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.
Error Statistics Philosophy 