Concepedia

A paradox in illative combinatory logic.

M. W. Bunder

Notre Dame Journal of Formal Logic · 1970 · 11 citations · 3 references

DOI

Concepts

Abstract

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:

References

3

The combinatory foundations of mathematical logic

Haskell B. Curry · Journal of Symbolic Logic · 1942 · 48 citations

, , +4

Some Advances in the Combinatory Theory of Quantification

Haskell B. Curry · Proceedings of the National Academy of Sciences · 1942 · 15 citations · Full text

, , +7

Maarten Wicher Visser Bunder. Set theory based on combinatory logic. Dissertation Amsterdam 1969, 80 pp. + 3 pp. of corrections.

Jonathan P. Seldin · Journal of Symbolic Logic · 1970 · 11 citations

, , +6