H. P. Grice on "Grass is green" and "Snow is white" -- The Principle of Co-Reference NOT TO BE USED after The Principle of Logical Equivalence has been used.

Grice on "grass is green"

Davidson's ingenious argument may be summarised as follows.

Let 'sigma' abbreviate the operator "...consists in the fact that...", which, when prefixes to a sentence, produces a predicate (or epithet). 

Let 

'S' 

abbreviate

Snow is white.

and let 

'G' 

abbreviate

Grass is green.

Then,

First:

Sentence

(1) x sigma S

is true just in case

(2) 

x sigma (y(y=y & S) = y(y=y)

is true -- since the PARTS of the sub-sentences which follow the sigma
operator in the two main sentences are LOGICALLY EQUIVALENT. 

Second:

Sentence (2) is
true just in case

(3)

x sigma (y(y=y & G) = y(y=y)

is true, since 'y(y=y & S)' and 'y(y=y & G) are singular terms, which, if S
and G are both true, both refer to y(y=y), and are therefore co-referential and
inter-substitutable. 

Third:

Sentence (3) is true just in case 

(4) 

x sigma G

is true, since 'G' and the sub-sentence which follows sigma in (3) are logically
equivalent. 

So, provided that 'S' and 'G' are both TRUE, regardless of WHAT
THEY SAY, any event which consists of the FACT that S also consists of the fact
that G, and _vice versa_. 

That is to say, any pair of randomly chosen events
are identical.

Grice hastens to critique Davidson's slingshot argument:

To this argument Grice replies that this or that principle licensing this or that inter-substitution of this or that co-referential singular term and of
this or that logically equivalent sub-sentence is officially demanded because it is 
needed to license certain patently valid inferences.

If, in addition to providing
this benefit, the principle also SADDLES US with a commitment to the 'hideous
consequence', the rational course is to endeavour to find a way of retaining the
benefit while eliminating the disastrous accompaniment, much as it seems
rational to seek, in set-theory, as generous a comprehension axiom as the need to
escape this or that paradox permits.

Such a way seems to be available.

We might, e. g., while reatining this or that principle, prohibit the use of 

THE CO-REFERENTIALITY PRINCIPLE

*AFTER* 

THE LOGICAL-EQUIVALENCE PRINCIPLE 

has been used. 

Such a measure would indeed have some intuitive appeal, since in the cited argument, the initial deployment of 

the logical equivalence principle 

seems to be tailored to the production of a sentence which provides opportunity for trouble-raising application of the principle of co-referentiality.

And if that is what the game is, why not stop it?