Does Frege have too many thoughts? A Cantorian problem revisited
standard probabilistic practice of saying that E provides evidence for H just in case P(H|E) > P(H).) Whether one’s resulting credence in the theory of quantum mechanics would be so low that one would reject quantum mechanics would depend on details like one’s prior probability for Theory X. Even with a probability shift in favour of Theory X, one’s credences could still be such that quantum mechanics is judged vastly more probable than Theory X. Just as the observation of the decay can provide evidence for Theory X and against quantum mechanics, the observation that we are in a small civilization can provide evidence for or against various physical theories. For example, consider Theory Y, which predicts that all civilizations are small. The fact that our civilization is small could constitute evidence in favour of Theory Y and against inflationary theory. But depending on such factors as one’s prior probability for Theory Y, one’s credences could still be such that inflationary theory is judged vastly more probable than Theory Y. Thus, that our civilization is small could lead one to decrease one’s credence in inflationary theory, but nevertheless that credence could still be high. The issue we are discussing in the previous paragraph is a general issue about theory comparison in science; if that is the core of Olum’s paper then there is nothing surprising here. It would be surprising if there were a conflict between anthropic reasoning and observation, but Olum’s argument fails to show that this is the case.