The comment box was too small for my reply to Sober on falsification, so I will post it here:
I want to understand better Sober’s position on falsification. A pervasive idea to which many still subscribe, myself included, is that the heart of what makes inquiry scientific is the critical attitude: that if a claim or hypothesis or model fails to stand up to critical scrutiny it is rejected as false, and not propped up with various “face-saving” devices. Now
Sober writes “I agree that we can get rid of models that deductively entail (perhaps with the help of auxiliary assumptions) observational outcomes that do not happen. But as soon as the relation is nondeductive, is there ‘falsification’”?
My answer is yes, else we could scarcely retain the critical attitude for any but the most trivial scientific claims. While at one time philosophers imagined that “observational reports” were given, and could therefore form the basis for a deductive falsification of scientific claims, certainly since Popper, Kuhn and the rest of the post-positivists, we recognize that observations are error prone, as are appeals to auxiliary hypotheses. Here is Popper: Continue reading
Here are a few comments on your recent blog about my ideas on parsimony. Thanks for inviting me to contribute!
You write that in model selection, “’parsimony fights likelihood,’ while, in adequate evolutionary theory, the two are thought to go hand in hand.” The second part of this statement isn’t correct. There are sufficient conditions (i.e., models of the evolutionary process) that entail that parsimony and maximum likelihood are ordinally equivalent, but there are cases in which they are not. Biologists often have data sets in which maximum parsimony and maximum likelihood disagree about which phylogenetic tree is best.
You also write that “error statisticians view hypothesis testing as between exhaustive hypotheses H and not-H (usually within a model).” I think that the criticism of Bayesianism that focuses on the problem of assessing the likelihoods of “catch-all hypotheses” applies to this description of your error statistical philosophy. The General Theory of Relativity, for example, may tell us how probable a set of observations is, but its negation does not. I note that you have “usually within a model” in parentheses. In many such cases, two alternatives within a model will not be exhaustive even within the confines of a model and of course they won’t be exhaustive if we consider a wider domain.
*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.