 Self-reference factors into some paradoxes, such as the widely known liar paradox and Russell’s paradox. The set theoretical understanding of functions also discourages the idea of self-application. Thus it is remarkable that pure untyped CL does not exclude the self-application of functions. Moreover, its mathematical models showed that a theory in which functions can become their own arguments is completely sensible, in addition to being consistent (what was established earlier using proof theoretic methods).