Paying the Toll: Grice on Frege's Turnstile

--- by J. L. Speranza
------ for the Grice Circle.

R. B. Jones writes in "Strand 5", THIS BLOG:

"[Frege's] two
strokes combine to yield the turnstile".

which, oddly, Kleene, in "Introduction to Metamathematics" yields as '... yields...'. I was once such an anglophile that I looked, alla Levers, for ALL Anglo-Saxon ways to say these things, and '... yields ...' did things to me.

---

I'm never sure what a turnstile is for.

I know a horseshoe is perhaps misproperly so-called, but Anglophones use it to indicate the ')' operator.

The Turnstile, as Jones notes combines:

Ⱶ

For we have:

Ⱶp

as a well-formed sentence, but none of the primitive strokes would make sense for Frege as just followed by "p", i.e.:

i.e:

(a)

─p

(b)

│p

----

It irritates me slightly that while Grice uses the turnstile in "Aspects of Reason" (Clarendon, 2001), which he reads as 'assertoric' or 'alethic', he uses:

!p

for the corresponding operator which he reads as 'practical' or 'non-assertoric'.

But surely what we need is just ONE of the strokes being different. For we can keep

the horizontal stroke as being shared by both 'assertoric' and 'non-assertoric' (or boulemaic, as I prefer) utterances:

─p

So, we only need to apply a different stroke from

│

which would indicate the 'judicative' judgement, if I may be redundant. I propose:

!─p

i.e. rather than the simpler one used by Grice,

!p.

In this way, a judgement is a judgement is a judgement.

There are TWO faculties for Kant and Grice which Frege and the Fregeans Kant See: the judgement proper (which I think Americans spell judgment -- how can they pronounce that?) and the 'volitive' or 'boulomaic'. Grice uses 'volitive'.

Grice wants further to generalise to

"Accept".

What philosophers should be concerned with is "accept". And 'accept' is something that both 'judging' and "voliting" or 'willing' are.

Chapman quotes from some archival material, which I think illustrates a level of abstractedness I never saw in another philosopher (than Grice, not Chapman, who teaches English at Liverpool -- I love her!)

Chapman is quoting from a manuscript by Grice misquoted by Levinson as "Probability, Defeasibility, and Mood Operators". It's really, "Probability, Desirability, and Mood Operators". It predates the Kant lectures and it got into so much detail that Grice had to leave it at that. So abstract it hurts.

Grice writes, or rather Chapman writes:

"Going further than Davidson, Grice argues that
structures expressing probability and
desirability are not merely analogous; they can
both be replaced by more complex structures
containing a common element"

----

"Generalising over attitudes using the symbol 'ψ' (which he had used in 1967 -- repr. WoW:v)

Grice proposes:

'X ψ p'

Further he uses 'i' as a dummy for subdivisions of
attitudes,

Grice uses

"Op supra i sub α"

(Read: "Operation supra i sub alpha" -- Grice was fastidious enough to provide 'reading' versions for these).


and where 'alpha' is a dummy taking the place of either "A" or "B", i.e. Davidson's "prima facie" and "probably".

---

In all this, Grice keeps using the 'primitive' "!" (cited by Chapman, p. 131) where a more detailed symbolism would have it correspond exactly to Frege's turnstile (that Grice of course also uses, Chapman, op. cit., same page), and for which I propose, then:

!─p

There are GENERALISING movements here but also merely SPECIFICATORY ones. The 'alpha' is not generalising -- it's a dummy to serve as 'blanket' for 'specifications'.

On the other hand

ψ

is indeed generalising.

The "i" -- is it generalising or specificatory?

It is a dummy for specifications, so it's not really 'generalising'.

----

But Grice generalises over specifications.

Thus he wants to find 'boulomaic' or 'volitive' as he prefers (I prefer the Greek root) for both his 'protreptic' and exhibitive versions (Operator supra A and Operator supra B):

I note that Grice (WoW:110) had used the asterisk (*) as a dummy for 'assertoric' (Frege's turnstile) and 'nonassertoric (the "!─" 'imperative turnstile', if you wish).

----

Operators A are NOT mood-operators, they are, in Chapman's paraphrase, such that they "represent some degree or measure of acceptability" (or justification).

I prefer 'acceptability' because it connects with "accept" which IS a psychological attitude (if a general one).

Thus Grice wants to have:

ii. "It is believable that p"
i. "It is desirable that p"

as understood by the concatenation of three elements:

First, the A-type operator.

Second, the B-type operator.

Third, the proposition itself.

i and ii share the A-type operator and the proposition. They only differ at the B-type operator.

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Grice uses "+" for concatenation", but it's best to use "^", just to echo who knows who.

----

Grice spoke in that mimeo (which he delivered in Texas, and is known as Grice's "Performadillo" talk -- Armadillo + Performative) of various things.

("We regret that due to technical problems, Grice's paper will not be published in the proceedings", the introduction of this expensive thing I ordered read).

He spoke, transparently enough, of

V-acceptance

and

J-acceptance

"V" not for "Victory" but for 'volitional', and J for judicative. The fact that both end with "-acceptance" would accept you to believe that both ARE forms of 'acceptance'.

----

In "Probability, Desirability, and Mood Operators" Grice irritatingly uses "1" to mean belief, and "2" to mean 'desire'.

But two years later, in 1975, "Method", he defines '1' in terms of '2' (and CARES NOT to do otherwise -- i.e. define 2 in terms of 1). So whenever he wrote '1' in 1973, read 2, and vice versa.

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(Chapman omits this arithmetic when she merely reports on Grice's use, on p. 131).

---

Chapman notes that Grice uses further numerals:

3 and 4.

These, Chapman deciphers -- I find her as an archeologist in Tutankamon's burial ground --: as

"relexive" attitudes.

In Chapman's paraphrase:

"3" i.e.

ψ3 ------ (where we need the GENERAL operator, "psi", not just specificatory dummy, butd the idea that we ACCEPT something).

ψ3 --- Chapman writes: "is concerned with an attitude of V-accepting towards J-accepting [p] or J-accepting [~p]"

why we should be concerned with "~p" is something to consider.

In Chapman's paraphrase:

"x wants to decide whether to believe p or not".

I find that very Gricean. Suppose I am told that there is a Volcano in Iceland. Why would I NOT want to believe it?

It seems that one wants to decide whether to believe p or not when "p" involves a tacit appeal to 'value'. But Grice will note that even when it does not thus involve, we still need trust and volition reigns supreme.

---

On the other hand there's

4

or more formally

ψ4

This is "concerned", Chapman paraphrases, "with an attitude of V-accepting towards either x V-accepts [p] or x V-accepts [~p]".

i.e. again in Chapman's paraphrase:

"x wants to decide whether to will p or not".

This indeed IS CRUCIAL, for as Judith Baker notes (in PGRICE), for Grice, morality does cash in DESIRE.

Grice smoked.
He willed to smoke.
But did he will to will to smoke?
Possibly yes.
Did he will to will to will to smoke?

---

Regardless of what he willed, I claim this holds for serious imperatives (not "You shalt not smoke", but "Though shalt not kill", say) or for any "p" if you must (because if you KNOW that 'p' causes cancer ('p' stands for cigarette, not for proposition) you should know you are killing yourself -- but then Time also kills us, so what gives?).

----

So I would submit that for Kant, the categorial imperative is one which allows for an indefinite chain (not of smokers) but of good-willers:

If, for some p, we find that at some stage, we will NOT to will that we will that we will that...', then 'p' can NOT be universalisable. I proposed that in an essay referred to in "The Philosopher's Index" but Marlboro took no notice.

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Chapman goes on to note Grice's obsession on 'make believe'.

If I say, I utter x because U wants A to believe that U believes that p, there's

U

and

A.

I.e. there are TWO people here -- or things -- for my cat means things to me (he even implicates: the other day he miaowed to me while I was in bed -- He utterered 'miaow'. He meant that he was hungry, he meant (via implicature) that he wanted food (as provided by me). On another occasion he miaowed explicating, "The door is closed", and implicating "Open it, idiot".

---

On the other hand, today's Andy-Capp's cartoon read:

"When budgies get sarcastic". ("Wild-life programmes are repeating).

---

Chapman then notes that

one can want some other person to hold an attitude.

---

Grice is using "x" for U, and "y" for A.

--- of course, U and A are mere ROLES. The important formalism is indeed x and y.

x is one person.
y is the OTHER person.

(Grice disliked menages a trois, apparently, for he never symbolised a 'third' party, z).

----

So,

"X psi supra 3 sub A [p]" is true

just in case

"X psi supra 2 [x psi supra 1 [p] or x psi supra 1 [~p]"

is true.

----

And -- here 'y' features:

"x ψ³ sub B [p]" is true

just in case

"x V-accepts (ψ²) [y V-accepts (ψ²) [x J-accept (ψ1) [p] or x J-accept (ψ1) [~p]]]"

is true.

Grice ssems to be happy with having reach "four sets of operators," Chapman sums it up, "corresponding to four sets of propositional attitudes," and for which Grice provides the paraphrases:

i. [doxastic] proper.
They are what Grice calls 'judicative', and which are either "indicative" or "informative" (if addressed to 'y' which is different from 'x' -- for surely one cannot inform oneself).

ii. [boulomaic] proper
What Grice dubs 'volitive' (but I prefer the Greek root].
These are either self-addressed and they are "Intentional" (or 'is' intentional, if you want to stick with the singular), or other-addressed and they are "Imperative" (for surely one cannot say to oneself, "Don't smoke, idiot!"

iii. doxastic-interrogative (how we create "?" here is minimal compared to the vagaries of what I called the

"!─" (non-assertoric or 'boulomaic' turnstile).

---

and which I propose to symbolise by

?─p

where "?─" stands for the 'erotetic turnstile'. "Erotetic" somehow Grice ignored, as he seems to prefer the latinate "interrogative" at this point ("Surely more people know what 'interrogative' means than what 'erotetic' means", he would not say -- but he would).

These 3-types come in two varieties: self-addressed, 'reflective' ("Should I go?") and again, 'imperative' ("Should YOU go?" -- with a strong hint that I'm expecting you to make up your mind in the proceeding, not just inform me).

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iv. (Last but not Least): "volitive" or boulomaic cum erotetic. Here the varieties are again reflective (or autophoric, as I prefer) and 'inquisitive' (for which I'll think of a Greek pantomime).

Grice regreted that Greek (and Latin, of which he had "less" -- cfr. Shakespeare who had none) "fares better" in this respect than English.

Ode on a Gricean urn, indeed!