Grice, Dummett and Kripke on conditional probability and appropriate assertability

--- by JLS
---- for the GC

As we have seen, thanks, inter alia, to Doctorow's interest on this (vide "Probably Grice", this blog), there's Grice's paradox: Yog and Zog playing chess. Grice quotes Dummett and Kripke on conditional probability vs. probability of a conditional. Doctorow aptly refers to the entry by the Richards (Grandy and Warner) on Grice in the Stanford.

Richards write:

"Symbolically, A → B should not be asserted in
circumstances where the speaker knows that A is
false because the statement not-A is true and
simpler; similarly, if the speakers knows B
is true, B is a shorter simpler statement; and if
the speaker knows both of those facts, then not-A and
B, is more informative. Thus the only circumstances
in which the conditional is appropriate is
where the speaker is ignorant of the truth
values of A and B, but has some good reason to
think that if A does prove to be true, B will
as well. On this account, the truth conditions of
the conditional are those of the material
implication, but the appropriate assertibility of
a conditional tracks the conditional
probability of B given A."

Rewritten:

"'p ) q' should not be [uttererd] in circumstances
where U thinks p is false (because the statement "~p" is true and simpler). Similarly, if U thinks q is true, q is a shorter simpler statement. And if
U thinks that both of those facts hold, "~p /\ q" is more informative. Thus
the only circumstances in which "p ) q" is appropriate is where U does not think he knows the truth values of p and q, but has some good reason to think that if p does prove to be true, q will as well."

It is in the next sentence that the Richards manage to quote (if not Dummett and Kripke on this) at least Grice on 'conditional probability'. Again rewritten:

"On this account, the truth-conditions of "if p, q" are those of "p ) q", but the appropriate assertability of "if p, q" tracks the conditional probability of q given p".

--- Grandy has expanded on this in his "Legacy of Grice" contribution back in 1991, at Berkeley, repr. in K. Hall, Berkeley Linguistics Society. Grandy's essay in K. Hall is concerned with Strawson's alternatve view of "if p, q" as involving a CONVENTIONAL rather than a conversational implicature. Grandy and Warner were fortunate to have Strawson agree to have his "If and )" reprinted in the Grice festschrift.

I have a good recollection of this. I was being taught by Edgington on the lack of truth-values of 'if p, q' -- and during an interlude, I took her to the library, and showed her the Grice festschrift. Apparently, she was unaware that Strawson's thing had been published there. But with Eddington I learned many other interesting views some of which had some overlap with Strawson.

There is, for example, J. L. Mackie. This is credited by R. Walker (in "Conversational Implicature") as the most complete Griceian treatment of 'counterfactual conditionals'. Then there's Lewis -- repr. in his Philosopical Papers. The Australian infuence of Lewis is seen in Jackson, whose study of conditionals I find of great interest and subtlety and doing justice to Grice's puzzles on this. Appiah, too, has considered the 'conventional-implicature' view as it overlaps with the rather terse dictum by the Richards that "the appropriate assertability" "tracks the conditional probability of q, given p".