now, there is no such thing as &quot;4-identity&quot;, &quot;5-identity&quot;, etc., in 
    the standard predicate calculus.  It is more that such concepts are not needed,
    just as teridentity is not needed, since the general apparatus of the predicate
    calculus allows us to express identity among any number of terms without special
    provision beyond &quot;=&quot;.

No, that is not the case.  Standard predicate calculus allows the expression
of predicates I_k, for k = 2, 3, 4, ..., such that I_k (