> your idea of physical realizability seems to me to be questionable. I made it abundantly clear that is not my idea but an ongoing discussion in the philosoph

> your idea of physical realizability seems to me to be questionable. I made it abundantly clear that is not my idea but an ongoing discussion in the philosophy of mathematics. You're telling me to not get caught in philosophical arguments and in the very sentence before that presuppose the idea that mathematics is a mental construction, which is just one out of many philosophical views in that area. By the way, I'm interested in philosophical issues because I am a philosopher. Just because you don't like these issues or find them "questionable" doesn't mean anything. Some of my colleagues defend an Anti-Fregean formal foundation of mathematics to which physical realizability seems to pose a huge problem. If they want to get their papers published, they'll have to address the issue. I'm aware of Wigner's paper, it's a well-known classic. Finally, to conclude this thread from my perspective, while I'm personally not interested in the (broadly conceived) metaphysics of mathematics and am happy to leave these issues to mathematicians interested in them, the way you're just presupposing that mathematical objects are mere mental constructions cannot really count as engaging with the problems yet. If you read what I wrote above again, you'll realize that I presented an argument why irrational numbers cannot be abstractions, yet you keep talking about abstractions. In a nutshell, it's not that simple.