Grice on ηn (Glossary 1 -- Natural Deduction System', p. 125, in Davidson/Hintikka)

by J. L. Speranza
for the Grice Club.

The first point in the "Glossary" for his 'natural deduction system' involves a variable over a system. Grice uses the Greek letter, η.

Let η denote any symbol of [G_HP.

"η_n" will thus denote "the result of attaching, to [η], a subscript denoting n" -- where n is a natural number.

As Grice notes, it's only relations of magnitude that are relevant to the System.

i.e.

=, >, and <.

Grice states this as a law of isomorphism:

"Phi and psi are isomorphs iff

(1) subscripts apart, phi and psi are identical,

and (2) relations of magnitude ... holding between

any pair of subscripts in phi are preserved between

the corresponding pair of subjscripts in psi."