Second feature concerning scope procedence in Grice's natural deduction system (in Davidson/Hintikka, p. 122)

-- By J. L. Speranza
for the Grice Circle.

If the introduction of the numerical subscripts "to indicate scope-procedence (the higher the subscript, the larger the scope)" is the first feature concerning scope in Grice's natural deduction system, the three formational stages in the building up of a simple quantificational formula constiutes the second feature. This allows for a direct and indirect derivation of a second member of the distinguished pair of formulae, and similar provisos for the first member -- In particular, the following inference for example, is NOT licensed:

~3F1a2
_____
-.
. . Ex4~2F1x3