I think they meant it's inconsistent with the 'memory value recorded vs memory address value' distinction in a Turing machine (as in, it's not consistent with its physical instantiation: "the real world"), not inconsistent with axioms of formal logic. I'm getting confused because I think these are two or more different research camps (computability, philosophy, logic, etc) and I don't know how much jargon is shared.

OP's other post's comment is related https://news.ycombinator.com/item?id=19265632

I have tossed set theory out entirely. I consider Lambda foundational.

I am not even talking about comparing sets. I am talking about comparing infinite-precision floats to themselves.

Any system that does it in O(1) is broken.