On Monday, October 30, 2017 at 11:53:10 PM UTC+1, John Gabriel wrote:
> **** A number is the measure of a magnitude ****
From the Greek Arithmetike meaning the art of counting. But a reduction of mathematics to arithmetic is just naive, there is algebra, i.e. mathematics and numbers as a symbolic game, which comes later, from the Arabs, and in fact subsumes arithmetic. We can now use mathematics (numbers) to talk about literally anything (that is coherent and precise enough as to be formalisable). E.g. about where exactly Achilles reaches the tortoise, and if "your system" cannot answer a valid question, that is only about limitations intrinsic to "your system", not to mathematics itself: just use a system that is correct and powerful enough for the job.