Primes

What is 'natural' about the 'natural numbers'?  Without some primitive (and, so, poorly defined) conception of 'sequence', we cannot generate them.

We could just as well regard the primes as 'prim-ative' and define an operator for their combination into complexes.  ('Multiplication').

Would these primes appear in a 'natural' sequence if there was nothing peculiar about our conception of sequence?  Maybe we're trying to make it do the wrong thing.

The combination of sequence and primes gives us the 'no largest prime' proof, and sequence generates unlimited quantities and unlimited complexities in a counter-intuitive way.  We know these cannot exist in any articulable world.  To say that they exist in the word 'prior' to articulation is to say something about this world, to partly articulate it ... and to say, about it, that it cannot be completely articulated.  'There will always be things we don't know'.  Is that all?  Or will there always be important things that we don't know?

I don't want to know the position, mass, and velocity of every molecule; but I do want to know whether my bath water is too hot.