Two Goals for Grice's Natural Deduction System (Grice in Davidson/Hintikka, p. 120)

by J. L. Speranza
for the Grice Club.

Grice posits two goals for the construction of his natural deduction system. These are listed in ssection II of "Vacuous Names" entitled, "Objectives".

First goal:

To allow for a reading of "Pegasus does not fly" (with caveats for formulae, which, in Grice's words, 'do not explicitly involve [the] negation-device')

such that, on that reading, an utterance of "Pegasus does not fly" CANNOT BE TRUE -- "given that Pegasus does not exist".

This is a reading where ~ does not have the standard maximal scope. So the reading will involve a subscript device appended to the formation rules of the system. In Grice's notational variant, elsewhere, perhaps vis a vis Quine's reply in Davidson/Hintikka -- 'forbiddingly complex' -- Grice opted for 'square brackets' --.

Interestingly, Grice expounds the caveat as being,

given that Pegasus does not exist

and never has existed --

for all we know, that is!