System GHP

by J. L. Speranza
for the Grice Club

----

THIS IS EASY ENOUGH. I did post a post on "System G_HP" on February, which I was happy to edit as I wanted thanks to L. J. Kramer's point about the 'sub' -- which is something that Jones is also very familiar with, since he is the master of things like LaTex and all that.

So the point is that when you see

System G_HP

-- besides that simplicity there's some typing on my part: I have to write "sub" in angular brackets, propose the subscripted material inside, the "HP" and then write "sub" again inserted in angular brackets with a bar before it.

Anyway, it was MYRO's invention.

Myro died in 1987, but I contacted the Dept. of Philosophy with a word to the effect, "I want to know EVERYTHING about his System G". Sally Haslanger was VERY kind to reply, -- 'beware you credit his name properly when you quote him --, and I did. I was amazed by the complexity of System G. Most of his material was APPLIED. Myro was only into the 'relative identity' thesis that Grice refers to as the "Grice Myro theory of identity", which is really Geach rehashed -- but don't spread the word. In some cases, the Myro papers had made it to official publications, like his "Time and Essence" and other essays which he did publish during his lifetime. But my pet in the Myro papers was this thing which he entitled -- I have it somewhere and should have a closer look at it --:

"A sketch of System G, with gratitude to Paul Grice
for the idea".

So it's a tribute to Myro's tribute to Grice which moves me here.

---- Now, I think Myro DOES mention, in his "Time and Identity", which he contributed to PGRICE, ed. Grandy/Warner ("pHILOSOPHICAL gROUNDS OF rATIONALITY: iNTENTIONS, cATEGORIES, eNDS"), that he was borrowing from Grice's System Q.

If one reads that old volume, "Words and objections: essays in the work of W. V. Quine" to which Grice contributed (Reidel, 1969, ed. Davidson/Hintikka) one is marvelled. I like to think: "How did the man find so much time to write all that?". This was just one year after he had settled in Berkeley, bought the house, leave Oxford behind, etc. And yet he is happily citing "George Myro" for help on this or that. So that Myro should have revisited Grice's System Q as Myro's System G is only appropriate --. And we are getting closer to System G_HP.

What IS Grice doing with his System Q?

I hd never seen anything before. I mean, I had seen ZILLION things before. What I mean, is the use of a letter to just mean a person. I suppose there are MANY other examples of "System" followed by a letter. I can think, infamously, of Kripke's System S" -- but I'm not very aware. So I am happy that, now, R. B. Jones is considering something like System C_R on which we should discourse mainly in "City of Eternal Truth", this blogger. (Jones has done so much fruitful work on this that his exegetical point about Carnap is secondary to him; he has a PRIMARY motivation that I sometimes lack; add to that that I am VERY amused to talk about Grice).

So, Grice's "System Q" (to tribute Quine) is really just a formal language. The letter Q is immaterial -- but you HAVE to call it somehow. And also, he is interested in scope devices. I.e. for each element in the formation rules, symbols don't come in naturally but subscripted.

Thus we would have

(x)Fx

indicated as -- let me see if this works with the "sub" device:

(x)₃F₁x₂

--- which should be read then as "x" being primary, "F" being secondary, and "(x)" being tertiary. Grice proposes these rules about subscripting (the above is just an illustration and actually is NOT yielded by System Q -- or System G_HP in algebraic abstract terms: he uses "n" and "m - n", for example. Since his explicit point is of course that the number itself is immaterial. Only that the the expression '>' or, strictly '<', should count. So, by having 'm - n', we do know that, for example, m - n < m. (I should revise that).

In the long run, Grice's explicit interest is about issues of 'existence' -- and for some reason he speaks of his System G (and a forteriori, System G_HP) as "creat[ing] no Meinongian jungle" for which, incidentally, we need the exact Meinong reference, since this genial philosopher (Meinong) is seldom credited explicitly in discussions of things which are meant to illutrate the latest developments (by 1960) of analytic metaphysics when it was all said some pretty good decades before by Alexius.

---- So, the point of the subscript device, for Grice, in his System Q (and a forteriori, System G_HP concern the attachment of a subscript to things like the existential quantifier, the constant (which System Q, if not System G -- or System G_HP display), the variable of individual, and the negation sign, say.

Matter of fact, Grice refers to something like his System Q (and thus a forteriori what Myro will have as System G -- and cfr. System G_HP --) in Strand 6 of WoW -- where he refers to 'scope indication' device, I think his phrase is, in the plural: 'scope indication devices' -- There is no sign of the subscript device, which System Q deals with, in WoW, but Grice is careful to make some good references to the SQUARE-BRACKETING device, which also pertains. Just to have Grice in his 'formal key' allow me to quote him directly from WoW:280.

This is one page in WoW (p. 280) where Grice (1970) is going back to his 1967 William James fourth lecture (also reprinted in WoW) -- and thus predating his explicit System Q (in Davidson/Hintikka, 1969). Grice writes:

----

1.(a) If expression A is of the denominated type T,
then A[B]C is rewritten as BABC.
--(b) if expression A is NOT of type T, or is null, then
A[B]C is rewritten as ABC.
2. In rewriting, nested brackets are eliminated, seriatim,
from exterior to interior.
3. If no connective directly precedes a closing (right-hand)
square bracket, "[/\]" is supplied in rewriting, where needed,
to preserve syntactical admissability.
4. Any opening (left-hand) parentheses are introduced in
rewriting are closed terminally.
5. In preposing an expression containing a bound variable, the
variable is changed.

---- --- From Grice, "Studies in the Way of Words", 1989, p. 280

The square bracket device yields the same results of the subscript device in Grice's System Q (our System G_HP). Note incidentally that Myro says NOTHING about the subscript devices in sketching his System G -- his interest lies elsewhere). While I HAVE seen treatment of this elsewhere (notably in work by Harnish and Horn), Grice's alternative subscript device (lay the blame on plain text) has fared worse. (As if he cared).

----

In Harnish, this concerns hot philosophical issues; in Horn, the manoeuvre is perhaps more general, and he refers to it as "assertion inertia", or "assertive inertia". The point being, in Horn, the use of immunity. Horn wants to have, with Grice, certain operators or fragments of formula as being 'immune' to negation, I think is the phrase Horn uses in his "Inertia" paper. In Harnish case, the application, as I recall it, concerns, say,

K = JTB

Knowledge (K) as belief (B) which is true (T) and justified (J): Gettier's point against Plato and Ayer. Harnish is concerned with negating a claim of knowledge:

"She doesn't know it".

If 'knowledge' is justified true belief, what does THAT mean? Surely 'not' may apply to any of the three elements in the analysis:

-- it is not the case that what some may allege she knows IS the case (Challenge to the truth of 'p').

-- it is not the case that what some may allege she knows she believes (challenge to the 'belief' condition)

-- it is not the case that what some may allege she knows she has adequate evidence for (challenge to the 'justification' requirement).

Harnish's illustrations include:

--- A: I didn't know you were pregnant.
--- B: You still don't.

The implicature seems to be, "I am not". Rather than: "You have no adequate evidence to say that" or "Surely you don't believe what you say". (Leaving manners aside).

So, if we work with some ordering of clauses here we have

'p'
Bp
Jp

And it would seem that Bp and Jp are thus immune to negation. The issue seems particularly tricky here in that, what kind of justification can A have if he is WRONG about what he says? So I should revise all this! But hopefully you should get Harnish's point.

Grice's examples concern, typically, existence. For example, in his heroic attempt to have this deal with more than 'assertion', but to cover operators like "!", he provides the example:

"Don't arrest the intruder!"

----

This should be an odd thing to say if there is NO intruder. Why? Well, because in ordering you to arrest the intruder, what I say ENTAILS that there is an intruder. Whereas in the negation of the order, the prohibition, Do NOT arrest the intruder, such entailment is dropped and is merely implicated. So we need to explicate, however, why is it that the 'preferred reading' (I borrow from Schwartz here, David Schwartz, 1977, "Notes from the pragmatic wastebasket") is one where "there is an intruder" is "immune to negation" (to use Horn's wording -- I would believe)?

The slate in Grice, WoW:281 undergoes 3 stages -- to which we add a fourth stage to introduce "~".

1. "Arrest the intruder!" could be thought of as representable (using "!" as an imperative operator as
2. !([E₁x) (x is an intruder) /\] (Ay) (y is an intruder ) you will arrest y)).
Provided "!" is treated as belonging to the denominational type T, (2)
will be rewritten as
3 (E₁z) (z is an intruder) /\ !((E₁x) (x is an intruder /\ (y)(y is an intruder ) you will arrest y))

---

The negation, which would be equivocal in 1, is not in 3, which yields, then:

4 (E₁z) (z is an intruder) /\ ~(E₁x) (x is an intruder /\ (y)(y is an intruder ) you will arrest y)).

(Or something). (The point is clearer with his analysis of "x does not regret phi" -- which avoids the topic he will come back later in "Aspects of Reason" as to the best formalisation of prohibitions featuring some (wrongly) alleged 'truth-value' or satisfactoriness'-value gap). For "x does not regreat p" Grice expresses as:

First, "~([x thinks [phi] /\ x is anti phi)". We then go to 'replace exterior square brackets', yielding, second, "x thinks [phi] /\ (x thinks [phi] & x is anti phi). Now, third, 'replacing remaining square brackets,' one gets "phi /\ x thinks phi /\ phi /\ ~(x thinks phi /\ x is anti phi). By 'eliminating redundant occurrence' of phi, we get, fourth: "phi /\ x thinks phi /\ ~ (x thinks phi /\ x is anti phi), which, fifth, is indeed 'equivalent' to "phi /\ x thinks phi /\ ~ (x is anti phi)".

Grice's example here is

"He regrets that Father is ill" (WoW: 280). This seems to be an earlier stage, conceptually, to his example in WoW, p. "He thought he regretted his father's death".

--- "He thought he regretted his father's death".

Grice's amusing, charming, and so Griceian commentary is worth quoting in full! I rarely encounter so much wit in other recognised philosophers of his generation, never mind Descartes.

Grice writes:

"There is a distinction between [a case such as -- Kapirkys' cases -- he does not care to mention P. & C. Kapirsky by name] and a fourth case, because, though both the affirmation and denial of statement s about particular people KNOWING that p carries with it a commitment to P, you can weaken the verb in such a way that the implciation is lost"

-- but never for good, for Grice. He goes on:

""He knew that p" and "He didn't know that p" both carry this implication"

--- although it is, respectively entailment and impicature --

"but, "He thought he knew that p" does not. When I say, "He thought he knew that p," I am not commiting myself to its being thae case that p."

"BUT -- there ARE verbs in which EVEN THIS WEAKENED form also SEEM
to carry this implciation, particularly, perhaps, a verb like 'regret'."

--- As if philosophers were waiting in line to write philosophical essays on just ONE tricky English verb --

Grice goes on:

"i.e. "He thought he regretted his father's death, but it afterwards turned out that he didn't", as far as it MAKES SENSE, would, I think, STILL imply the commital to his father's death)"

One may disagree with Grice there, but note that he is talking about HIS idiosyncratic procedure with 'regret'.

He goes on, genially:

"I am NOT sure about the last distinction, and I think
perhaps it does not matter very much."

---- but he was guiding the audience's attention back in 1970 in an American university, when he delivered those genial lines!

Implicature: Beware the philosopher who like Heidegger is 'the greatest living philosopher" but who may say things which, on fourth reflections, 'perhaps [don't] matter very much'!