Sure I understand that, but nevertheless I have seen at least 3 people who were confused in the same way. (c.f. https://youzicha.tumblr.com/post/728810860450136065). I think the issue is that if you see an equation f(c) = c you think about trying to evaluate the function f at the point c, since that's what you do in almost all other situations involving a function call.
Indeed. I think this something that people are often confused about, e.g. one blogger[0] comments:
> The key to understanding the fixpoint theorem, for me anyway, was realizing that when it says FG=G, it does not mean that for every F there is a G such that by calling F with parameter G one can get back G. I mention this in the blog post, above. The equality operator in FG=G is the equivalence relation induced by the calculus rewriting relation: that is, it's the symmetric reflexive transitive closure of the rewriting step relation. When you look at the proof of the theorem, it actually works by constructing an expression G such that evaluating G produces, as an intermediate result, FG. There is no need for F to even be a function, and if F is a function it doesn't matter what, if anything, F would actually do when called, because the proof of the theorem doesn't involve calling F.
I think the name "fixpoint combinator" is kindof bad, it it was called e.g. the "recursion combinator" I think people would find it more intuitive.
> Suppose you publish an article that happens to contain a sentence identical to one from this article, like "The law sees Colour." That's just four words, all of them common, and it might well occur by random chance. Maybe you were thinking about similar ideas to mine and happened to put the words together in a similar way. If so, fine. But maybe you wrote "your" article by cutting and pasting from "mine" - in that case, the words have the Colour that obligates you to follow quotation procedures and worry about "derivative work" status under copyright law and so on.
There was a real court case in 2012 which I think is interesting because it's very similar to this example. A photographer was accused of "copying" the concept of taking a photo of a red bus in front of a grey Houses of Parliament. He defended himself by saying that that those ideas are very common and should not be copyrightable---but failed: