[jepler]

I'd take recourse to https://en.wikipedia.org/wiki/Bremermann%27s_limit

All human thought processes appear to require some irreversible physical processes in order to occur. (not some fancy quantum process that might turn out to proceed in a way that avoids the energy limit of computation)

Together with Bremermann's Limit, this means that we can put a limit (albeit a very large one!) on the amount of thought that can ever happen. You'd get a smaller limit considering the earth or solar system vs the entire universe, but it'd still be finite.

So if you just start with the infinite thoughts "There is a natural number 0", "There is a natural number 1", and so on, there must be a unique smallest (finite!) natural number X for which the statement "There is a natural number X+1" will never be thought.