Goedel and Grice -- the bad and the good, etc.

Dale was commenting on Goedel, and his (Goedel's) cursory remarks on the lack of an explicit syntax in "PM" Principia Mathematica. In my PhD, under E. A. R., I, having nothing less interesting to do, I hoped, managed to examine, in a peacemeal way, all that Grice says on those two pages, 22-23 of "Logic and Conversation". So let's share!

The context: The only way (I'm being polemic here) to understand Grice's main motive in "Logic and Conversation" is to entertain himself with a detailed reply to Strawson's manoeuvre in "Introduction to logical theory". Without Strawson's impertinences, Grice could have focused on a development of his own lines of thoughts. Note that he quotes his own "Causal theory of perception" as the same type of manoeuvre. So why is it that the rest of the William James lectures are on 'logic' and 'conversation' (at least nominally), then? The answer: Strawson.

So Grice needs caricatures. He caricatures Strawson as an 'informalist' -- responding of course to the "Formalists". These are -- but he won't mention, Grice won't: Russell-Whitehead (and Carnap) -- This is 1967, so Davidson IS publishing as we speak as it were, on these issues -- as is (Dale charmingly points out) Vermazen in the same issue of "Synthese".

So what _is_ Grice saying:

---- Can we name and number the theses -- of course we can. Think always in terms of what Strawson says about 'if' since THIS is the specific manoeuvre Grice has in mind.

Grice wants to say that he has nothing to say about 'reform of languge'. Yet...

"An outline of a not uncharcteristic formalist
position"

-- as the one in Whitehead-Russell, drawing on Frege, and in Carnap --

"may be given as follows."

Note that Peano as a source may also be quoted here, as far as the symbolism of "PM" is concerned.

"Insofar as logicians are concerned with
the formulation of very general patterns
of inference, the formal devices ['~', but
also the 'horseshoe'] posess

A DECISIVE ADVANTAGE

over their natural counterparts" ('not', 'if').

Yet, Grice IS entertaining the Identity thesis. The alleged difference is 'implicatural', loosely put.

Grice continues:

"For it will be possible to construct
in terms of the formal devices a SYSTEM
of very general formulas, a considerable
number of which can be regarded as, or
are closely related to, patterns of
inference the expression of which involves
some or all of the devices."

Modus Ponens, Reductio ad Absurdum, Double Negation Elimination, and so on.

Grice goes on:

"Such a system"

--- what he'll have as System Q, and which I and Jones have as System G_HP in Jones, pdf, on Grice on Vacuous Names, e.g. --

"may consist of a certain set of simple formulas"

--- Our idea of System G is inspired by Myro, who indeed left a couple of notes entitled, "System G" -- which Sally Haslanger keeps --.

"that must be ACCEPTABLE"

rather than plain 'meaningful'? --

"if the devices HAVE THE MEANING"

-- procedural meaning, as it were, as per a 'classic two-valued interpretation', as Grice has it in the first paragraph of "Logic and Conversation", and cfr. Quine and Haack on 'deviant logic' --.

"that has been ASSIGNED to them, and
an

INDEFINITE

---- echoes of Chomsky on recursion, starting with Peano, Frege, and the rest of the formalists -- cfr. Schiffer on productivity of language understanding and 'compositional semantics' --

"number of further formulas,"

-- language's open-endedness in the words of Chomksy and Grice in the later segments of his teological account of 'communication devices' in "Meaning Revisited"

"many of which are less obviously acceptable"

--- indeed rejected by Strawson -- on 'if' cited by Grice in the previous chapter.

"and each of which CAN BE SHOWN to be
acceptable if the members of the original
set are acceptable. We have, thus, a way
of handling dubiously acceptable patterns of
inference"

--- Grice will play, more reactionarily, with this a decade or so later, when in 1986 he published for "Pacific Philosophical Quarterly" his excellent essay on the logical form of events and actions. This essay is seldom quoted, alas. One finds a reference to it in Warner's intro to Grice's Aspects of Reason". But it is all about anti-compositional views. I have referred to it elsewhere, typically.

---

Grice goes on:

"and if, as is sometimes possible, we
can apply a decision procedure"

--- NOT in the case of quantified formulae, as Goedel shown --

"we have an even better way. Furthermore, from
a philosophical point of view,"

--- here he seems to be bringing Carnap into the picture, and his 'early' phenomenalist interpretants for such systems --

"the possession by the natural counterparts
of those element in their meaning, which they
do NOT share with the corresponding formal
devices,"

---- e.g. what Carnap would say about non-substitutional quantification, say --

Cfr. this amusing 'history of compositional semantics' powerpoint presentation, online, and the involved maxims: "Be superficial", "Avoid commitment!" --

---

"is to be regarded as an IMPERFECTION
of natural languages"

such as English. But not MARKERese or PM.

Grice goes on:

"the elements in question"

like the 'inferrability' condition of appropriateness under 'if' which would make you think it is not "Philonian"

"are undesirable excrescences".

Metaphysical excrescences, if you must.

"For the presence of these elemenets
has the result both that the concepts
within which they appear cannot be
precisely or clearly defined,"

--- cfr. Austin's marvelling at Chomsky's guidance into "formal grammar", or "logical grammar" that Chapman suggests Grice is parodying. With the caveat that Chomsky IS dealing with English, of course.

"and that at least some statements
involving them cannnot, in some
circumstances, be assined a definite
truth value"

--- He is thinking of Strawson's flirting with truth-value gaps, after the expression had been used by Quine.

Grice goes on:

"and the indefiniteness of these
concepts"

-- e.g. inferrability in an account of 'if' --

"not only is objectionable in itself"

--- cfr. "When Clarity is not enough", though.

"but also leaves open the way
to metaphysics".

Recall taht Grice has parodied Heidegger as "the greatest living philosopher" in the previous chapter, and that Carnap's motivations in the "Aufbau" seem to be connected with problems he detected in things Heidegger had said (Notably, that Nothing Noths).

Grice goes on, finally:

"We cannot be certain that none of
these natural language expressions
is metaphysically 'loaded'. For these
reasons, the expressions, as used in
natural speech, cannot be regarded as
finally acceptable,"

-- unless, with Chomsky, you are stuck with them!

"and may turn out to be, finally, not
fully intelligible"

--- read: meaningless.

Grice:

"The proper course is to conceive and bein
to construct an IDEAL language"

--- PM --

or as Grice prefers, just first-order predicate calculus with identity. His system Q, in honour of Quine.

"incorporating the formal devices, the
sentences of which will be clear,"

in meaning, that is -- plus their syntactics will be unobjectionable. Since only wff count -- as intepreted in a two-valued way.

"determinate in truth value, and certifiable
free from metaphysical implications; the
foundations of science"

--- Carnap's and indeed Morris's programme of Unified Science --

"will now be philosophically secure, since
the statements of the scientist"

--- the point of Vienna Circle rendezvous: their analyses -- versus what Grice will later call "The man in the street".

"will be expressible (though not actually expressed)"

-- hence Carnap's rather schematic 'general functions' just as to give you an idea of what a 'system' for a language will or would look like --

"within this ideal language" -- But Dale is perfectly right that, for a change, Carnap is dealing with a "natural" language there -- unspecified, though. And for which I provide with "Homo habet canem". And so on!