Peircean Induction and the Error-Correcting Thesis

Deborah G. Mayo Peircean Induction and the Error-Correcting Thesis Peirce's philosophy of inductive inference in science is based on the idea that what permits us to make progress in science, what allows our knowledge to grow, is the fact that science uses methods that are self-correcting or error correcting: Induction is the experimental testing of a theory. The justification of it is that, although the conclusion at any stage of the investigation may be more or less erroneous, yet the further application of the same method must correct the error. (5.145) Inductive methods — understood as methods of experimental testing — are justified to the extent that they are error-correcting methods. We may call this Peirce's error-correcting or self-correcting thesis (SCT): Self-Correcting Thesis SCT: methods for inductive inference in science are error correcting; the justification for inductive methods of experimental testing in science is that they are self-correcting. Peirce's SCT has been a source of fascination and frustration. By and large, critics and followers alike have denied that Peirce can sustain his SCT as a way to justify scientific induction: "No part of Peirce's philosophy of science has been more severely criticized, even by his most sympathetic commentators, than this attempted validation of inductive methodology on the basis of its purported self-correctiveness" (Rescher 1978, p. 20). In this paper I shall revisit the Peircean SCT: properly interpreted, I will argue, Peirce's SCT not only serves its intended purpose, it also provides the basis for justifying (frequentist) statistical methods in science. While on the one hand, contemporary statistical methods increase the mathematical rigor and generality of Peirce's SCT, on the other, Peirce provides something Transactions of the Charles S. Peirce Society Spring, 2005, Vol. XLI, No. 2 300 Deborah G. Mayo current statistical methodology lacks: an account of inductive inference and a philosophy of experiment that links the justification for statistical tests to a more general rationale for scientific induction. Combining the mathematical contributions of modern statistics with the inductive philosophy of Peirce, sets the stage for developing an adequate justification for contemporary inductivestatistical methodology. 2. Probabilities are assigned, to procedures not hypotheses Peirce's philosophy of experimental testing shares a number of key features with the contemporary (Neyman and Pearson) Statistical Theory: statistical methods provide, not means for assigning degrees of probability, evidential support, or confirmation to hypotheses, but procedures for testing (and estimation), whose rationale is their predesignated high frequencies of leading to correct results in some hypothetical long-run. A Neyman and Pearson (NP ) statistical test, for example, instructs us "To decide whether a hypothesis, H, of a given type be rejected or not, calculate a specified character, x0, of the observed facts; if χ > x0 reject H; if χ a\x); H0). If this probability is very small, the data are taken as evidence that H*: cancer risks are higher in women treated with HRT The reasoning is a statistical version of modes tollenr. If the hypothesis H0 is correct then, with high probability, \-p, the data would not be statistically significant at level p. χ is statistically significant at level p. Therefore, χ is evidence of a discrepancy from H0, in the direction of an alternative hypothesis H. (i.e., H* severely passes, where the severity is 1 minus the p-value)} For example, the results of recent, large, randomized treatment-control Peircean Induction and the Error-Correcting Thesis 309 studies showing statistically significant increased risks (at the 0.001 level) give strong evidence that HRT, taken for over 5 years, increases the chance of breast cancer, the severity being 0.999. If a particular conclusion is wrong, subsequent severe (or highly powerful) tests will with high probability detect it. In particular, if we are wrong to reject H0 (and H0 is actually true), we would find we were rarely able to get so statistically significant a result to recur, and in this way we would discover our original error. It is true that the observed conformity of the facts to the requirements of the hypothesis may have been fortuitous. But if so, we have only to persist in this same method of research and we shall...