Bertrand Russell introduced orders on propositions to block construction of paradoxes such as “The Liar” [Russell 1908]. Without orders on propositions, the “

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://papers.ssrn.com/abstract=3603021 https://www.youtube.com/watch?v=AJP1VL7shiI https://www.youtube.com/watch?v=AJP1VL7shiI