log[P(h/eb)/P(h/b)] Is the One True Measure of Confirmation

Plausibly, when we adopt a probabilistic standpoint any measure C b ( h, e ) of the degree to which evidence e confirms (or is evidentially relevant to) hypothesis (or theory) h relative to background knowledge b should meet these five desiderata: (1) C b ( h,e ) > 0 when P ( h / eb ) > P ( h / b ; C b ( h,e ) < 0 when P ( h / eb ) < P ( h / b ); C b ( h,e ) = 0 when P ( h / eb ) = P ( h / b ). (2) C b ( h,e ) is some function of the values P (·/ b ) and P (·/· b ) assume on the at most sixteen truth-functional combinations of e and h . (3) If P ( e / hb ) < P ( f / hb ) and P ( e / b ) = P ( f / b ) then C b ( h,e ) ≤ C b ( h,f ); if P ( e / hb ) = P ( f / hb ) and P ( e / b ) < P ( f / b ) then C b ( h,e ) ≥ C b ( h,f ). (4) C b ( h,ef ) – C b ( h,eg ) is fully determined by C b ( h,e ) and C be ( h,f ) – C be ( h,g ); if C b ( h,ef ) = 0 then C b ( h,e ) + C be ( h,f ) = 0. (5) If P ( e / hb ) = P ( e / tb ) then C b ( h,e ) = C b ( t,e ).