An argument against global no miracles arguments
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An argument against global no miracles arguments Florian J. Boge1,2 Received: 12 April 2018 / Accepted: 28 August 2018 © Springer Nature B.V. 2018
Abstract Howson famously argues that the no-miracles argument, stating that the success of science indicates the approximate truth of scientific theories, is a base rate fallacy: it neglects the possibility of an overall low rate of true scientific theories. Recently a number of authors has suggested that the corresponding probabilistic reconstruction is unjust, as it concerns only the success of one isolated theory. Dawid and Hartmann, in particular, suggest to use the frequency of success in some field of research R to infer a probability of truth for a new theory from R. I here shed doubts on the justification of this and similar moves and suggest a way to directly bound the probability of truth. As I will demonstrate, my bound can become incompatible with the assumption specific testing and Dawid and Hartmann’s estimate for success. Keywords Base rate fallacy · No miracles argument · Scientific realism · Inductive skepticism
1 Introduction: the base rate fallacy and the frequency-based NMA The no-miracles argument (NMA) for scientific realism states that scientific realism “is the only philosophy that doesn’t make the success of science a miracle.” (Putnam 1975, p. 73) Howson (2000, pp. 52–54) has famously argued that this is a base rate fallacy (BRF). In a probabilistic reconstruction of the NMA this means the following. Let s mean that a given theory T succeeds in empirical testing, and t that it is true. The probability p(s|t) of a correct positive in empirical testing is sometimes called the test’s sensitivity and the probability p(¬s|¬t) of a correct negative its specificity
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Florian J. Boge [email protected]
1
Interdisciplinary Centre for Science and Technology Studies (IZWT), Bergische Universität Wuppertal, Gaußstr. 20, room S.11.19, 42119 Wuppertal, Germany
2
Institute for Theoretical Particle Physics and Cosmology, RWTH Aachen University, Otto-Blumenthal-Straße, 52074 Aachen, Germany
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Synthese
(e.g. Rothman et al. 2008, p. 354). f = 1 − p(¬s|¬t) defines the probability of a false positive. Now assume that (i) p(s|t) = g ≈ 1 (empirical tests in question are quite sensitive) (ii) p(s|¬t) = f 1 (empirical tests in question are quite specific) (iii) p(t) = r > 0 (T has a non-vanishing prior r to be true). What is the probability p(t|s) of T being true given empirical confirmation? From a version of Bayes’ theorem, we have p(t|s) =
p(s|t) p(t) , p(s|t) p(t) + p(s|¬t) p(¬t)
(1)
which we can re-express, using (i)–(iii), as p(t|s) =
g·r g r >0 = . (g − f )r + f (g − f ) + f /r
(2)
In case r is very small (r f ) this number tends to 0, since the f /r -term in the denominator becomes very large. Setting e.g. g = 0.95, f = 0.05, and r = 0.001 = 1/1000, we have 0.95 0.95 = < 0.02. (3) p(t|s) = 0.9 + 100/2 50.9 In words: If the prior for T ’s truth is very small, there is less than a 2% probability conveyed to T ’s truth by it’s success in
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