--- the truth-value gap, that is.
----- By J. L. Speranza
------- for the Grice Club.
KRAMER, in comment to "Two senses of 'certain'?", expressed his antipathy, which I share, for truth-value gaps. Having referred to Noel Burton-Roberts and Horn's showdown at truth-value gap, I offer:
Grice:
"There is, indeed, something UNNATURAL
about assigning a truth-value, as far
as ordinary discourse is concerned,
to statements made by means of
sentences containing vacuous descriptions".
-- or for that matter, to statements made by means of sentences containing nonsense:
as in the title of Pantagruel's book, "Whether chimeras should eat secondary intentions".
----
Here, Grice did some editing. "Presupposition and conversational implicature" had first appeared elsewhere, in Cole (and had circulated even earlier in mimeo form). Grice deleted a precis of the implicature theory, but kept the 'Now'. Page 270 thus reads:
"Now, what about the present king of France? As far
as I could see, i the original version of Strawson's
TRUTH-GAP [sic]
theory,
[rightly so, because adding 'value' every time can be fastidious. JLS]
he did not recognise any
particular asymmetry between [affirmative and
negative]" -- to his loss, of course.
The comments by Grice on the truth-value gap as originating metaphysical puzzles lies elsewhere.
They connect with his emphasis at the beginning of "Logic of Conversation" on his desire to stick with "a standard two-valued interpretation" for ~, /\, /\, and ):
"It is a commonplace of philosophical logic that there
are, or appear to be, divergences in meaning between, on the
one hand, at least some of what I shall call the formal
devices -- ~, /\, \/, ), (Ax), (Ex), (ix) (WHEN THESE
ARE GIVEN A STANDARD TWO-VALUED INTERPRETATION --
and, on the other, ... 'not', 'and', 'or', 'if', 'all', 'some'...
and 'the'". (WoW, p. 22)
----
FOR: Try to see if you succeed in making sense of "if" in trivalent logic!
---
For one, the wiki entry for 'ternary logic' stops at 'p v q':
p ----- q ------- "pvq" ---- "p/\q" --- "~p"
True -- True ---- True ----- True ----- False
True -- Unknown - True ----- Unknown -- False
True -- False --- True ----- False ---- False
Unknown True ---- True ----- Unknown -- Unknown
Unknown Unknown - Unknown -- Unknown -- Unknown
Unknown False --- Unknown -- False ---- Unknown
False - True ---- True ----- False ---- True
False - Unknown - Unknown -- False ---- True
False - False --- False ---- False ---- True
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It seems to me that we must include at least some implied propositions when assigning truth values of explicit sentences.
ReplyDeleteShe is poor but she is honest has the implicature that poor women are often dishonest, but that implicature is not necessary to determining whether she is poor and she is honest. In contrast The King of France likes sushi implicates (or does it entail?) that there is a King of France, and the truth of that proposition is necessary to determining the truth of the explicit statement. Is there a term of art for this distinction? The existence of the King of France seems non-cancellable, whereas the the thing about poor and honest seems like it might be (although it would be awkward). Is "entail" the right word? "Imply"?
Anyway, I wonder if the "unnatural" problem of assigning truth values to statements with vacuous descriptions isn't solved by a rule that such non-cancellable premises be included in the statement for purpose of testing its truth:
There is a king of France and if there is a King of France, he likes sushi.
That sentence is false if there is no king. IS there a reason not to treat it as the role and te king of France likes sushi as the actor in testing the role's truth value? Isn't the truth of the logically necessary assertions what matters, however they are asserted.
Good. I would think, as per the post I posted when I had an interim in reading the commentary, and posted as "implies", "entails" and "implicates" -- or something -- the strategy seems to be:
ReplyDelete"The present king of France loves sushi"
---- ENTAILS 'there is a present king of France'
To echo Grice, differently: "This looks like 'logical implication'".
On the other hand, the NEGATIVE version is BOUND to implicate an implicature:
"the present king of France does NOT like sushi -- never mind, 'love' -- France has been a republic since 1789. I mean, there is NO king of France'.
I think the problem IS tricky. Strawson, possibly, was thinking of Collingwood. Presuppositions CAN be fun. And in any case, he merited a reply from the Grand Lord of Logic himself, "Mr. Strawson on referring" (Russell).
ReplyDeleteMost of this had already been discussed, to tears, bitter ones -- by the inceptors and others in the universities of Paris, etc. It was called "suppositio" rather than 'pre-suppositio" and I think Kneale covers pages about it in his "Development of Logic" (a thick book with Clarendon -- which grew from Oxford lectures better entitled, "Growth of Logic").
The mediaevals called it a 'pregnant' premisse. One example was:
"You have not ceased to eat iron since I saw you today" (Tu non cessas comedere ferrum). This transpires in Grice as
"You have not stoped beating your wife"
----
In the case of 'You have not stopped beating your wife', the 'suppositio', however, pertains more to 'presupposition' proper than implicature.
The example, "She was poor but she was honest" was Grice's use of this pretty funny song from the Great War ("'Tis the same the whole world over'").
He would say the thing conventionally implicates a contrast -- and would NOT be cancellable. As Kramer says, 'awkward' to go: "But I don't mean she is in any way the exception to the rule" or something.
In the case of a genealised conversational implicature proper of a statement or utterance involving a definite description -- it being expanded to a triple clause A: there is at least an entity S that is P; B: there is at most an entity S that is P, and C: Whatever is S is P -- the rule seems to be to get the first two clauses as being immune to negation.
So that when you add the "~" you apply it to the last conjunct, "Whatever is S is P". Thus, "The king of France does not favour sushi" is heard as disagreeing with Partner at the predication of this further property P, rather than objecting to the unique existence of S. Or something.