The natural numbers exist in about the strongest possible sense: I can get a computer program to spit them out one by one, and it won’t stop until it runs out of resources. It’s more accurate to say I don’t believe that they’re well-ordered, see here.
You might find my reasoning preposterous, I only wanted to point out that it’s essentially the same as EYs reasoning about uncountable ordinals.
So what you’re saying is that you don’t believe the natural numbers exist.
The natural numbers exist in about the strongest possible sense: I can get a computer program to spit them out one by one, and it won’t stop until it runs out of resources. It’s more accurate to say I don’t believe that they’re well-ordered, see here.
You might find my reasoning preposterous, I only wanted to point out that it’s essentially the same as EYs reasoning about uncountable ordinals.