When is it possible to decide that a theory is confirmed by the availa
ble evidence? Probabilities seem first to be the good framework for ad
dressing this question. But the philosophers of science did not succee
d in building any probabilistic criterion of confirmation beyond dispu
te. We examine two of the main reasons for this failure. First, the pr
inciples of adequacy used by philosophers are often logically inconsis
tent with each other. We show in the paper how to build consistent sub
sets of these principles. We identify three main subsets which embody
the principles of adequacy for two main kinds of confirmation, namely
the relative confirmation and the absolute confirmation. Second, we pr
ove the impossibility of building any probabilistic criterion for abso
lute confirmation.