Kramer was referring to 'undefined expressions'. Consider 'undefined probability'. As per wiki's probability.
First the definition of
"conditional probability" trades on, or depends on
p ∩ q
---
"Conditional probability is the probability of
q, given p."
"Conditional probability is written as below."
P(q|p).
"It is read
"the probability of q, given p".
"It is defined by
P(p ∩ q)
________
Pp
(Peter Olofsson,(2005) Probability, Statistics, and Stochastic Processes, Wiley-Interscience, p. 29).
And where
p ∩ q
is itself defined as
Pp MULTIPLIED BY Pq
-- From wiki: "If both p and q occur on a single performance of an experiment this is called the intersection or joint probability of p and q, denoted as "p ∩ q". If p and q are independent, the joint probability is Pp X [multipled by] Pq." "For example, if two coins are flipped the chance of both being heads is 1/2 X 1/2 = 1/4".
Where probability gets "undefined"
From wiki:
"If P(p) = 0, P(q/p
If P(B) = 0 then P(q|p) is [naturally] undefined".
Which may relate to Kramer's point about undefined expressions.
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Well, sure.
ReplyDeleteI think your wiki quote got garbled. If the probability of A, given B is to be determined, and the probability of B is 0, then we can't be given B, so the calculation is impossible.
As represented in your post:
P(p ∩ q)
________
Pp
If Pp=0, we are dividing by 0, which is undefined, so, naturally, the conditional probability where Pp=0 is undefined.
What an excellent comment:
ReplyDeleteKramer:
"If the probability of [q], given [p] is to be determined, and the probability of [p] is 0, then we can't be GIVEN [q], so the calculation is impossible."
Exactly. I like those quizes. We should get more of those. Imagine turning back the paper to the instructor:
"Impossible"
"Impossible"
"Indefinite"
"Undefined"
"Undefined"
"Impossible"
---
I think we got all garbled when Doctorow started quoting from the Stanford. It read, rightly that Grice is 'tracking'
the 'conditional probability of q, given p'.
-- where, exactly as Kramer points out, we should give proper consideration to 'given'.
Strictly,
consider
War is not war.
The probability is 0.
So, really, we cannot be 'given' "War is not war".
It's not that we asked for it, either.
I think philosophers overrate the 'given'. They call it a Datum -- a Modal Element. Peacocke, for example, is usually heard using "Modus", "Modal", Datum, etc. In Husserl it was even 'presupposition': "Philosophy without presuppositions" was the title of one of his books. As if that were possible!
We need a datum.
"the probability of q, given p"
----
In a way, it relates to other term philosophers, including Grice, use more often than not: 'ceteris paribus' -- other things being equal. I think I've read at least ONCE Grice granting, "but other things are, notably, NOT equal".
As with "Enough is enough," I don't find "War is war" tautological. What we have is one actor in two roles:
ReplyDeleteIn tonight's presentation of "War Sucks," the roles of Armed Conflict between Nations AND of Actions taken by Nations when in a State of Armed Conflict will both be played by the word "war."
And don't get me started on women.
YOu need to flesh it out with black and white balls in an urn, or some dice tossing, or the actuarial table, JLster! Serio, while conditional probability has some relation to logic (related to inclusive OR vs exclusive, right), bringing in the conditional probably serves to bemuddle things; for that matter, the axiomatic probability--like Kolmogorov (a bit beyond conversational imp.s)--while rather elegant (when you, or if you work through proofs..buena suerte), has limited application. Kolmogorov might work, with circuitry, or very well-defined discrete events. Not for inoculation in a jungle, or GDP over the last 20 years, or urban poverty .
ReplyDeleteWhich is to say, probability theory (or Jr's Stats 101 at Peoria JC) works well for dice, death ratios, or maybe Wisconsin dairies, but barely works at all with..the weather, or stock market, or any stochastic phenomena...(scuzi rant)
Okay, Kramer and J.
ReplyDeleteI'll start with some simply stochastic phenomenon.
Women are not women.
No, women are women.
ReplyDeleteBut
~(women are not women)
is not necessarily the same thing as
women are women.
That's because, in natural language, the apparent tautology demands the implicature of different usages:
Members of the female sex are people with the stereotypical attributes of members of the female sex.
Why don't men ask for directions?
Because men are men.
But the negation of the apparent tautology is nonsense, and no convenient implicature can save it, so we don't translate it as:
Members of the female sex are not people with the stereotypical attributes of members of the female sex.)
Thus, the negative version of the actor does not play the negative of the role. Something like "Not all women are women" might do, but now we're performing La Cage aux Folles...
N'est-ce pas?
Women are women.
ReplyDelete+> (Kramer's gloss)
"Members of the female sex are people with the stereotypical attributes of members of the female sex."
Thank you! Took me some time to decipher that! Grice never gave a gloss!
He irritatingly just paired it with the totally different thing, 'War is war':
"Extreme examples of a flouting of the first maxim of Quantity are provided by utterances of patent tautologies like Women are women and War is war. I would wish to maintain that at the level of what is said, in my favoured sense, such remarks are totally
uninformative and so, at that level, cannot but infringe the first maxim of Quantity in any conversational context. They are, of course,"
--- not MY course!
"informative at the level of what is implciated, and the [addressee -- not me!]'s identification of their informative content is dependent on his ability [not mine!] to explain the [utteer]'s selection of this particular patent tautology".
I conceived the scenario. During the sinking of the Belgrano, by Margaret Thatcher:
"And her policy should be taken to the Convention of Geneva?"
-- (a) "Well, women are women."
-- (b) "Well, war is war".
Kramer proposes this gloss as the conversational implicatum for Grice's out of the blue example, "Women are women":
ReplyDelete"Members of the female sex
are people with the
stereotypical attributes
of members of the female sex."
----- Yes. That seems to do. Not necessarily YOUNG members, though?
Geary has noted that
"Girls will be girls" can be offensive.
Whereas he has claimed that 'will be' (in "Boys will be boys") is timeless. Dunno.
"Members of the female sex are people with the stereotypical attributes of members of the female sex."
ReplyDeleteAha.
Kramer proposes the good variant:
A: Why don't men ask for directions?
B: Because men are men.
--- I suppose the enthymeme then is to retrieve what stereotype applies to each scenario.
I also see the point that by committing yourself to nothing really ("Women are women", "Men are men") you are saving yourself from the putting yourself in the uncomfortable situation of having to explicitise [sic] what stereotypical attribute applies.
I should do a google hit and report what the implicatures are in the first ten hits -- for "Women are women" and report back. Or something. I hope it's a nice stereotypical attribute.
ReplyDelete