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We will extend the well-known Church encoding of Boolean logic into λ-calculus to an encoding of McCarthy's 3-valued logic into a suitable infinitary extension of λ-calculus that identifies all unsolvables by ⊥, where ⊥ is a fresh constant. This encoding refines to n-valued logic for n∈{4,5}. Such encodings also exist for Church's original λI-calculus. By way of motivation we consider Russell's paradox, exploiting the fact that the same encoding allows us also to calculate truth values of infinite closed propositions in this infinitary setting.