Timeline for Relationship of lambda calculus to the rest of math

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Dec 10, 2016 at 16:55	comment	added	Bjørn Kjos-Hanssen		@Polymer I guess you can try to get into Russell's paradox-like trouble like this: if you define $f(g)=1$ if $g(g)=0$, and $f(g)=0$ if $g(g)=1$, then what is $f(f)$?
Dec 10, 2016 at 16:51	comment	added	Bjørn Kjos-Hanssen		@Polymer well, functions can still "call themselves" in a different sense, like say $f(n+1):=2^{f(n)}$.
Dec 10, 2016 at 16:36	comment	added	Polymer		So id is weird. To verify your thought, I define an "application" function $id \times x = x$. Now $id \times id = id$, and we can use it $(id \times id) \times 2 = 2$. No more functions "calling themselves". I'm still confused why I haven't seen something like this sooner. Would studying ZFC closer clarify why functions calling themselves is strange? If I wanted to use this in some mathematical context, what problems might come up?
Dec 10, 2016 at 5:32	history	answered	Bjørn Kjos-Hanssen	CC BY-SA 3.0