Grice defines a 'segment' (Grice, p. 123 of Davidson/Hintikka)

by JLS
for the GC

Regarding the third feature of scope-precedence of Grice's natural deduction system, involving the caveat about free and bound variables and their correlation with constants of individual, Grice sets to define a 'segment' of a formula.

F1x2

or

G1x2y3

are, as he notes, NOT formulae of the system.

Yet, each is a 'segment' of a formula.

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A segment relates to the function, role, or metier, that the free variable (x, in the first example; x and y in the second) is supposed to play.

As Grice has it:

"the sole function of [the] free variable[...] is

TO ALLOW the introduction of a [constant of individual]

at different FORMATIONAL stages.'

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As an example he gives the 'segment':

F1a2 )3 G1a2 \/4 H1x

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Here 'x' occurs freely, and its sole function is to allow the introduction of 'b', where 'b' will have maximal scope. To wit:

F1a2 )3 G1a2 \/4 H1b5