*See also earlier posts from the CMU workshop here and here.
Elliott Sober has been writing on simplicity for a long time, so it was good to hear his latest thinking. If I understood him, he continues to endorse a comparative likelihoodist account, but he allows that, in model selection, “parsimony fights likelihood,” while, in adequate evolutionary theory, the two are thought to go hand in hand. Where it seems needed, therefore, he accepts a kind of “pluralism”. His discussion of the rival models in evolutionary theory and how they may give rise to competing likelihoods (for “tree taxonomies”) bears examination in its own right, but being in no position to accomplish this, I shall limit my remarks to the applicability of Sober’s insights (as my notes reflect them) to the philosophy of statistics and statistical evidence.
1. Comparativism: We can agree that a hypothesis is not appraised in isolation, but to say that appraisal is “contrastive” or “comparativist” is ambiguous. Error statisticians view hypothesis testing as between exhaustive hypotheses H and not-H (usually within a model), but deny that the most that can be said is that one hypothesis or model is comparatively better than another, among a group of hypotheses that is to be delineated at the outset. There’s an important difference here. The best-tested of the lot need not be well-tested!
2. Falsification: Sober made a point of saying that his account does not falsify models or hypotheses. We are to start out with all the possible models to be considered (hopefully including one that is true or approximately true), akin to the “closed universe” of standard Bayesian accounts[i], but do we not get rid of any as falsified, given data? It seems not.