Bertrand Russell introduced orders on propositions to block

construction of paradoxes such as “The Liar” [Russell 1908].

Without orders on propositions, the “self-referential”

proposition I’mFalse (such that

I’mFalse⇔¬I’mFalse) could be constructed using the

following recursive definition:

I’mFalse:Proposition<i>≡¬I’mFalse. Since Ψ is a

propositional variable in the definition, ¬Ψ:Proposition <i+1>. Consequently,

I’mFalse:Proposition <i>⇒I’mFalse:Proposition<i+1>, which

is a contradiction.

For more information see the following:

https://papers.ssrn.com/abstract=3603021

https://www.youtube.com/watch?v=AJP1VL7shiI