FOM: iterative conception of set

[Neil Tennant]

M. Randall Holmes wrote

 > The notion "set of ZFC" can be coded into higher order logic as
 > "isomorphism class of (pointed) well-founded extensional relations".
 > This notion is purely logical if the notion of set (class) as the
 > extension of a concept is taken as purely logical.  It is a third-order
 > concept in higher order logic.  
 > 
 > To get this notion to satisfy the axioms of ZFC, one needs to suppose
 > that one has "enough" objects.  Nothing else is needed.  One
 > doesn't even need any concept of iterative construction, though this
 > concept is certainly intuitively appealing.

What would this establish for one who thinks that second order logic is just set theory in disguise?

Neil Tennant