On Tue, Sep 11, 2012 at 9:21 PM, Paul Tanner <firstname.lastname@example.org> wrote:
>> >> The so-called "real numbers" are a relatively recent cultural >> invention, and multiplication was going on a long time before they >> were promulgated. >> > > They just didn't understand the continuum even though they were using > it, and so it is not recent. > Just because you don't give it a name or know its nature does not mean > that it therefore does not exist.
That's a telling statement. You consider the "real numbers" to "exist" and "to have been discovered". They're an empirical phenomenon in your mental geography, like Mt. Fuji. Those who don't use them, don't play the same games, are "science deniers" because they deny the "fact" or these "real numbers".
I hope you're aware that not even every distinguished professor of mathematics with peer reviewed published papers believes as you do about the reals. What you have stated is one among many points of view, by no means universally accepted, even among scientists.
To say the real numbers are "a cultural artifact", "an institution", "a set of conventions", "a set of practices", "a set of language games" is not unheard of or "fringe" in any way. Many anthropologists will discuss numeracy and alpha-numeracy in this manner. All math is ethno-math, for them and for me.
Nor is the meaning of "real numbers" fixed for all time. Their character changes as the language games around them change, just as Euclidean geometry took on a different meaning in light of topology. The way we look at domain B is affected by what goes on in surrounding neighborhoods. The meaning of "dimension" was affected by the invention of "fractional dimensions".
Anyway, it's becoming clear to me that you're more of a dogmatist than I'd realized, yet in your own mind you're a champion of "science" as a result.