Quæstio Subtilissima

Is, of course:

chimaera bombinas in vaccuo posset [vel non posset per illa
materiam] comedere secondas intentiones.

i.e. whether a chimaera can eat secondary intentions. Grice says it can-not. But he is using 'not' in a way which Quine found 'forbiddingly complex' ('Reply to Grice', in Davidson/Hintikka.

Grice's idea is to distinguish between

A chimaera cannot-1 eat secondary intentions.
(since that's such an absurd thing to say, anyway[s])

versus:

A chimaera cannot-2 eat secondary intentions.
(since she's eaten too much already, or something).


In his contribution to the festschrift for Quine (Words and ObjectIONS), Grice introduces a subscript negation to deal with the alleged ambiguity of negation – retrieving a reply from Quine to the effect that while he thought the whole idea and system “forbiddingly complex” -- yet one he “would go on personally”
(some day).

The idea – later to be taken by Montague, etc. -- is that any constitutent of a formula gets a subscript to mark 'the order of arrival', as it were. In the negation of a basic formula of predicate calculus,

“~Fa"

would thus have at least two readings.

In both of them, “F” may have subscript 1, -- but it's either “a” or “~” which gets a higher subscript (than the other).

In the case of formula with an existential 'assumption' (presupposition, implicature, or what have you), it is assumed that “a” will have a higher
subscript.

The notation being:

“~2F1a3”.

In a formula 'free of existential supposition', we must take “~" to have
scope over the whole formula:

“~3F1a2”.

Note that the subscript notation restricts the inferences to be validly made: only a formula where “~” does not have maximal scope allows for a consequence regarding existence:

“~2F1a3 ╡Ex4~2F1x3.”

While the corresponding formula is marked as yielding an invalid inference:

“~3F1a2 ╡Ex4~3F1x2”.

For definite descriptions (iota operator) --

“~2G1ix3F1x2” versus “~4G1ix3F1x2”

yield similar results.

In Parsons' notation, Grice's

“~2F1a3”

becomes

“[a](~Fa)”

while Grice's “~3F1a2”

becomes

“~[a](Fa)”

-- “Ex4~2F1x3” becomes “(Ex)([x](~Fx))” and “Ex4~3F1x2” becomes
(Ex)(~[x]Fx)).

Grice uses square brackets in 'Logic and Conversation', too, but that's another story (for another day, perhaps). And see, (if you so desire) "What the eye no longer sees", this blog. :)

Etc.