We Turing Machines Can't Even Be Locally Ideal Bayesians. (26th October 2016) - Mount, Beau Madison
Abstract : Vann McGee has argued that, given certain background assumptions and an ought‐implies‐can thesis about norms of rationality, Bayesianism conflicts globally with computationalism due to the fact that Robinson arithmetic is essentially undecidable. I show how to sharpen McGee's result using an additional fact from recursion theory—the existence of a computable sequence of computable reals with an uncomputable limit (a Specker sequence). In conjunction with the countable additivity requirement on probabilities, such a sequence can be used to construct a specific proposition to which Bayesianism requires an agent to assign uncomputable credence—yielding a local conflict with computationalism.