Fourth feature concerning scope-precedence in Grice's natural deduction system (Davidson/Hintikka, p. 123)

by JLS
for the GC

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This is explicated on p. 123 of "Vacuous Names" (Section III: Scope).

Here Grice notes that he takes up ONE approach to the viewing of closed formulae in a system.

According to this approach:

"actual lexical entries (lexical rules)"

--- the influence of Chomsky's "Syntactic structures", that Grice had studied under Austin in 1959 is obvious)

"are provided ONLY for the

logical constants

and the quantifiers."

"An atomic [i.e. non-molecular, but neither involving ~] formula"

such as

Fa

is

"a categorical subject-predicate sentence"

in the language.

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Why does Grice's method of subscripting reflect this approach?

Well, because in an atomic formula

the subscripts on individual constants

are ALWAYS higher than that on the predicate-constant."

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This is in consonance with the fact, Grice notes,

that

'AFFIRMATIVE' (rather than apophetic, or negative]

categorical subject-predicate sentences"

--- Grice gives two examples: "Socrates is wise", "Bellerophon rode Pegasus" --

'IMPLY'

or as he would later have, 'entail'

---

'the non-vacuousness of the names which they contain.'

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