The Big Test of Corroboration

Abstract

This paper presents a new ‘discontinuous’ view of Popper’s theory of corroboration, where theories cease to have corroboration values when new severe tests are devised which have not yet been performed, on the basis of a passage from The Logic of Scientific Discovery. Through subsequent analysis and discussion, a novel problem for Popper’s account of corroboration, which holds also for the standard (‘continuous’) view, emerges. This is the problem of the Big Test: that the severest test of any hypothesis is actually to perform all possible tests (when ‘possible’ is suitably interpreted). But this means that Popper’s demand for ‘the severest tests’ amounts simply to a demand for ‘all possible tests’. The paper closes by considering how this bears on accommodation vs. prediction, with respect to corroboration.

Acknowledgements

I should like to thank Joseph Agassi and David Miller for insightful comments on (and discussions of) an embryonic version of this piece. I am also grateful to James McAllister and two anonymous referees for International Studies in the Philosophy of Science for detailed constructive criticism of a subsequent version.

Notes

[1] Accidental observation of a black swan could therefore refute ‘All swans are white’, but not corroborate ‘All swans are black’. Hence, corroboration is not just a surrogate for inductive confirmation. See also Popper (1983, 235).

[2] Crucial in Popper’s account is that ‘unexpected’ is understood in a logical, rather than subjective, sense (because Popper adopted a logical interpretation of probability). For a more detailed discussion of this, see Rowbottom (2008a; forthcoming).

[3] Joseph Agassi has suggested to me, in personal correspondence, that ‘Popper … rightly said that the initial degree of corroboration of a theory as it appears in public prior to any test has to be fairly high’. From a formal point of view, however, it appears that it could at best be zero. The crucial measure of corroboration, putting aside considerations relating to normalisation, is P(e, hb)—P(e, b). But clearly this measure is only relevant if e is true, and we should not classify e as true unless we have made the relevant observations. Now consider a new hypothesis which hasn’t been tested. Our prior evidence—and therefore any e which we can reasonably classify as true—is part of b. Therefore P(e, hb)—P(e, b) = 0, provided h is consistent with b, unless we consider a hypothetical situation in which our background information does not contain all the evidence that we now have. Yet even if we do consider such a hypothetical scenario, it would only show whether the hypothesis nicely accommodates something we already know. Popper, on the other hand, advocated actual—rather than merely hypothetical—bold conjectures. (In addition, Popper 1983, 236, later declares: ‘Only if the most conscientious search for counter‐instances does not succeed may we speak of a corroboration of the theory’.) See also the discussion in Section 4.

[4] Consider also: ‘The appraisal of the corroboration … can be derived if we are given the theory as well as the accepted basic statements. It asserts the fact that these basic statements do not ontradict [sic] the theory, and it does this with due regard to the degree of testability of the theory, and to the severity of the tests to which the theory has been subjected, up to a stated period of time’ (Popper 1959, 266).

[5] If we just discuss increments of basic statements, rather than distinguish between test reports and background information, there is a simpler objection. Let the statements in question concern the results of repeated spins of a roulette wheel. Today these may cast serious doubt on the hypothesis that the wheel is fair. Next week, however, they might cast no doubt whatsoever.

[6] More carefully, this hypothesis might be framed in terms of propensities. We might suggest that the relevant experimental set‐up results in a ‘heads’ result with propensity ½ and a ‘tails’ result with propensity ½.

[7] See also the discussion of Miller (1994, §2.2e).

[8] My thanks to the editor, James McAllister, for this suggestion.

[9] Note that either suggestion is compatible with the adoption of a logical interpretation of probability. As Keynes (1921, 7) puts it, ‘We may fix our attention on our own knowledge and, treating this as our origin, consider the probabilities of all other suppositions,—according to the usual practice which leads to the elliptical form of common speech; or we may, equally well, fix it on a proposed conclusion and consider what degree of probability this would derive from various sets of assumptions, which might constitute the corpus of knowledge of ourselves or others, or which are merely hypotheses’. For more on this issue, see Rowbottom (2008b).

[10] These examples are primarily illustrative. We need not really imagine ourselves in such scenarios, although this may be an aid to calculation. It should also be noted that in both cases the background knowledge is that of science as a whole (rather than any particular individual.)

[11] This sort of approach is discussed by Musgrave (1974, §3), who also finds it wanting (although for different reasons). Musgrave (1974, 19) instead prefers a ‘variant [which] takes “background knowledge” to include only the best existing competing theory’. However, I would emphasize that corroboration relative to the best alternative to h at the time of its construction may not be the same as the corroboration relative to the best alternative to h at present. And it is difficult to see why we should be interested in the former, except to explain why we once preferred (or would have been right to prefer) h. The latter option remains a viable alternative to using b†, although not one that needs to be considered in depth in order to see the significance of the Big Test. For further discussion, see Rowbottom (forthcoming).