On Jul 13, 2013, at 9:39 PM, Robert Hansen <firstname.lastname@example.org> wrote:
> You are not saying anything different here than you were saying before, that rational thought has more than one point of origin. Does the geometer develop different instincts and intuitions than the algebrist? Absolutely. But mathematics requires rational thought, which derives from a sense of reason, which has one point of origin, and those instincts and intuitions are developed to serve that. In other words, even though the algebrist and geometer develop different instincts and intuitions, they do so under the same sense of, and requirements of, reason.
Let me ask you this Joe. Do you think you could develop the instincts and intuitions for geometry or for algebra or for anything mathematical, without the sense of reason and a capacity for rational thought?