1. Bertrand Russell studied the "I am lying" paradox, which I always thought was nothing more than a clever meme. 2. Bertrand Russell is responsible for type theory 3. That type theory came out of his study of the paradox.
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:
Think along the lines that you have some sentence Px which asserts that sentence Py is false. Now imagine a table where both the rows and columns are P0, P1, P2, .. populated with these sentences. The diagonal is where you have the self-reference: Pi asserting that Pi is false.