Global Warming, second hand smoke, speed limits, airport security, bans on powerlines, types of food, cellphones, economic decisions, the decision to invade Iraq, etc. ~ a vast number of public policy issues depend for evidence upon the statistical analysis of data which, in turn, depends upon the philosophy of probability. Yes, statistics is that rare "science" for which the philosophical position one takes on its foundations actually effects one's conclusions. Given the same set of data, a subjective Bayesian and a frequentist may produce very different analyses. Furthermore, Kahneman and Tversky have demonstrated empirically that probability is an area which humans are very poor at analyzing. In particular, when the same scenario from a probabilistic standpoint is presented in different terms (say to emphasize the potential gain in one instance and the potential danger in another), people will make different (i.e. logically inconsistent) choices.
So, science which rests upon statistical analysis is qualitatively different from that which does not (in that the conclusions it returns are indexed by a particular philosophical view), and thus our treatment of its conclusions as evidence should, likewise, be qualitatively different from that of evidence from other sources. In particular, we should be careful to consider our own philosophical position on probability and how it accords with the analysis of the data presented to us. Finally, evidence suggests that our innate sense on this question is very poor and subject to manipulation through framing effects.
next: subjective Bayes and the "fair coin"