Grice's Paradox: Grice on 8/9, 1/2 and 9/10 and the probability of "if p, q" -- rather than the (implicated) conditional probabiliy of q, given p

by J. L. S.
for the GC

DOCTOROW aply quotes from the precis on Grice's thought in the entry for the Stanford by the Richards (Grandy and Warner) -- cfr. Grice, Reply to Richards:

"the implicature [of if p, q] tracks the conditional probability of [q] given [p]", they write and right they are too. This is a conversational implicature for Grice, Lewis and most; a conventional implicature for Jackson.

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Conditional probability thus does enter the picture. But Grice is more concerned with 'entailment' of "if p, q" and the paradox of contraposition -- at least in the latter bit of his fourth William James lecture to which the Richards refer.

On p. 78, he has a special section, which he calls "Grice's paradox" and concerns 8/9, 1/2, and 9/10, and how you have to mind not just your ps and qs but their probabilities, too.

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Here Grice uses "h" for the evidence -- which relates to the principle of Total Evidence as had been used by Davidson, and which Grice will later apply to practical arguments (via desirability, as well) later in the Kant lectures of 1977.

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Grice formulates his paradox as follows:

"Yog and Zog play chess according to normal rule, but with two special conditions: (I) Yog as white 9 out of 10 times, and (II) there are no draws. To date there have been 100 games and the following held: (a) When white, Yog won 80 out of 90 games, and (b) When black, Yog won 10 out of 10 games. They played when of the 100 games last night. The Law of contraposition states that "if p, q" is equivalent to "if ~q, ~p". So, seemingly, the probabilities are: (i) 8/9 that if Yog had white, Yog won; (ii) 1/2 that if Yog lost, Yog had black; (iii) 9/10 that either Yog didn't white or he won. -- What is to be done? Abandon the Law of contraposition."

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It is then that Grice cares to mention Dummett and Kripke. No references given so we assume they were at Harvard. Dummett incidentally will later the William James lectures himself ("The logical basis of metaphysics", which really is the metaphysical basis of logic). Grice knew Dummett since his VERY early Oxford days (Dummett had made a lot of enemies at Oxford since his rather 'vulgar' it was called paper for the Greyfriars -- 'vulgar' as Gellner was thought 'vulgar' in his attack. Grice has a note where he points (in the Grice collection) that Dummett was never accepted in the Play Group). Kripke will later be criticised by Patton (in unpublished work he allowed to share with the Club) as misinterpreting Grice in his 'semantic reference' versus 'speaker's reference' paper.

Grice writes:

"Dummett and Kripke suggest that we distinguish between I and II."

"I. the notion of the probability of a conditional relative to certain evidence h, a notion which is NOT altered if, for that conditional, we substitute the standard counterpositive, or, for that matter, its standard disjunctive countepart."

"For:

(if p, q)/h

is equivalent to

(if ~q, ~p)/h

and also to

(~p v q)/h"

II. "the notion of CONDITIONAL PROBABILITY as it is
exemplified in the probability of p, relative to
both q and h -- a notion which cannot
be treated as identical with the probability of
the negation of q, relative to the conjunction
of the negation of p and h."

"Further, they suggest that the puzzle about Yog
and Zog should be taken to relate to
CONDITIONAL PROBABILITIES and not to the
probability of conditionals."

But Grice suggests this is not so.

-- How Grice solves the Grice paradox:

"The [puzzle] is solved if we assume that

"if p, q" is (as I have suggested) naturally

adapated for (looks forward ) a possible

employment of modus ponendo ponens."


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"We then think that the background information

we would use if given the second premise"

--

To wit:

"Yog had white"


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"(when we would not, of course, consider that happened

when Yog had black)"

---.


"Similarly, if we are asked the PROBABILITY that

if Yog did not win, he did not have white, and if we take

this question to "look forward" the possession of

informtion that Yog did not win, we consider ONLY

what was the case when Yog did NOT win (as regards his

having white OR black) and IGNORE [or disregard. JLS]

cases in which Yog won."

---

"If we are asked the PROBABILITY that Yog

either did not have white or won, there is NO

direction (pointeering) to modus ponendo ponens,

so we consider the whole series of games which

were either ones in which Yog had black or ones

in which Yog won."



------------------ Grice, WoW, p. 80.



Mackie (early in 1972) had adopted Grice's conversational manoeuvre (i.e. the emphasis on the conversational implicatum) as regard counter-factive conditionals, "if p, q" for modes other than the indicative. Lewis brought the news to Austrlalia where it paid with Jackson who abandoned (but not for good) the conversational implicatum view and adopted a less beautiful 'conventional implicatum' view -- the term 'beautiful' I borrow from Strawson, 'If and )': "Grice's theory may be more beautiful, but mine is more boringly true" (or words). Good researchers who do this (Velasco, Adams, Stephen Barker, etc.) HAVE to go back to Grice to reconsider -- and good researchers -- as Arlo-Costa in "the logic of conditionals" (Stanford encyclopedia entry) will take up the notion of 'appropriate assertability' referred to by Grice and by the Richards in their entry for Grice for the same encyclopedia -- and which was quoted by Doctorow in his "Probably Grice".