In formal epistemology, consistency condition states that:
An evidence E can't confirm both H and its negation, not-H.
Carnap states that for the concept of absolute confirmation, the consistency condition holds:
if E confirms H iff P(H/E)>k for a certain k in [0,1], then consistency is valid.
But i do not get why this should be so:
For instance, we know that P(H/E) = 1 - P(not-H/E)
if P(H/E)>k, then 1 - P(not-H/E)> k, and so P(not-H/E)< 1 - k.
But it could happen that 1-k<k, for example when k=0.2. We can have that P(H/E) = 0.3 and so P(not-H/E) = 0.8. Then 0.3>k, and also 0.7>k, so the consistency condition would be false. What am I missing here?
