A paradox in illative combinatory logic.
M. W. Bunder · Notre Dame Journal of Formal Logic · 1970
Curry, in [1] and [2], has shown the inconsistency of a system of illative combinatory logic containing the axiom: hH^X for all obs X, for k = 2 (and 1).("HX" stands for "X is a proposition''.)He also stated that the inconsistency held for k > 2, this more general result is proved below.Assume the following: