Slingshot

 Grice

Let “σ” abbreviate the operator “… consists in the fact that…,” which, when pre-fixed to a sentence, produces a predicate, or epithet. 

Let S abbreviate “Snow is white,” and let G abbreviate “Grass is green.”

In that case:

xσ(y(y=y and S) = y(y=y) is 1 just in case xσ(y(if y=y, G) = y(y=y) is 1, 

since 

y(if y=y, S) 

and 

y(if y=y, G) 

are each a singular term, which, if S and G are both true, each refers to y(y=y), and are therefore co-referential and inter-substitutable. 

So:

Provided that S and G are both 1 — and regardless of what an utterer explicitly conveys by uttering a token of any:

any event which consists of the otiose fact that S is also an event which consists of the otiose fact that G.

i. e., this randomly chosen event is *identical* to any other randomly chosen event. 

I hasten to criticise this slingshot fallacy licensing the 

inter-substitution 

of 

— this or that co-referential singular term 

and 

— this or that logically equivalent sub-sentence 

as officially demanded because it is needed to license a patently valid, if baffling, inference. 

If, in spite of this alleged benefit, the manoeuvre slso saddles you with a commitment to some hideous consequence, the rational course is to endeavour to find a way of retaining the alleged benefit while eliminating the disastrous accompaniment.

I’m hardly being original here:

In standard set theory it is always rational to search for as generous a comprehension axiom if it permits you to escape this or that paradox.

I propose then to retain the principle of co-reference, and only prohibit its use *after* any  appeal to the principle of logical equivalence.

Note that the initial deployment of the principle of logical equivalence — involving snowing being white and grass being green — is tailored to the generation of a conjunctive sentence which provides opportunity only for a very trouble-raising application of the principle of co-referentiality. 

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

Especially when there other ways around!