Content deleted Content added
Line 373:
::::: "Mathematics" is the thing which is not a theory. ZFC set theory is a (mathematical) theory. Euclidean geometry is a (mathematical) theory. First order arithmetic is a (mathematical) theory. Lambda calculus is a (mathematical) theory. I'm not sure of the best way to interpret "value" in the context of this discussion, but "equals" is easy; it's whatever the axioms of the theory say, and the axioms of lambda calculus say it's convertibility (see Barendregt for example; I don't have my copy handy just at the moment). With regard to a fixed point combinator in "mathematics", i.e. the (informal) meta-theoretic question, I'm less sure what to say. The meta-theoretic concept of a fixed point is reasonably clear, because the meta-theoretic concept of a (first order) function is reasonably clear, but I don't think a combinator is, because higher-order functions aren't (at least to me). [[User:Haklo|Haklo]] ([[User talk:Haklo|talk]]) 00:50, 15 January 2014 (UTC)
:::::: By mathematics I loosely mean ZFC based stuff. My only problem is saying that the Y combinator gives a solution of the fixed point equation. But then the fixed point equation is expressed in "mathematics", not LC. Anyway for me a value is a property of an expression (wff) that is the same iff the two expressions are equal. And a solution is a value that satisfies the equation. But maybe this not the standard definition for mathematician (only for other humans). My objection before was you referring to Y f as a solution of x = f x. I will re-read what you wrote in light of this discussion later. Regards [[User:Thepigdog|Thepigdog]] ([[User talk:Thepigdog|talk]]) 02:22, 15 January 2014 (UTC)
==Its not magic==
| |||