Licensing inferences in Grice's natural deduction system

by J. L. Speranza
for the Grice Club.

We see that applying the three formational stages in the building up of simple quantificational formula, we yield a distinguished pair:

Ex4~2F1x3
Ex4~3F1x2

--- What inferences do we license, and which we don't.

Well, for one:

~2F1a3
_____
-.
. . Ex4~2F1x3

---

But, obviously, we should NOT license

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

Similarly, regarding the second member of the distinguished pair. We license the inference:

~3F1a2
______
-.
. . Ex4~3F1x2

For the conclusion, Grice notes, "is derivable directly (by E.G.)". He adds that an 'indirect' derivation from '~2F1a3' should also be available, though.