Numerical subscripts of scope-precedence and formational stages of Grice's natural deduction system

-- by J. L. Speranza
for the Grice Club

The 'obvious link' that Grice sees between his numerical subscript device and the formation rules involve the quantifiers.

Grice proposes three stages ('formational stages')

Step 1:

F1x

--

Step 2 (appearance of subscript 2)

F1a2

---

Step 3 (apperance of subscript 3)

Ex3F1x2.


As this connects with which inferences are licensed or not in his natural deduction system we need to consider a distinguished pair such that is yielded by those formational stages.