ABSTRACT
It is an appealing thesis, which has rightly tempted many authors, 175 that probabilities o f conditionals are conditional probabilities, in symbols,
(6 ) P (A > B ) = P (B , A) for every wff A and B ,
for a (suitable) conditional connective > . 176 Call such a conditional a probability conditional (for function P ). Hardly surprisingly, such a conditional must be different from the material conditional, for P (A D B) and P ( B , A ) coincide generally only for extremal values. Rather more surprisingly, the connective > must differ from most other studied conditionals. However we should expect to ‘discover a good deal about’ the logic and semantics of a probability conditional ‘just by using what we know about conditional probabilities’. Exactly this obvious procedure, which Lewis suggests (p.298), will be applied to locate a probability conditional.
