# FOM: Boole, Probability, and Material Implication

Robert Black Robert.Black at nottingham.ac.uk
Thu Jun 21 15:43:36 EDT 2001

```Well, you may know this already, but I think the key article on the topic
is David Lewis's 'Probabilities of Conditionals and Conditional
Probabilities', _Philosophical Review_ 1976, reprinted with a postscript in
volume 2 of Lewis's _Philosophical Papers_. The main point is that,
roughly, not only are conditional probabilities not the probabilities of
material implications, i.e. truth-*functional* conditionals, they can't be
the probabilities of *any* sort of conditionals with truth-*conditions*:
there is *no* sense of 'if' such that uniformly p(C/A) = p(if A then C).

Robert

>
>Theodore's Hailperin in *Boole's Logic and Probability* makes the
>point that Boole seemed confused over the difference between
>conditional probability and the probability of a implication
>statement. If he did, he probably inherited it from Bayes and
>Laplace.
>
>E. T. Jayne in his "cult", on-line probability text
>*Probability Theory: The Logic Of Science* at
>http://bayes.wustl.edu/etj/prob.html also discusses this issue of
>confusion over conditional probabilty and implication statements.
>
>Does anyone have references to discussions of this issue. My naive
>contention is that Bayes rule is not a proper translation of material
>implication although it is proper for subjective implication.
>
>
>steve

Robert Black
Dept of Philosophy
University of Nottingham
Nottingham NG7 2RD

tel. 0115-951 5845

```