Other blog posts:

• _{Mon, 24 Jun 2010 Suggestion to improve ASDF}
• _{Mon, 24 Jun 2010 Experience with libraries}
• _{Wed, 19 Jun 2010 Finally have rss}
• _{Tue, 18 Jun 2010 About the recent proof that Absence of evidence is evidence of absence}
• _{Tue, 18 Jun 2010 My blogging system sucks}
• _{Tue, 18 Jun 2010 Type calculation}

The problem is in the definitions,(not in the equivalence steps) the first one is reasonable P(B|A)>P(B|¬ A) finding A true is evidence for B is reasonable. P(B|A) can be stated as 'the probabilty of B given that A is true', so the whole statement can be stated as: 'the probabilty of B given that A is true, is bigger then if A is not true.'

But the two definitions following are simply not reasonable; there is no reason to say that ¬ A is 'absence of evidence' or that ¬ B is 'absence'. Those are just the statements that A is false, and B is false, not absence of anything.

With that, there is no longer a definition of evidence of absense in the article, so it can't make the mathematical claim connect to the connotation that attaches to it.

Indeed, we can spell out the statement of the equivalence like we did before:

P(B|A)>P(B|¬ A)	A is evidence for B
P(¬ B|¬ A)>P(¬ B|A)	A being false is evidence for B also being false.

The equivalence the article proofs does in no way sound like 'About the recent proof that Absence of evidence is evidence of absence'

Absense of evidence is evidence of pointlessness.

I am sure there is a proof that for statements A for which P(B|A)=P(B|¬ A) is essentially ignored by rational agents in the sense of the interpretation of probability.

The definition of rational agent there is essentially that rational agents act/bet according to the probabilities they assigned to things, and that they cannot consistently lose with the way they bet.(If they can, they're by this definition, not rational.)

Notes