On the Uniguity of "Ⱶ"

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

--- I WAS SUGGESTING THAT R. B. JONES concentrate some of his attention to "Ⱶ" as a good operator. Grice uses it to mean, 'assert' -- which should do general duty for the trio that Jones lists: 'declarative', 'indicative' and 'descriptive' (with caveats of course, due to the multifarious uses of that trio).

For Jones writes:

Declarative, indicative, descriptive? I'm wanting to describe the notion of deduction in a broad 'sense'. I have the idea that this arises in the use of a certain kind of language. The kind of language in which one finds various bits of logical vocabulary such as "and", "not", and "all". However, for a broad notion of deduction one wants a broad notion of logical truth, viz. analyticity, and this mitigates against a characterisation through some particular kind of vocabulary, predication suffices where we have concept inclusion, irrespective of whether the vocabulary is 'logical'. A deductive inference is sound if whenever its premises are true its conclusion is true (i.e. in every possible world). We can use this to characterise deduction. This only works with language which has truth-conditional semantics, it appeals to the truth-conditions in the definition of soundness (think "under all conditions" instead of "in every possible world"). So what I am really looking for is the word which can best be used to describe the kind of language which conveys
information by afirming truth of a sentence of which the truth-conditions are understood (are part or all of the meaning). Do any of 'declarative', 'indicative', 'descriptive' [foot] the bill, or do [G]riceans have a better word? And then there is the question of what is going on in the rest of language, and how this relates to the concept of rationality.

--- There is, of course, 'alethic'. Grice uses this a lot. I discussed 'alethic' a lot with Mrs. Fields -- who works in Oxford for the OED -- Julie, if you mustn't. Julie told me, "It intrigues me that you should be interested about the inclusion in the OED of 'erotetic' seeing that it was a Romanian by the name "Sperantia" that first used it in a Congress in Turkey. Any connection?". I replied, "No that I know of".

But 'alethic' is there alright. It is a NEW word. Von Wright invented it. He just used 'alethes', which is Greek for 'true', and added '-ic' (as in 'dentifr-ic').

Of course, he was wrong on various fronts. "a-" + "-lethos" is possibly one of the worst metaphors ever invented by a Greek (and Von Wright was a Finn, to boot). It means, un-veil, literally. And there is also some connotation (if not downright implicature) of 'oblivion' (also "leth-").

So we don't want to go there. Yet Grice uses it almost obscenely, vis a vis, to boot, "practical". I feel that he should have used "practical" to oppose "theoretical", not 'alethic' --. Perhaps he should have used von Wright's other neologism (sort of), here, 'deontic' for 'practical'.

-----

But the point I want to make here now is that of

Ⱶ

which Grice uses to signify 'alethic', of course. His most technical technicism is "factual satisfactoriness". He wants to say that the type of inference Jones is elucidating is one of 'factual satisfactoriness'. Here he may be having in mind some treatment on the topic by R. M. Hare in "Practical Inferences" as criticised by A. J. P. Kenny in Analysis -- and brought to the forum to me by discussion by J. D. Atlas, who was at Oxford (Wolfson) for some time.

(In this respect, Levinson -- who collaborated with Atlas -- is less of a philosophical figure, which shows in his misquoting Grice's "Desirability, Probability and Mood Operators" as "Probability, DEFEASIBILITY, and Mood Operators" -- e.g. in Pragmatics, 1983).

But back to the turnstile:

Ⱶ

---

why wouldn't that do?

Well, if it just means, "I assert that..." (and cfr. Ross-type paradoxes here, as brought to the philosophical forum by D. Holdcroft, "Problems in the theory of speech acts", Clarendon Press, Oxford -- If I assert that it rains, am I also asserting that I am asserting that it rains, and so on ad infinitum?) then this relates to Jones's previous point (in reply to a point by Kramer, this blog -- on the enthymeme) re: what counts as a premise.

For suppose I say

If it rains, it pours.
It rains
-----
It pours.

Are we to allow for Grice's rather macabre use of "Ⱶ" to mean, "I assert"? In which case we could replace the above by:

I assert that: if it rains, it pours. (versus: "If I assert that it rains, I assert that it pours").
I assert that it rains
----
I assert that it pours.

INVALID!

But why would someone who says,

"if it rains, it pours" would be IMPLICATING, "If I assert that it rains, I assert that it pours?"

--- "Never mind;" says Grice -- "it's a mere implicature".

But this soon became the laughing stock of Oxford. And you can let that -- except when the laughers are from St. John's!

--- For it was G. P. Baker and P. M. S. Hacker who pour scorn on the idea that when we say

"if p, q"

what we mean is:

Ⱶp --> Ⱶq

Rather, the neustic applies to the hypertactical construction, "p --> q". To read:

Ⱶ (p --> q)

---

This explains the insidious (so-called) Geach point.

"If you torture the cat, your mother will scold you".

(discussed by M. Silcox). In "Assertion" (Philosophical Review), Geach had argued that 'assertion' NEVER applies in conditionals.

R. M. Hare wrote a long essay on this, for J. O. Urmson's festschrift. Unfortunately, it was the pedant of J. Dancy (I love his son) who found that "it was so infested with strange symbolism, that I could not have that in the festschrift". The implicature was that Hare was to re-shape the thing into "some sort of intelligible English, or something".

Instead, Hare declined, and published it in Mind, instead -- and later repr. it in his "Practical Inferences". I should pdf my review of it, elsewhere.

----

It would be very sad if "Ⱶ" turned out to be ambiguous. It's not like 'vice', say (meaning, on occasion, a 'sort of tool used by a carpenter', Grice says, or 'a bad character trait') -- and 'vice' is not even ambiguous.

But apparently, it is the multifariousness of LOGICIANS, rather than the multifariousness of 'uses' of "Ⱶ" that would lead you to believe "Ⱶ" is ambiguous.

As logicians use it, "Ⱶ" is best used for the conclusion.

I.e.

p
p --> q
---
q

So we say (using the 'associated conditional' method):

IF (p & (p --> q)) q

---

and we mark the validity and soundness of this by prefixing it with "Ⱶ":

Ⱶ(p /\ (p --> q)) --> q)

which is of course a 'theorem'. (Vide this blog for Jones on Ⱶ versus "semantic consequence" -- a different sign altogehter): /=.

--

Similarly, logicians use the 'empty set', $, and would say things like

$ Ⱶ p v - p

which is equivalent, at the meta-level, to the briefer (vide Grice's maxim, "be brief"):

Ⱶ p v - p.

For a tautology is a theorem, which follows from nothing.

---

This shows that "Ⱶ" is best understood, however, as the dyadic relation it is -- or connective, if you must. It holds between formulae:

p Ⱶ q

but that was NOT the usage intended by the CREATOR of the turnstile, Frege. Etc.

One problem for a Carnapian from a Gricean standpoint is that 'information', 'truth-condition', 'assertion', turnstiles, etc. -- are abstractions. Because we cannot assume that the utterers are aware of 'truth', 'truth-condition', and 'informative status' of what they say. At least Joan Rivers is not.