Grice's link between scope and formational steps

by J. L. Speranza
for the Grice Club

Grice had some criticism to his numerical subscript but he meant to keep it for the 'link' it showed with formation rules.

Cfr. his use of 'before'

in the phrase

'name before negation'.

---

I.e. in S1

"Pegasus does not fly"

it may well be the case that the name has been intoduced, as Grice has it, 'before negation'.

Therefore,

what "Pegasus does not fly" does is

"the result of denying the result of

substituting 'Pegasus' for 'x' in 'x flies'

(the name being introduced before negation).

---

In the alternate reading, it's just the other way round: negation being introduced before the name. Thus,

"Pegasus does not fly" indicate

"the result of substituting 'Pegasus' for 'x' in

'x does not fly' (negation having already

been introduced)."

This Grice sees as an 'obvious link' with the formation rules, or the formational stages in the building up of a formula, as it pertains to the scope-differences which reflect an ontological distinction.

As Grice puts it:

"It seems to be natural to regard

[this] distinction as a distinction

between different possible scopes ...

---"

He then mentions the 'connectives' and the negation-device (not really a connective, but a truth-functor alright):

"In the case of connectives [and ~], scope-differences

MIRROR the ORDER in which the

connectives [and ~] are introduced in

the building up of a formula (the application

of formation rules)."

Thus, the two readings of S1 can be represented as

the difference between regarding S1 as

I. 'being the result of substituting 'Pegasus'

for 'x' in 'x does not fly',' i.e. with negation

having been introduced 'before' the name.

II. 'being the result of denying the result

of substituing 'Pegasus' for 'x' in 'x' flies,'

i.e. with the name having been introduced before

negation.

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The link of the scope-difference and the formation rules is enhanced, Grice thinks, by the subscript notation, but not necessarily the square brackets -- that he had used in 1967 and that he credits Parsons for reminding him about them in 1969, or by a notational convention as suggested by Quine in his reply.