Abstract: What is the relationship between probability and confirmation? Carnap and modern
Bayesians, among others, have claimed that confirmation should simply be identified as
probabilistic favourable relevance. In other words, evidence e confirms hypothesis h if
and only if the probability of h given e is greater than the probability of h in the absence
of e. Conversely, evidence e is irrelevant to h when the probability of h given e is identical
to the prior probability of h without e. This paper shows through examples that this yields
unsatisfactory accounts of the intuitive notion s of confirmation and irrelevance. To
determine the relationship between confirmation, irrelevance, and probability we need to
first gain a better understanding of logical content. With such an understanding in hand we
can then define more fine grained notions of confirmation and irrelevance in probabilistic
terms in a way that captures our intuitive notions of confirmation and irrelevance. It is
further shown that this better understanding of logical content allows for a definition of the
long problematic notion of empirical significance. This further allows us to see why attempts
to define empirical significance in terms of confirmation relations are fundamentally
misguided.