Grice's System

by JLS
for the GC

While we await a closer examination of System G-hp, I should address this point by R. B. Jones in his "Neotraditionalists and modernists" (while I agree that Grice is using Strawson as his strawman, and perhaps knowingly so).

Jones writes:

"Even with his project construed in the more
liberal terms there are general difficulties which
strike me, and one wonders how they can be overcome.
Of which the relevant variants on the paradox of
analysis are perhaps the most sweeping. Surely no
precise account can be faithful
if the original is vague?

--- italic emphasis mine.

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I would throw a few points at this point:

I.

While the Strand 6 speaks of the 'connectives', the "Logic and Conversation" piece speaks of 'formal devices', or 'devices' as I prefer --. Why not 'formal'? Well, the choice of 'formal device' is in the first paragraph of that lecture. In the second, he goes on to oppose Formalists (his later modernists) and Informalists (his later neo-traditionalists, aka Strawson) -- but surely even Strawson would say that 'and' is SOME kind of a 'device'. An informal device, if you like. So it's best to speak of 'devices', like '~', '/\', '\/', ')', '(x)', '(Ex)', and '(ix)' --. In this way, it makes sense to say that what Grice calls the 'natural' or vernacular 'counterparts' of the 'formal' devices, whatever they are, are still devices of some sort.

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The caveat of 'device' also applies to "~" not really connecticting and the three quantifiers mentioned by Grice not really being 'connectives' (let alone truth-functional) either.

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II. We have discussed elsewhere with Jones and others the tricky issue of the identification of a 'constant'. So perhaps Grice is into 'logical' constant. Peacocke has made the issue so difficult to tackle that I'm no longer sure. We do say that 'all' and 'some' are logical constants. But what about 'many', and 'few', and 'enough', and 'fewer', ... -- Or 'but'?! But I do think that Grice is into some kind of 'constant' identification. In particular, this is evident when in Lecture I he opposes anti-Searlean views and notes that he agrees with Searle in looking for a solution of the puzzle that then engages him in 'general' constraints of conversation, and not the semantic features of this or that predicate. So he is into the general categories and structures of language per se -- which we hope the so-called 'logical' constants are have something to do with.

III. semiotics for system G: syntactics, semantics, and pragamtics.

a. Semiotics. Or Semeiosis. Grice was well read in Peirce, so he possibly had in mind the idea of providing a general 'account' of the 'logical' signs. In the Morris tripartite division, this comprises three components:

a. 1. Syntactics. For Grice, this -- an examination of this should follow a look at System G -- proceeds via Gentzen's 'natural' deduction rules which apply directly after the 'formation' rules which work on the 'vocabulary' list of the system. So, we need specifics as to what counts as a "well-formed" formula. Considering even Jones's example,

"She got into bed and took off her nickers"

(Urmson's example is perhaps odder -- well, --- in that it is "He got into bed and took off his trousers" -- for it is certainly uncomfortable to sleep with your trousers on) -- the example is in Urmson, 1956, Philosophical Analysis, parodying Strawson, "She got pregnant and married").

The vocabulary and formation rule then yields:

if Phi and Psi are formulae, phi /\ psi is a formula.

No such thing as

"And did those feet in ancient times walked upon England's mountains green?"

-- i.e. initial 'and' is a logical no-no.

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So, it's only occurrences like

~p
p/\q
p\/v
p)q
(x)Fx
(Ex)Fx
(ix)Fx

that pass the 'muster' of the 'syntactics'. But that is not enough. For Grice the syntactic component of System G (the syntactics, rather than syntax) should provide schemata for '/-' (where that odd sign is the assertion sign of Frege or 'syntactic' entailment). This is provided, for each device, via the familiar

(+, fd)

(-, fd)

where 'fd' indicates 'formal device' and + is introduction, and - elimination.

E.g. DNE (double negation elimination) is (-, ~). Conjunction reduction ("She likes peaches and cream; therefore, she likes peaches") is (-, /\), and so on. RAA (reductio ad absurdum) is (+, ~), and then there's MPP and the -- in total -- 14 formula.

For the seven devices cited by Grice there are

seven introduction 'rules', and
seven elimination 'rules'.

Each rule features the '... yields ...' sign '/-'.


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b. Only we are armed with the syntactics for System G, we proceed to the 'semantics' for System G. This proceeds via correlation with assigned values. System G is two-valued (classical) -- note first paragraph of "Logic of Conversation" -- 'when these [formal devices] are given a two-valued interpretation' --. And so, Grice works with 0 and 1. p/\q is correlated with 1 iff p and q are correlated with 1. And so on with ~, \/, and ). In the case of (x), (Ex), and (ix), we need an interpretation, but the procedure is not radically different.

c. Pragmatics for System G. So, I would like to say that of the 5 meaning-specifications that Grice introduces in the first section of his Lecture 5, we can claim

"not" means '~'
"and" means '/\'
"or" means '\/'
"if" means ')'
"all" means '(x)'
"some (at least one)" means '(Ex)'
"the" means '(ix)'

----- the main component of the pragmatics of system G in a way agrees with Carnap's views on 'the pragmatics' of a system. It deals with 'assertion' and 'belief' (Carnap's main 'pragmatic' concepts). Grice would perhaps prefer 'assertability'. The main components, in Grice's parlance, would be IMPLICATURE, and, I add, disimplicature.

Consider Chomsky 1966, Aspects of a theory of syntax. In a note Chomsky credits Grice (this is before the William James of 1967) for alleging that the 'temporal' implication of "It rained and everybody was happy" is 'pragmatic' or 'due to a factor of discourse'. It's the 'be orderly' pragmatic pressure. I mention 'and' for it being the FIRST connective. Similar explanations can be given for ~ and the other connectives. Grice's WoW dedicates special attention to "or" in Lecture III, to tackle "if" in Lecture IV -- which was the goal he had set in the Prolegomena. Not much is said of "all", and "some" -- but his Lecture on "Presupposition and Conversational Implicature" is all about 'the', and surely some of his points about 'a' (the indefinite article), also in Lecture II, can apply to (Ex) -- "I met a tortoise on the frontyard to my house" (not mine). It wasn't long before everybody was applying the scheme to 'any device' you please. Burton-Roberts, notably, on the modality ("It must rain; therefore, it MAY rain"), Horn (as early as 1972, and in conference with Grice in 1973, on the 'scales' of "Some of my friends can speak Chinese" -- if not all), etc.

I add the disimplicature just for fun. For Grice, the essential implicature is 'cancellable', defeasible, indeterminate, yet CALCULABLE. Sometimes, it is the DISimplicature which has to be calculated, though. Consider '(x)'. If we adopt a substitutional account of the universal quantification, an utterer may disimplicate that this is what he means, and adopt instead a different account. This does not make the framework necessarily unpredictable. It shows that the pragmatic component depends on general 'rationality' considerations -- and it is, to use Jones's apt word, also a matter of 'design' -- even teleological design.

Grice hoped that those 'pragmatic' constraints dealing with an implicature of, say, 'or', such that a suggestion of some non-truth-functional evidence for 'p\/q' is offered which does NOT proceed via p or q, were 'natural', and 'rational' -- a matter of 'natural reason', as it were. He was NOT going to overregulate the pragmatic universe like that! His qualms had to do with the oversensitiveness of his system G -- not as HE used it, but as others did! (Or something).