Women are not women

---- by JLS
------- for the GC

--- IN THIS POST, and the next, War is not war, I will apply (and fail) Carnap's and Bar-Hillel's account of 'semantic information' status of contradictions ('too informative to be true') to the implicature of 'Women are not women', not cited by Grice (he cites 'Women are women', and 'War is war', WoW:33).

--- I will argue that this is what I call a conversational implosion. The utterer utters what he utters, but the addressee in trying to figure out the implicature, opts for a disimplicature, and failing on that, too, 'implodes'.

----

What is 'implosion'? First, a rewrite of what Grice says on that (in)famous p. 33:

"Extreme floutings of the first
maxim of [Qualitas] are provided
by utterances of PATENT tautologies
[rather than patent contradictions]
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 thus their contraditictions
are too informative too be true.

"and so, at that level, cannot but
infringe the first maxim of
[Quantitas] in any conversational
context."

He goes on:

"They are, of course, informative
at the level of what is
implicated, and the [addressee's]
interpretation of their informative
content at this level is dependent
on his ability to EXPLAIN the
[utterer's] selection of this
particular patent tautology."

---

Which is of course absolutely true. And not yet too totally informative as to be false.

Floridi -- who, as it happens, credits Speranza at

http://plato.stanford.edu/entries/information-semantic/#4.1 --

proposes various solutions to what he calls, with a bit of hyperbole (genially) Carnap's and Bar-Hillel's 'paradox'

----

And he proposes a couple of ways out (or way-outs, if you mustn't):

"Since its formulation,"

-- back in the day --

Carnap's and Bar-Hillel's paradox (briefly, that a contradiction is 'too informative to be true')

"has been recognised as an unfortunate, yet perfectly correct and logically inevitable consequence of any quantitative theory of weakly semantic information."

Why is this 'weakly'? Floridi relies on this quote by Grice (that I'm happy to say I provided with -- as gone publicly in PHILOS-L and CHORA) to the effect: "False (so-miscalled) 'information' is NO information" (WoW:RE: 371).

Floridi has it:

"[The theory] is “weakly” semantic because truth values play no role in it."

'Strongly semantic information', on the other hand, is, by necessity (analyticity), true.

Floridi goes on:

"As a consequence [of its being a logical consequence of an apparently misguided theory], the [paradox] has often been either ignored or tolerated (Bar-Hillel and Carnap [1953])" ---

i.e. ages before Grice was even THINKING about "War is not war". (Strawson 1952, granted, does cite Grice in a footnote to the effect that there are 'pragmatic rules' which govern discourse and which obviously deal with informativeness and/or strength, though.

And this, Floridi goes on,

"as the price of an otherwise valuable approach."

But here's the beef:

"Sometimes, however, attempts have been made to
circumscribe its counterintuitive consequences."

Are the consequences counterintuitive? It seems to me that the choice of a theory may have this consequence which we HAVE to make room for, EVEN if counterintuitive. Theory is the opposite of "INTUITION". A theoretical account of 'weakly semantic information' is what it is. A theory of 'strongly semantic information', on the other hand, looks counter-intuitive to me in the first place. By reductio ad absurdum, I would argue that what Carnap and Bar-Hillel (and Grice) are postulating is not a THEORY, but an 'analysis'. For the distinction, vide Grice, WoW: 358.

In his response to Mrs. Jack (of Somerville, Oxford), Grice distinguishes between "a theory of X" and 'an analysis of X'. He is concerned with 'meaning' but what he says can be applied, mutatis mutandis, to 'information':

Grice writes:

"It remains to inquire whether there is any REASONABLE
alternative program for the problem[s] [about informativeness]
other than that of the provision of a reductive
analysis of the CONCEPT of [informativeness]. The ONLY
alternative which I can think of would be that of
treating [informativeness] as a theoretical concept, which,
together perhaps with other theoretical concepts, would provide
the primitive predicates involved in a [information] system,
an array whose job it would be to provide the laws and
hypotheses in terms of which the phenomena of [informativeness]
are to be explained. If this direction is taken, the [informativeness]
of particular expressions will be a matter of hypothesis
and conjecture rather than of INTUTION, since the
application of theoretical concepts is not generally
thought of as reachable by intuition or observation. But some
of thoese ... who object to ... analysis are also anxious
that [informativeness] SHOULD BE INTUITIVELY RECOGNISABLE."

---- By reductio implying that the theoretical approach is not viable.

Back to Floridi. He goes on:

The ways out to the paradox of Carnap/Bar-Hillel (1953) are prominent in some fields especially:

"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 where "Women are not women" and "War is not war" do not COUNT.

"and in Decision Theory, where inconsistent information is obviously of no use to a decision maker."

--- which is a good point. Unless the decision maker is concerned with other remarks by other 'pirots' that have to be taken into account when we 'decide'.

Floridi goes on:

"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."

And any Griceian should be pleased by the systematicity of it all, so let us proceed.

First, "assigning to all inconsistent cases the same, infinite
information value (Lozinskii [1994])."

Explanation.

"This is in line with an economic approach,
which defines x as impossible if and only if
x has an infinite price;"

Oddly Grice touches on 'prices' tangentially in "Aspects of Reason" vis a vis rational vs. reasonable. The price of my shoes can be said to be unreasonable, but hardly irrational, Grice says.

---

Second, "eliminating all inconsistent cases a priori from consideration, as impossible outcomes in decision-making (Jeffrey [1990])."

Explanation:

"This is in line with the syntactic approach developed by MTC;"

and which should please Carnap and Grice, when in their syntactical modes.

---

Third, "assigning to all inconsistent cases the same zero information value (Mingers [1997], Aisbett and Gibbon [1999])."

This is good in that we keep the strategy of '0' for contradiction ('false in all possible worlds') verus tautology (1 in all possible worlds or interpretations).

Explanation:

"The latter approach is close to the strongly semantic approach." But yet not identical to it, for it still is in line with the view that regards 'information' as being a quantum, rather than a quale.

In the long end, the way out to Carnap's and Bar-Hillel's paradox comes from a clear acceptance of Grice's dictum, "False so-miscalled 'information' is no information". Or so it seems to us.