In his recent bookThe Advancement of Science,Philip Kitcher endorses eliminative induction, or the view that confirmation of hypotheses proceeds by the elimination of alternatives. My intention here is to critically examine Kitcher's eliminativist view of confirmation, and his rejection of the widely held Bayesian position, according to which an hypothesis H is confirmed by evidence E just in case the probability of H conditional on E is greater than the simple unconditional probability of H [i.e. p(H/E) > p(H)]. Here, I (...) will maintain that while there are aspects of the eliminative approach which Bayesianism must incorporate, as has been argued by John Earman, the eliminativism advocated by Kitcher is unsatisfactory. In addition, I will suggest that Kitcher's reasons for rejecting Bayesian confirmation theory are unconvincing and depend on an overly restrictive version of the position and that indeed Bayesianism has resources needed by an eliminativist account of confirmation. (shrink)