA’s Astrobiology Biogeocatalysis Research Center (Grant number # 4w 1781) and the Scholarships and Creativity grant from Montana State University.
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Bandyopadhyay, P.S., Bennett, J.G. & Higgs, M.D. How to Undermine Underdetermination?. Found Sci 20, 107–127 (2015). https://doi.org/10.1007/s10699-014-9353-3
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DOI: https://doi.org/10.1007/s10699-014-9353-3