First precise definitional feature of scope for Grice's natural deduction system

We see that on pp. 124-125 Grice feels ready to provide a more precise definition of scope for his natural deduction system, which he characterises by three definitional feature.

The first concerns the Greek letter, eta.

"eta" is "a logical constant, or quantifier,

ocurring in a colosed formula, phi"

Now,

"the SCOPE of 'eta', then",

is

"the largest formula in phi which meets two requirements."

First,

"phi contains the occurrence of eta"

and

Second,

"phi does NOT contain an ocurrence

of a logical constant or quantifier bearing

a HIGHER subscript than that which

attaches to the occurrence of eta".

-- it all sounds very plausible. The second requirement is just a closure clause, as it were.