> The phrase "uncountably large collections" isn't uncountably large. Your brain is a finite object or finite size and there is a limit to the complexity of the things it can think about. The concept of "uncountably large" is not sich a complex thing.

Quite so. And one of the inferences we can make in doing that non-infinite reasoning is that, using the relevant senses of the words, there is no mapping with the property you propose. You can't just retreat behind puns when someone calls you on that...

But, you know, room for all kinds. I hope you and Brouwer have a nice beer together.