Frist of five features regarding scope-precedence in Grice's natural deduction system (Grice, in Davidson/Hintikka, p. 121-2)

by J. L. Speranza
for the Grice Club.

The first feature, then, is the numerical subscripting itself. Numerical subscripts merely 'indicate,' then, 'scope precedence (the higher the subscript, the larger the scope)'. And they are meant to replace the parentheses of Principia Mathematica that he had used in Lecture IV in 1967, 'Logic and Conversation' ("Indicative Conditionals", in fact).

----

By this feature, of the distinguished pair

~2F1a3
~3F1a2

the first will represent the reading of S1 'in which S1 is false if Pegasus does not exist'. I.e. 'a' 'has maximal scope'.

--- In the second member of the pair, 'a' has minimal scope, rather.

----

Grice provides an interesting illutration involving the overlap of the numerical subscripts with the quantified formulae, too.