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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?

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  • For consistency to hold for absolute confirmation, is one of the assumptions k ≥ 0.5? – Adam Sharpe Feb 22 at 17:56
  • Honestly, I do not know. From my source it is not specified, and I am reading Chap. 6 of Foundations of Bayesianism by Titelbaum. – PwNzDust Feb 22 at 20:34

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