****Logical Identity is Foundationless; Logic is Relative Nested Tautologies.
****Logical Identity is Foundationless; Logic is Relative Nested Tautologies.
((A=A)=(A=A))=(A=A).....
The identity law has to be subject to itself if it is to have identity, but as being subject to itself it results in the distinction being subject to itself, and infinite regress occurs.
((A=A)=(A=A))=(A=A).....
If the law of identity is not subject to itself than the law of identity ceases:
((A=A) =/= (A=A))= -(A=A).....
Now if infinite regress or absence of the laws, non-law, occurs it is subject to the laws of identity and the same process ensues:
IG = IG
((IG=IG)=(IG=IG))=(IG=IG).....
NL = NL
((NL=NL)=(NL=NL))=(NL=NL).....
But if the infinite regress and non-law is subject to an absence of identity than nothing can be said, but neither can identity be claimed for anything else.
What remains if the identity law is subject to itself is nested tautologies.
These nested tautologies are relative to other nested tautologies if a proposition is present:
((A=A)=(A=A))=(A=A)..... -> ((B=B)=(B=B))=(B=B).....
All logical rules, syntax, formalisms, semantics, etc. are subject to the identity laws if they are to have an identity. Thus to argue standard x-order logic against this meta-formalism is to enact said formalism.
In these respects syntax become a performance of invariant constraint as tautology becomes invariant by nesting, constraint as the form of the tautology and performative by degree of its emergence. What remains of logic and logical identity is empty loops within loops.
If the axiom of identity is left unexamined than the foundations of logic is nested assumption thus logic is not required as assumption remains regardless of its depth.