--- by JLS
------ for the GC
--- SORRY FOR THE CUMBERSOME title, but I may edit it. I wanted to bring to attention this quote by Carnap/Bar-Hillel in Floridi's online entry on information. I relate it to Grice when he says
War is war
Women are women -- (Grice, WoW:ii)
as totally UNINFORMATIVE. I follow him there, and I quote myself in the title because in written work Floridi was kind enough to credit me (!).
Now, the quote I provided to Floridi, and which he did use: is "False information is no information" by Grice (WoW:RE). Floridi makes good use of this, -- and indeed quotes from Carnap as to the following.
If the two sentences above, as Grice notes, are totally uninformative (at the level of what is 'semantically' said, i.e. 'semantic information' in Carnap/Bar-Hillel's sense) then what about
War is not war
Women are not women.
This is what Carnap/Bar-Hillel write and what Floridi brightly calls the "paradox" -- 'with a bit of a hyperbole', he writes: "too informative to be true". It seems Carnap would do with being refreshed by Grice that 'false information is NO information' (the wording by Grice is clumsy but we know what he means -- strictly: "False so-called 'information' is NO information").
Carnap/Bar-Hillel:
"It might perhaps, at first, seem
strange that a self-contradictory
sentence,"
War is not war.
Women are not women.
"hence one which no ideal receiver would accept,"
as per theoretical pragmatics -- none wich an ideal receiver would ASSERT.
"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."
Which seems to be JUST their sense.
"Whether the information it carries is
true or false, scientifically valuable or
not, and so forth, does not concern us."
Then perhaps QUANTITAS has nothing to do with 'informativeness'. Grice plays in 1961 with the idea of defining quantitas (a strong move, versus a weak move) in terms of entailment:
Where is your wife? (in Bayne's website, Grice 1961)
-- In the garden or the kitchen
------ In the garden
------ In the kitchen
p v q --> p
p --> p v q
----
But with other examples, no way to define informativeness in terms of entailment is possible:
What colour is the pillar box?
Red.
--- It SEEMS to be red.
Neither "It seems to be read" nor "It IS red" entail the other.
----- cfr. O'Hair, cited by Harnish, "Logical form and implicature".
Carnap/Bar-Hillel end the passage cited by Floridi:
"A self-contradictory sentence asserts
too much; it is too informative to be true."
(p. 229) -- Literally. I.e. it is NOT informative, strictly. It is MIS-informative, rather.
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I'm not sure that I like the use of the word "information" here.
ReplyDeleteMainly because it potentially muddles up two different measures.
Information is what you get in Shannon, measure in bits and bytes and bandwidth (and some say entropy).
This has a quantitative measure, which is a very special kind of linear ordering.
There is another word which we could use instead of "information" when talking about the stuff we get in propositions, and that is "content" (there may be others but thats the one which comes to mind).
If we take the Grice's "central significance" to be truth conditions, and regard them also as a minimal content of propositions, then we do get a natural partial ordering which corresponds to entailment.
If A entails B then A has greater content.
But this time we don't have a quantitative order, not even a linear order.
So long as this is an order on all propositions (true or false, consistent or incoherent) then it has a maximum which is the contradictions (i.e. all the propositions which share the truth condition "everywhere false", of which there are more than one only if we admit that a proposition has more to it than truth conditions).
I think this separation goes some way to resolving the apparent "contradiction" (which I think really is only apparent). If you confuse the entailment ordering on content with a quantitative measure of information then it is odd to get more information from a contradiction. But if you clearly distinguish the ordering by entailment from anything to do with quantity of information it goes away.
There is a residual "paradox", the one to do with material implication (which I also don't think a real paradox), i.e. the little concern about everything being implied by false.
RBJ
Excellent commentary, and I trust Floridi will read them. What's the point of bringing, grandiosely, a paradox, and leaving it like that? Anyway... He was just writing for an online source, and he had to be brief. I do think he has expanded on this in other publications and stuff.
ReplyDelete----
I loved your distinctions, and the idea to go by 'byte'. In my PhD I entitled that section (at some stage): 'byte by byte'. When dealing with Grice's Quantitas.
I agree with you and Grice that the paradox of 'material implication' is nowhere to be seen. Put the blame on Philo (of Megara).
-----
I would NOT know why Grice focuses so much on
"It seems red to me"
and
"It IS red"
if he cannot claim 'entailment' via 'content' or 'information'. The two sentences seem to be about such disparate 'states of affairs'! But of course I get his point.
Carnap and Bar-Hillel should be given a lot of credit, and also Floridi, for bringing this apparent 'paradox' to the formu, though. It is _fun_ and thought provoking. It may even provoke the thought of my aunt.
----
Bar-Hillel was born in Vienna, and studied with Carnap in Chicago. If that's not cosmopolitan I don't know what is. Genius.