Subscripts and Square Brackets (Grice in "Vacuous Names" and on p. 280 of "Presupposition and Conversational Implicature")

by JLS
for the GC

The use of subscripts in "Vacuous Names" is pretty complex -- and it does not just apply to 'vacuous names' as the essay suggests, but to -- LIFE in general!

"Vacuous Names" was written in 1969. Two years earlier Grice had delivered the William James lectures where he had used square brackets, rather.

He refers to them on p. 280 of "Presupposition and Conversational Impicature", where he notes he is 'a revised and slightly more complicated version of the square brackets device which was introduced in [WJ, lecture IV]''.

In this version, he applies it to 'some'.

The rules are five in number:

RULE 1:

(a) If expression A is of the denominated type T, then A[B]C is rewritten as BABC.
(b) If expression A is NOT of type type, or is null, then A[B]C is rewritten as ABC.

RULE 2:

In rewriting, nested brackets are eliminated, seriatim, from exterior to interior.

RULE 3:

"IF no connective [or truth-functor in general, to include ~ -- these he calls 'logical constants' in "Vacuous Names") directly precedens a closing (right-hand) square bracket, "/\" is supplied in rewriting, where needed, to preserve syntactical admissability."

---- But don't overdo this, as Milton did, "AND did those feet in ancient times, walk upon England's mountains green?"

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RULE 4:

"Any opening (left-han) parentheses introduced in rewriting are closed terminally.

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RULE 5:

"In preposing an expression containing a bound variable, the varaible is changed.


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He applies the rules to

"Some F is G"
"Every F is G"

and their negations:

including:

"Some F is not G"

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Consider his case of "Every F is G".

"We could use the revised version to handle the
alleged existential presuppositions"

which comes out as cancellable implicature, then,

"of 'some' and 'every'"

"'Every F is G' could be represented as'

~[(Ex)(Fx /\] ~Gx)."

This will have, as per rule 1(a) above -- and (5), the rewrite:

(Ey)(Fy /\ ~(Ex)(Fx /\ ~Gx))"

and Abra cadabra, hocus pocus.

What the eye no longer sees the heart no longer grieves for!

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