 In the 1930s, an alternative route to solve the antinomies emerged. This approach exploits the duplication (contraction) combinator \(W\) which satisfies \(Wfx=fxx\); if \(N\) represents negation and \(Babc=a(bc)\), then \(W(BN)(W(BN))\) is a fixed point of negation, and it is a functional analogue of the Russell class. On the logical level, assigning a type to \(W\) leads to the essential inference applied in the derivation of Curry’s paradox, i.e., the contraction rule \(A\rightarrow(A\rightarrow B) \Rightarrow(A\rightarrow B)\). The role of contraction was noticed by Fitch 1936, who observed that, in order to derive the Russell paradox one considers a function of two variables, then one diagonalizes and regards such an object as a new unary propositional function. But this step only works if \(W\) is accepted. Fitch then proposed a “non-contractive” logic, but his paper did not go beyond a brief sketch of a fragment of classical logic with predicates. One has to wait until the mid eighties to see contraction-free logics used systematically in proof theory and in theoretical computer science (see the entry  linear logic).