And a short shameful confession: I no longer believe in the standard natural numbers. I don't know exactly what it is that I do believe, but I don't believe that something like the standard natural numbers exist. I shouldn't have tried to study logic: it destroyed my faith. (And then Albert told me it's consistent to suppose that the models of set theory all have non-standard internal natural numbers, thus confusing me even more :-)) But of course I do believe something. For instance, I believe that some kind of natural numbers exist. Of course! Because otherwise nothing would be. There are lots of natural numbers, actually... but only all kinds of non-standard ones.

There are lots of natural numbers, actually... but only all kinds of non-standard ones.