--- by JLS
---- for the GC
Grice is a harmless two-valued logician (I am amused that the Merriam-Webster online dictionary, Heritage, defines Grice as a "British logician" -- he never taught the Wykeham!).
There is a good problem, which R. B. Jones does not think too problematic, which I read in Floridi's Stanford entry for "information":
"The Bar-Hillel-Carnap Paradox. Insofar as they subscribe to the Inverse Relationship Principle, the extensionalist approaches outlined in the previous section can be affected by what has been defined, with a little hyperbole, as the Bar-Hillel-Carnap Paradox (Floridi [2004b]). In a nutshell, we have seen that, following IRP,
the less probable
or possible p is the more semantic information p is assumed to be carrying."
"This explains why most philosophers agree that tautologies convey no information at all, for their probability or possibility is 1."
Grice has two examples here:
War is war.
Women are women.
"But," Floridi notes, "it also leads one to consider contradictions — which describe impossible states, or whose probability is 0 — as the sort of messages that contain the highest amount of semantic information. It is a slippery slope."
"Make a statement less and less likely and you gradually increase its informational content, but at certain point the statement “implodes” (in the quotation below, it becomes “too informative to be true”)."
"Bar-Hillel and Carnap [1953] were among the first to make explicit this prima facie counterintuitive inequality. Note how their careful wording betrays the desire to defuse the problem."
Floridi goes on to quote directly from Carnap and Bar-Hillel:
"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)
---
Floridi comments:
"Since its formulation, BCP has been recognised as an unfortunate, yet perfectly correct and logically inevitable consequence of any quantitative theory of weakly semantic information."
"It is “weakly” semantic because truth values play no role in it. As a consequence, the problem has often been either ignored or tolerated (Bar-Hillel and Carnap [1953]) as the price of an otherwise valuable approach. Sometimes, however, attempts have been made to circumscribe its counterintuitive consequences. This has happen especially in Information Systems Theory (Winder [1997]) — where consistency is an essential constraint that must remain satisfied for a database to preserve data integrity — and in Decision Theory, where inconsistent information is obviously of no use to a decision maker."
"In these cases, whenever there are no possible models that satisfy a statement or a theory, instead of assigning to it the maximum quantity of semantic information, three strategies have been suggested."
FIRST
"Assigning to all inconsistent cases the same, infinite information value (Lozinskii [1994]). This is in line with an economic approach, which defines x as impossible if and only if x has an infinite price."
SECOND:
"eliminating all inconsistent cases a priori from consideration, as impossible outcomes in decision-making (Jeffrey [1990]). This is in line with the syntactic approach developed by MTC;"
THIRD:
"assigning to all inconsistent cases the same zero information value (Mingers [1997], Aisbett and Gibbon [1999])."
---- I am pleased that Floridi was able to find my quote of Grice of interest, as he acknowledges me in that entry and quotes directly from Grice, WoW, to the effect, post-dating the locus classicus of 1967, that 'false 'information' is no 'information'. In which case, beware to read Kant's Quantitaet, that Grice used amusingly for one of the four categories -- the others being Qualitaet, Relation, and Modus --.
Oddly, Grice did not consider the implicatures (if any) of:
War is not war
Women are not women.
----- but I suspect Disimplicature would be rearing its ugly head. (*)
(* -- Grice uses 'disimplicature' in unpublications only, to refer to the loose dropping of entailments. If you say, "No man is an island" the idea is still metaphorical, rather than trite. Similarly, in WoW:4 he considers, "You're not the cream in my coffee" need not literally (Grice's word) negate that you are a white liquid. In the case of "Women are not women" and "War is not war" then, we need to consider first the implicature of the affirmative, to proceed to make a better, more intelligent sense, of its negation, if any --. Another example Grice uses in WoW:4 is the negation of irony: "He is NOT a splendid fellow" -- meaning --??).
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I do sometimes wonder at the lengths people go to deal with the obvious. Consider:
ReplyDelete1. &*(_HJOI{ W U()}WE()CU()CE
2. This sentence is false.
3. [silence without context to give it meaning]
All are equally devoid of information because none removes any possibilities (which, recall, is what information does).
Assigning self-contradictory statements an information level of 0, then, seems so obvious as not to be worth the ink it takes to say so.
As for the BHP, feh! A well-formed, self-contradictory sentence is a logical nullity, not a polar case of low probability. It seems to me, admittedly a rank amateur, that even a "weakly semantic" system can be required to make sense. I understand that "the cat is dead" and "the cat is alive" may provide the same amount of information (if both are deemed equally likely) regardless of the cat's health, but "the cat karulizes elatically" does not provide any information at all, at least not in English, and is, I would think, not within the domain of any semantic system, weakly so or otherwise.
Floridi starts his paper:
“A triangle has four sides”: according to the classic theory of semantic information, there is more semantic content in this contradiction than in the contingently true statement “the earth has only one moon”
I find this assertion very odd, and I say that not knowing the first thing about the classic theory of semantic information. It seems to me that Floridi conflates falsity with contradiction. If you ask a four-year-old how many sides a triangle has, he might respond "A triangle has four sides." For him, that's an assertion. It's false, but it is completely valid and logical, laden with information, not at all a contradiction. What we need for a contradiction, I think, is "This three-sided triangle has four sides." Now we're contradicting, and now we can draw a line between contradiction and error that allows the latter to contain information and the former to be put in the trash.
Of course, I am prepared to be disabused, but only if it can be done on a standard keyboard!
I just thought of my earlier reference in another thread to the notion of logical and physical devices being analogous to roles and the actors who play them.
ReplyDeleteIn last night's performance of "The Proposition," the role of p was played by the nicely put-together "This sentence is false." She definitely looked the part, but I'm sorry to say she just didn't deliver.
Part of the problem is "the context of the same sentence"
ReplyDelete--- "This three-sided angles has four sides" contradicts the main clause in terms of the subclause.
"A triangle has four sides" may be thought of as definitional, and thus beyond matters of truth -- but stipulation, rather.
In fact, three-angled figures having three SIDES requires SOME knowledge. And it irritates me slightly that most figures get 'named' after names of sides, except for the very first figure (the three-angle), which is defined by the number of angles, rather.
It may connect with the Grice-Strawson example in "In defence of a dogma"
----
(adapted):
"My neighbour's three-year old son, who is an adult, is not an adult".
--- There is a level of redundancy too, played to some bad effect. In many cases, we do allow contradictions like that (chapter 1 of a long novel may define a triangle as a three-side figure, only to have the thing redefined in chapter 45 as a four-sided figure rather). It seems is the patentness of the clash with logic in the 'one fell swoop' of one utterance that does the trick? Or something. But great to have your thoughts and I may elaborate.
I don't think the issue is whether the contradiction is in the same English sentence. It's about what constitutes p. As it turns out, the role of p is usually played by a well-formed sentence, but one can imagine a falsidical paradox related as a story with many sentences. I would regard the whole story as a possible p, and reject it as a p on the grounds that it is self-contradictory. I suspect that any self-contradictory utterance can be restated as a well-formed sentence or symbolic abstraction "There exists a thingy such that..." , but that's just a matter of expression, not logic.
ReplyDeleteGood point. Talking of self-contradictory and self-referential. I would add that if I were to see, in a toilet, as a graffito:
ReplyDelete"This sentence is false."
-- call me Goedelian, but if I have a pen (as I usually do when I go to public toilets) I would draw an arrow, starting from the dot after 'false' and signalling the very sentence itself.
Kramer is right that 'sentence' has nothing to do with it. I was playing on Grice on 'patent'. He says "Women are women" and "War is war" are PATENT tautologies. So I was playing with patent contradictions.
It looked like
"This three-side triangular figure has four angles" is a patent contradiction.
On the other hand, "A triangle is only arbitrarily so called. Why, I could start stipulating that in MY idiolect, a triange has FOUR angles".
Or something.