SRH - is this it?

SRH:

A statement that refers to itself is either a tautology TT or a contradiction TF.

The most famous example is the liar paradox.

TT: "This statement is True."

TF: "This statement is False."

My favourite object of contemplation from a few years ago doesn't actually refer to itself!

T = {T}

Makes an equality between T and the set containing T which are different objects.

So SRH is not about Impredicativity. To define something in terms of itself is to enter a "temporal" version of the SRH which is a loop. One is then left with a different question of starts and ends which is not an immediate problem. Loops are the root of the Halting Problem, and I have speculated isomorphic with contradictions. Induction is maths famously has survived this problem.

I'm busy on other stuff so this will have to wait for further thought...