New arguments against Bayesian regularity and an otherwise plausible domination principle are offered on the basis of rotational symmetry. The arguments against Bayesian regularity work in very general settings.

The cosmological and teleological argument both start with some contingent feature of the actual world and argue that the best or only explanation of that feature is that it was produced by an intelligent and powerful supernatural being. The cosmological argument starts with a general feature, such as the existence of contingent being or the presence of motion and uses some version of the Principle of Sufficient Reason to conclude that this feature must have an explanation. The debate then focuses (...) on two points: first, whether the PSR in question is true, and second, whether the explanation must involve God or at least some God-like being. The teleological argument begins with a general feature of the cosmos judged to have value, such as the existence of intelligent life or the presence of order in the universe, and argues, usually inductively but sometimes deductively, that this feature is to be explained by the agency of a powerful supernatural being. Here, the debate tends to focus on whether there are alternate naturalistic explanations, such as Darwinian evolution. (shrink)

A simple argument is given that shows that conditional probabilities do not supervene on unconditional probabilities. In particular, one cannot in general define conditional probabilities using the ratio formula P ( U | V ) = P ( U & V )/ P ( U ), or using any more sophisticated method based on unconditional probabilities.

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