On Thu, 23 Jul 2015 02:58 am, Steven D'Aprano wrote: >> 1. We have reason to expect that the natural numbers are absolutely >> fundamental and irreducible > > That's wrong. If we had such a reason, we could state it: "the reason we > expect natural numbers are irreducible is ..." and fill in the blank. But > I don't believe that such a reason exists (or at least, as far as we > know).
Sorry, that's not as clear as I intended. By "a reason", I mean a direct reason for that choice, rather than some reason for the opposite choice. I hope that's clear? Perhaps an example will help. "Are tomatoes red?" We can have direct reasons for believing that tomatoes are red, e.g. "the light reflecting off these tomatoes peaks at frequency X, which is within the range of red light". Alternatively, we might not have any such reason, and be reduced to arguing against the alternatives. Only if all the alternatives are false could we then believe that tomatoes are red. "If tomatoes were blue, they would appear green when viewed under yellow light; since these tomatoes fail to appear green, they might be red." I'm suggesting that we have no direct reason for believing that the natural numbers are irreducible concepts, only indirect ones, namely that all the attempts to reduce them are unsatisfactory in some fashion or another. But neither do we have direct reasons for expecting them to be reducible. -- Steven -- https://mail.python.org/mailman/listinfo/python-list