Jan Sprenger (Tilburg): “Two Impossibility Results for Popperian Corroboration”

Abstract: According to influential accounts of scientific method, e.g., critical rationalism, scientific knowledge grows by repeatedly testing our best hypotheses. But despite the popularity of hypothesis tests in scientific inference, especially in statistics, their philosophical foundations are shaky. In particular, the interpretation of results that do not refute the hypothesis under test, but are consistent with it, poses a major philosophical challenge. To what extent do they ground our confidence in the hypothesis under test?

Karl R. Popper proposed that such results corroborate the tested hypothesis (which is, according to Popper, something different than to raise its probability). Corroboration guides our practical preferences over hypotheses which have been subjected to severe tests.

In the 1950s, Popper developed a probabilistic measure of corroboration in a number of BJPS articles. Popper’s explication has been frequently criticized, but nobody has taken the effort to draw general conclusions from the shortcomings of Popper’s particular measure.

In my contribution, I set up adequacy criteria for a probabilistic measure of corroboration that are distinct from the usual adequacy criteria for measures of evidential support. Then I prove two impossibility results showing that there can be no measure satisfying a plausible set of adequacy criteria. I argue that we should explicate degree of corroboration in a different way, abandoning (or at least modifying) the positive probabilistic relevance framework.

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