Subscripts and Square Brackets (Grice on C. D. Parsons), in Davidson/Hintikka, p. 124.

by J. L. Speranza
for the Grice Club

Since the square bracket device of Grice is possible better known than his subscript device introduced in Davidson/Hintikka 1969 -- Grice had used square brackets earlier in the 1967 William James lectures -- it may do to quote his correspondence with C. D. Parsons, of Harvard.

On p. 124 Grice provides his pair of formulae:

~₃F₁a₂

and

~₂F₁a₃


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In Parsons's suggested rewrite, alla Principia Mathematica, Grice has it, this becomes respectively:


For the former:



~[a](Fa)


For the latter:


[a](~Fa).




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Grice provides another illustration. First, his own pair of formulae:


∃x₄~₂F₁x₃

∃x₄~₃F₁x2>



These become, in Parson's rewrite, respectively.

For the former:

(∃x)(~[x](Fx))

For the latter:

(∃x)([x]~Fx)).

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Grice opts for the subscript device for showing, in a clearer way, "the link betweeen subscripts and formation rules" (Grice, p. 124)