Grice on System G-HP

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

-- Grice's System G, of course does not exist. What exists is Grice's System Q (after Quine). But Myro joked on this and created a system G (after Grice) and then he died. And I created a 'highly powerful' (H. P.) system G ("H. P. G." for short) -- which some have seen as merely "hopefully plausible".

In "Vacuous Names", never repr. in full (but cfr. Oestertag), Grice provides an essay with a sufficiently complex structure. The sections read:

1. The problem.

---- One specific problem, but his sytem has more of a generality: To be able to say that it is true that the King of France is not bald.

2. System Q: Objectives.

---- System Q after Quine (this appeared in the BOOK, not the SYNTHESE issue) on Quine, ed. by Davidson/Hintikka, Reidel, 1969). There is a "Reply to Grice" by Quine, one page long, where he calls Grice's System "forbiddingly complex" -- oddly hyberbolically of course.

3 Scope.

4. Natural Deduction System Q.

---- Here Grice relies on Gentzen. He is relying actually on Benson Mates, Boolos, Myro, and Parsons's treatment of Gentzen, notably in Mates's Elementary Logic, published by Oxford University Press. Grice says he learned mostly from Mates by "way of word of mouth", for he had OTHER things to do than read boring logic textbooks.

A. Glossary.

This is really the "VOCABULARY", in Carnap's terms.

B. Provisional set of rules for Q.


1. Symbols.

-- This is the 'grammar'.


2. Formulae.

-- This defines 'wff'.


3. Inference Rules.

-- This is the 'natural deduction' component, and includes introduction and elimination rules for each of the seven logical formal devices he had identified in Grice WoW:ii: not, and, or, if, every, some (or at least one) and the.

----

5. Existence.

This relates to (Ex) only, i.e. "some" or "at least one". Grice uses the inverted A for 'all' or 'every' and the inverted (Ex) for 'existence'). I prefer /\x and \/x respectively to analogue it with Grice uses for 'and' and 'or' in WoW:ii.

A. Closed formulae containing & individual constant alpha.

Individual constant refers to things like "Jones", or more like it, "Fido" in WoW:vi, i.e. alpha qua designating expression. 'Pegasus' is the one he focuses here apres Quine, "On what there is", "x pegasises". Grice wants to say that it is true that Pegasus does not fly.

---

B. Existentially quantified formulae.

(Ex)Ax

is for Quine the form for "Pegasus flies". So Grice has to be careful with this.


6. Objection considered.

Grice's objection. The point of reducing 'Pegasus' to the predicate, 'to pegasise'.

7. Identity.

The Russellian idea of introducing 'the' by the iota operator in terms of the identity of indescirnibles.

a = b iff they share all properties.

The a, as being the uniquely existent thing that is a, so that if there is an y such that is also a, then y equals x.


8. Semantics for Q.

The interpretation for \/x.Ax. There is an item x under the class A such that the item has the feature.

A. Interpretation

A section of 8. Deals with interpretation in a model, strictly after Mates.

B. Truth and Validity.

The relation between premises and conclusion, vis a vis the introduction and elimination for \/x, as provided by the natural-deduction component.


9. Names & Descriptions (this section repr in _Definite Descriptions_,
MIT).

----- and mostly discussed by the best of the Griceians among us. He distinguishes, contra Donnellan, between an identificatory and a non-identificatory use of 'the' phrases. The 'butler' example, taken to be a gardener, and vice versa. Things our intuitions lead us to say in those cases.

10.Concluding remarks

--- relates to transparent and opaque readings of things involving psychological attitudes like '... believes ...' and 'desires' which Grice symbolises as "W" (for 'want').

Etc.