Grice's Question: ∝ and λ

 And Grice's Answer, we should say. 

I have discussed this elsewhere, but I would like to make some remarks on Grice's notation.

His INTERROGATIVE mode others call the EROTETIC mode.

The symbol, of course, is "?"

For answers, he could well have thought of the inverted "?"

Grice is concerned with two types of interrogative utterances -- as they connecct with they psychic.

We have then BULETIC interrogative -- his Volitive Interrogative.

And we have the DOXASTIC interrogative -- his Judicative Interrogative.

Drawing from a clause in his 'Utterer's meaning and intentions,' the distinction between an 'exhibitive utterance' and the more brillaintly titled "PROTREPTIC" utterance comes ino play.

The way to symbolise this would be with "U" for utterer and "A" for addressee.

Grice sometimes uses "Audience," but Cicero forbade this for creatures without ears.

We have then the SUPRA-MODE of the INTERROGATIVE, and the two supra-modes of the BULETIC INTERROGATIVE and the DOXASTIC INTERROGATIVE, to which we now add what he calls, genially, a SUB-MODE: 

THE BULETIC INTERROGATIVE EXHIBITIVE

THE BULETIC INTERROGATIVE PROTREPTIC

and 

THE DOXASTIC INTERROGATIVE EXHIBITIVE

THE DOXASTIC INTERROGATIVE PROTREPTIC

So far so good.

It all boils down to 'want' and 'believe' -- or wants and believes -- since he uses the conjugated verbs and always refers the addressee as male ('himself'), like male is the utterer.

If in 'Utterer's meaning and utterer's intentions' he sometimes uses 'mean' in the past ("U meant that p iff") he occasionally does the right thing and uses "mean" in the present:

U means that...

the way to elucidate these four sub-modes then boils down to specifications involving iterations of believes and wants. 

Grice wants to keep a general format, usually using variables -- a general psychic operator to cover either want or desire.

The idea is simple and intuitive.

in a buletic exhibitive, the U asks himself.

In a buletic PROTREPTIC, U asks his A.

In a doxastic exhibitive, the U asks himself, as matter of course, and no 'want' appears other than in the preamble.

In a doxastic PROTREPTIC, the U asks the A for item involving the doxastic operator.

To these four modes, Grice provides definitions for further definifenda.

Questions -- as I. A. Richards well knew -- come in two varieties:

cf. Speranza, "First time at Magdalen?"

yes/no questions -- no truth value gaps -- any indirect answer to be glossed as implicature.

AND

x-questions

Grice uses the operator 'w' but I don't see the 'w' in HOW.

The intention of the questioner then is formed in terms of the expected reply.

The U does not know if he himself U or his A will say 'yes' or 'no'. In psychic terms, this comes out as whether the the radical p will be AFFIRMED -- Grice uses "+" here -- or DENIED "~". 

At this point, Grice uses the 'corresponding to' symbol 

∝

which looks like an 'alpha' and may indeed notated as such in transcribing Grice's lecture,

∝

occurs always as forming a quantifier

E∝

uniquely existential

E1∝

so the idea is that the utterer has to form an intention to the effect that he himself or his addresse will fill that with a positive or negative ANSWER -- attached now to p.

Since the answer is NOT known, hence the need of using the VARIABLE.

But a second SUB-SUB-type of questions are the tricky x-questions, that can take multiple variables

x y z...

Who and when and why killed Cock Robin?

Grice suggests leaving ? as default for yes/no questions and add a SUPER-SCRIPT x, or y, z, as the case may be, for X-, or X-Y, or X-Y-Z questions, etc.

In this case, the expected answer is again unknown but it does not resolve to the simple uttering on U himself or his A of a positive radical or negative radical for which the 'proportional to' sign was rather arbitrarily selected.

Instead, again, arbitrarily, Grice uses LAMBDA as the chamaleon variable. 

He gives ONE example. of an X-question, rather than an X,Y-Question, or further multiply x-question.

Who killed Cock Robin?

which was the example used in "Indicative conditionals" when venturing in a psychological explanation for the 'v' and the horse-shoe of logicians.

The intention by the U cannot make a reference to 'The Sparrow' (in which case 'Did the Sparrow kill Cock Robin?') would NOT be an x-question.

Rather the U forms his intention of this λ.

Unlike the 'proportional to' sign that ranges over radicals, the lambda sign ranges over variables.

x killed Cock Robin.

Had the answer been 'Who and where killed Cock Robin?' a second variable would have been used.

Etc.

Cheers