Plausibly, when we adopt a probabilistic standpoint any measure Cb(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) Cb(h,e) > 0 when P(h/eb) > P(h/b; Cb(h,e) < 0 when P(h/eb) < P(h/b); Cb(h,e) = 0 when P(h/eb) = P(h/b).
(2) Cb(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 Cb(h,e) ≤ Cb(h,f); if P(e/hb) = P(f/hb) and P(e/b) < P(f/b) then Cb(h,e) ≥ Cb(h,f).
(4) Cb(h,ef) – Cb(h,eg) is fully determined by Cb(h,e) and Cbe(h,f) – Cbe(h,g); if Cb(h,ef) = 0 then Cb(h,e) + Cbe(h,f) = 0.
(5) If P(e/hb) = P(e/tb) then Cb(h,e) = Cb(t,e).