I have written before about the claim that statistical reasoning is over-hyped in its claim that all the problems in the universe can be solved by statistical reasoning over past data (see also my report about Sethu Raman Keynote in DEBS'12).
A more blunt claim against statistical reasoning has been made by Noam Chomsky which claims that the fact that AI took a wrong direction by making statistical reasoning its mainstream, and claim that knowledge achieved by statistical reasoning, while having practical usages as "good enough" for various uses, creates shallow knowledge that only approximate the universe and does not create a solid model of the universe.
An interesting interview with Noam Chomsky was published recently in "the Atlantic".
Always thought provoking!
I'll write more about correlation vs. causality.