Second precise definitional feature of scope in Grice's natural deduction system

If 'eta' comprises the first definitionary feature, the second concerns a specification of 'eta'.

"Eta" can be a logical constant or a quantifier, and the first definitional feature provides for that.

But eta can also be "a term (individual constant or a bound variable)".

In which case,

'the SCOPE of eta' will be

"the largest SEGMENT of phi which meets two requirements."

First,

phi contains the occurrence of eta.

and

Second,

phi does NOT contain an occurrence of a LOGICAL constant [but surely NOT a quantifier] bearing a higher subscript than that which attaches to the occurrence of eta."