Abstract
Clark Glymour’s “bootstrap” account of confirmation rightly stresses the importance of selective confirmation of individual hypotheses, on the one hand, and the determination of theoretical constants, on the other. But in our view it is marred by a failure to deal with the problem of confounding, illustrated by the demonstration of a causal link between smoking and lung cancer, and by the apparent circularity of bootstrap testing (which is distinguished from statistical bootstrapping). Glymour’s proper insistence on a variety of evidence is built into our account of evidence and not added on as a way of handling the apparent circularity in his account. We discuss and dissolve his well-known charge against Bayesian theories of confirmation, that they lead to the paradox of “old evidence,” in Chap. 9.
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Notes
- 1.
See Glymour (1980).
- 2.
- 3.
To be discussed in Chap. 9.
- 4.
See Douven and Meijs (2006), for an elaboration of Glymour’s account as a quantitative theory of confirmation.
- 5.
Although his recent work on causal inference has shifted his focus to severe testing in which “explanation and explanatory virtues are essential to produce testable hypotheses …” Glymour (2010, p. 349), which, we noted in the last chapter, Mayo has incorporated in her own account of severe testing.
- 6.
Duhem (1954).
- 7.
Under the heading of “irrelevant conjunction.” If a hypothesis is confirmed when a successful observational prediction is derived from it, then so too is any hypothesis, relevant or not, with which it can be consistently conjoined, a matter of elementary logic. If H is confirmed by D, so too are H and H′, however irrelevant H′ might be to the derivation of D. But we do not have to worry about undeserved credit within our framework, first, because what Duhem refers to as “the common sense of the working scientist” (who ignores arbitrary and therefore irrelevant hypotheses) is built into the prior probability on which the confirmation of hypotheses in part depends, second, because within our framework and in the most common cases, observational predictions per se are not “derived” from hypotheses; what is derived from hypotheses are the probabilities or probability distributions of observations expected under hypotheses, third, because irrelevant hypotheses can be identified ab initio: if Pr(H│D) = Prob(H & H’│D), then H’ is “irrelevant,” i.e., not confirmed by D. So much, it would seem, for the confirmation of irrelevant hypotheses. But in an e-mail communication, Glymour contends that our likelihood-based account of evidence also leads to the irrelevant conjunction problem. If data provide evidence for one hypothesis against a competitor, then they also provide evidence for the first hypothesis + an irrelevant proposition, e.g., that the Pope is infallible. Consider H 1, the hypothesis that Jones has tuberculosis, and H 2, the hypothesis that H 1 is false. Let’s assume that Jones’s X-ray is positive, and that Pr(D│H 1) is very high, and Pr(D│H 2) is very low. In such a case, the LR value for H 1 over H 2 is very high, in which case the data provide strong evidence for the hypothesis that Jones has tuberculosis and the Pope is infallible as against the hypothesis that Jones does not have tuberculosis. We grant the objection, but it has little sting so far as scientific practice is concerned. The likelihood account of evidence is to be applied within a conventional statistical framework. In this framework, the hypothesis and the hypothesis + irrelevant conjunct are not an estimable pair. H 1 and H 2 are not estimable because, given the data in hand, there is no way in which to distinguish between them. They would be estimable if we were to gather data about Papal infallibility (and not simply more positive X-rays), but with the data in hand this point, they cannot be distinguished. As such, and as a matter of scientific and statistical practice, what we have dubbed the evidential condition cannot (yet) be applied to them.
- 8.
Duhem (1954, p. 185).
- 9.
For a notable example, it appears to undermine Karl Popper’s claim that whereas confirming consequences of a hypothesis, no matter how many, never prove that it is true, a single disconfirming evidence entails, as a matter of logic, that it is false As soon as two or more hypotheses are needed to deduce the consequences, as Duhem argues, disconfirming results can never show as a matter of elementary logic which one is false.
- 10.
Duhem (1954, p. 218).
- 11.
- 12.
As with every other author discussed in Part II of the monograph, Glymour does not distinguish between “data,” D, and “evidence,” E, a consequence of their all conflating confirmation and evidence.
- 13.
In this and other examples in Theory and Evidence, Glymour uses Hempel’s “positive instance” account of “confirming evidence” (to be described in the Chap. 9) as paradigm, but emphasizes that the use of one part of a theory to test other parts of it can and must be added to other traditional accounts. He does not assume the correctness of, still less defend, the positive instance account, although he does think that it provides a very good reconstruction of Newton’s method in Principia.
- 14.
We have very much simplified both examples. One of the many virtues of Glymour’s account is the detailed way in which he tries to align Newton’s own reasoning with it. At the same time, the alignment can be criticized in the same detailed way, as by Laymon (1983).
- 15.
Glymour (1980, p. 110).
- 16.
This is a common complaint, that Bayesian theories have not been employed, even implicitly, to any great degree in the history of science and that therefore they have little to do with actual practices. Our reply, very briefly, is that probabilistic methods were not generally available or very well understood until the 20th century, that traditional methodologies have difficulty in coping with the more recent discovery that a large range of phenomena can only be adequately described in statistical terms, and that many past paradigms of scientific achievement can be more deeply explained if probabilistic concepts are employed to reconstruct them.
- 17.
See Efron and Tibshirani (1994).
- 18.
Apparently both “bootstraps” take their names independently from the same American folklore. The folklore has some protagonist doing impossible things by applying his own force to himself. It was the bright idea of Glymour and Efron to extract large philosophical and statistical lessons from turning the entity of interest in on itself.
- 19.
This issue is not peculiar to statistical bootstrapping. Any statistical inference uses observed data (good or bad) to make inferences about unobserved data.
- 20.
We owe some insights about statistical bootstrapping to Mark Greenwood.
- 21.
For example, Glymour (1980, p. 110): “Confirmation or support is a relation among a body of evidence, a hypothesis, and a theory …: the evidence confirms or disconfirms the hypothesis with respect to the theory.”
- 22.
See, for example, Cochran (1964, pp. 134-55).
- 23.
Porter and McMichael (1984, pp. 24–42).
- 24.
See, for example, Chun Chao (2007), for more detail and references.
- 25.
Bagnaardi et al. (2011).
- 26.
In Theory and Evidence, Glymour assumed (in part for the sake of argument) that Hempel’s “positive instance” account of confirmation correctly characterized the evidential relation between data and hypothesis in observational studies and that bootstraps were necessary only when the hypotheses tested contained theoretical terms whose values could not be directly measured but were inferred.
- 27.
“Perhaps we should infer instead that there are better and worse justifications, and that arguments or confirmations (or, as I prefer, tests) which guard against compensating errors provide better grounds than those which do not” (Glymour 1980, p. 108).
- 28.
Ibid.
- 29.
Ibid.
- 30.
Once again, Glymour would seem to depart from his purely qualitative account in underlining an ordinal intuition.
- 31.
Ibid., p. 141.
- 32.
See Nye (1972).
- 33.
See Sarkar (2007) on these and related issues.
References
Bagnardi, V., Rota, M., Scotti, L., Jenab, M., Bellocco, R., Tramacere, I., et al. (2011). Alcohol consumption and lung cancer risk in never smokers: a meta-analysis. Annals of Oncology, 12, 2631–2639.
Chao, C. (2007). Associations between beer, wine, and liquous consumption and lung cancer risk: a meta-analysis. Cancer and Epidemiological Biomarkers, 16, 2436–2447.
Cochran, W. (1964). The planning of observational studies of human populations. Journal of the Royal Statistical Society, Series A, 128, 134–155.
Douven, I., & Meijs, W. (2006). Bootstrap confirmation made quantitative. Synthèse, 149(1), 97–132.
Duhem, P. (1954). The Aim and Structure of Physical Theory (translation of the second edition of the French original published in 1914). Princeton: Princeton University Press.
Efron, B., & Tibshirani, R. (1994). An Introduction to the Bootstrap. New York: Chapman and Hall/CRC Monographs on Statistics and Applied Probability.
Glymour, C. (1980). Theory and Evidence. Princeton: Princeton University Press.
Glymour, C. (2010) In Mayo & Spanos (Eds.), Error and Inference Cambridge: University Press Cambridge.
Kuhn, T. (1962/1970/1996). The Structure of Scientific Revolutions. Chicago: University of Chicago Press.
Laymon, R. (1983). Newton’s demonstration of universal gravitation and philosophical theories of confirmation. In Earman, J. (Ed.), Testing Scientific Theories, Volume X in Minnesota Studies in the Philosophy of Science (Minneapolis: University of Minnesota Press).
Nye, M. (1972). Molecular Reality. Amsterdam: Elsevier.
Porter, J., & McMichael, A. (1984). Alcohol, beer, and lung cancer—a meaningful relationship? International Journal of Epidemiology, 13, 24–42.
Sarkar, S. (2007). Doubting Darwin? Creationist Design on Evolution. New York: Wiley-Blackwell.
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Bandyopadhyay, P.S., Brittan, G., Taper, M.L. (2016). Selective Confirmation, Bootstrapping, and Theoretical Constants. In: Belief, Evidence, and Uncertainty. SpringerBriefs in Philosophy(). Springer, Cham. https://doi.org/10.1007/978-3-319-27772-1_7
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