𝜖𝑄 ≡ ∀𝑥[𝑃(𝑥) ≡ 𝑄(𝑥)], leads to contradiction. ∘ 𝜖𝑃 denotes the set of elements satisfying predicate 𝑃. ∘ 𝑅 can be expressed as ∃𝑃[𝑥 = 𝜖𝑃 ∧ ¬𝑃(𝑥)] in predicate logic. ∘ Substituting 𝑥 as 𝜖𝑅, we find 𝑅(𝜖𝑅) ≡ ¬𝑅(𝜖𝑅). ∘ In Frege’s work, there is a distinction between objects, predicates, and predicates of predicates. This hierarchy can be seen as an early notion of type theory. 20