 Here MP is a version of modus ponens, and Cont is a principle of contraction: two occurrences of the sentence \(\alpha\) are “contracted” into one. (We will soon encounter related principles that are more commonly referred to as  contraction.[14]) The Curry-Paradox Lemma entails that any Curry-complete theory must violate one or more of Id, MP or Cont on pain of triviality.