-- by JLS
-- From wiki, 'probability':
"In mathematics, a probability of an event A is
represented by a real number in the range from 0 to 1
and written as P(A), p(A) or Pr(A).[6] An impossible
event has a probability of 0, and a certain event
has a probability of 1."
Grice liked to amuse himself going Cartesian. There is this 1965 essay he wrote on "Descartes on 'clear and distinct perception' which he cared to keep and reprint in his book with Harvard UP. (The contract with Harvard was for the publication of the William James Lectures, only, delivered at Harvard -- but he managed to get some 200 extra pages with his earlier 'unpublications').
In the "Descartes" essay, which SHOULD be reprinted in the "Cartesian Journal" if there is one, distinguishes, aptly, between:
"I am certain she is a darling"
and
"It is certain she is a darling."
---- What IS the distinction?
Grice calls the first 'subjetive certainty'; and 'objective certainty' the second, but his labels can mislead. So let us stick to his words:
""Certain"", Grice notes,
"occurs in at least two distinguishable
contexts: (i) "it is certain that p" (label this
"objective" certainty), (ii) "x is certain that
p" (label this "subjective certainty"). Perhaps,
then, Descartes is subscribing to TWO rules
(conflated): (1) whatever is clearly and
distinctly perceived is objectively certain, (2) whatever
is is objectively certain is true."
-----
A problem for Descartes:
Grice goes on:
"While it MIGHT be legitimate to define
'x is certain that p' as 'x clearly and
distinctly perceives that p', it owuld not be
SO ATTRACTIVE to attempt to define 'it
is certain that p' (objective certainty)
in terms of clear and distinct perception. Indeed,
the problem about certainty might be posed as the
question when and how a step from "I am
certain" to "it is certain" IS justified."
(WoW: 192).
---- Grice's secret heart of the sceptic one can hear beat:
"The question might arise whether the achievement
or procedure has after all been successfuly realised,
whether something may not have gone wrong, and if
such a question is not disposed of, we are NOT
in a position to say "it is certain that p," even
though IN FACT nothing MAY have gone wrong. ..."
Back to the wiki:
"In mathematics, a probability of [p] is
represented by a real number in the range from 0 to 1
and written as ... p(p). ... An impossible
event has a probability of 0, and a certain event
has a probability of 1."
---- Why not 'incertain' or 'uncertain' for 'im-possible'? Because of the implicature. Why not 'necessary' for 'certain' -- because of Kripke!
---
Wiki:
"a certain event has a probability of 1"
This may be back to Grice's patent tautologies -- or not so patent:
"Women are women" (I was led to write that as "Women is women") and
"War is war"
Probability: 1
---
"War is not war".
Probability: 0
--- back to the Carnap-Bar-Hillel paradox:
"It might, perhaps, at first, seem
strange that a self-contradictory sentence,
hence one which no ideal receiver would accept, is
regarded as carrying with it the most inclusive information. It
should, however, be emphasized that semantic information
is, here not meant as implying truth. A false sentence
which happens to say much is thereby highly informative
in our sense. Whether the information it carries is
true or false, scientifically valuable or not, and so forth,
does not concern us. A self-contradictory sentence
asserts too much; it is too informative to be true
(p. 229)
which should explain Grice's maxim,
"Do not be more informative than is required" rendering yet another lovely affair of Quantitaet with the more basic (some think) Qualitaet.
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"War is not war".
ReplyDeleteProbability: 0
What is the probability of
(a2-b2)/(a-b)=a+b
Are you allowing for the possibility that a=b, in which case the expression is undefined? Where a=b, does (a2-b2)/(a-b)=a+b create a truth-value gap? (I hope not, as I don't believe there is such a thing.) But what then? If we assume that a=b 10% of the time in any particular environment, the probability that (a2-b2)/(a-b)=a+b is .9. But the probability that it is false is 0. Is that what makes truth-value gaps troublesome?
More later.
Yes. And undefined expressions, too! But more later, I hope. Horn once wrote a paper whose title had to be explained to me:
ReplyDelete"Showdown at Truth-value Gap". It was meant as an irony on some sort of westerns he'd seen, he'd see -- where there is usually a showdown at gap. I believe the irony or pun was at one specific western, and I forget if he cared to mention which in the body of the essay.
Grice feared those gaps, too.
There is a Western called "Showdown at Eagle Gap." There may be others; it's very clichéd.
ReplyDeleteThe "more later" I had in mind relates to degrees of certainty.
If I say that I am 70% certain of p, I think I mean that when, in the past, I have felt that something was true with the same degree of conviction that I feel about p, I have been right about 70% of the time. Of course, if you ask me how certain I am of that statistic, I have to say some other percentage, and from there it's turtles all the way down. Still, paradoxically recursive or not, it's what I think I mean.
So if I get to 100%, I mean that every time I have been thissure of something, I have been right. As for when "I am certain" becomes "it is certain," I think that's a false dichotomy. "It is certain" means "If you think about this, take p as a premise." "I am certain" means "My thinking on this includes p as a premise." The difference lies in U's purpose, not his commitment to p.
Mmm. Should elaborate.
ReplyDelete"Difference in U's purpose then?" Why not porpoise then -- since it's turtles all the way down with you?
(Recall Carroll: Would you walk a little faster, said a whiting to a snail: there's a porpoise right behind me and he's treading on my tail")
U's purpose in uttering,
"I am certain that p": "My thinking on this includes p as a premise"
U's purpose in uttering:
"It is certain that p": "If A[addressee] thinks about this, take p as a premise".
But would you say one 'implicates' the other?
When an uncle says "It is certain that p" I don't think he is being charitable as to what his nephew should think -- but I may be wrong.
On the other hand, uncles rarely say, "I'm certain" -- do they?
But I do like Kramer's point: "I am certain", having a focus and topic on "I" and providing the comment, "am certain about p" is all about you.
"It is certain that p" may allow for two collocations: the it-focused version that Grice gives and a less-ejaculatory one: "That it rained is certain".
With the proper subject of '... is certain' properly expanded it is less obvious that this relates to one's addresee?
And in any case, wouldn't one entail the other?
It would be otiose, and slightly cruel, to have different standards of 'certainty': one for me, and one for you. I am trusting that if I say "it is certain that p" I SHOULD include "I am certain".
But the implicature may be in the choice as to how much you want to project this 'hollier than thou' attitude.
Wittgenstein 'wrote' a posthumous book on this, "On certainty". "It is certain that you have a toothache", he thought, I think, 'verbose', if not impossible?
While I elaborate on this, and thanks to Kramer for his input, it seems obvious (if not certain) that was Grice is having in mind midway between:
ReplyDelete"I am certain that p"
and
"It is certain that p"
is that hateful parenthetical: "to me"
"It is certain to me that p"
which is then dropped ad libitum.
The problem seems to be Gettier's. There's unknowable unknowns and knowns unknowns. Etc.
"It is certain" SOUNDS like "It is a well-known, or 'known' simpliciter, fact, that ..."
---
On the other hand, I think it is by quoting Ayer, "Empirical Knowledge", that Gettier starts his paper.
Surely, -- and we have discussed this elsewhere with Kramer, -- notably in Theoria vis a vis his report of Meryl Streep's film, "Doubt" --, Sister A. can be CERTAIN that p, but still wrong.
On the other hand,
"It is certain to me, but not to you, that p"
sounds patronising.
Note that the way to go seems to be:
"It MAY be certain to you, but not, alas, as certain to me as it is to you, that p".
"Sure" fares no better.
Descartes should have read Gettier -- or not!
(For Gettier, even having 'A knows that p' as 'p is true', 'A has justified adequate evidence for p' and 'A believes that p' is NOT enough. -- and "It is certain that p" seems to ENTAIL, 'p is known', and, therefore, 'p is true'?)