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.
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.