[FOM] The discrete and the continuous
a_mani_sc_gs at yahoo.co.in
Sun Nov 4 19:48:21 EST 2007
On Sunday 04 Nov 2007 5:23:41 pm Thomas Forster wrote:
> All of Mathematics can be reduced-to/interpreted-in/etc Set
I would like to define Mathematics as the science of exactly representing and
analysing objects, processes or states of affairs. So this falls out with
the "reduced-to" possibility. But I do accept that there is a set-theoretical
interpretation of everything ... however non-classicalist or classicalist it
may be. I suspect you mean "in a classicalist sense",
> Set Theory is Discrete;
There are set theories and interpretations thereof that may be discrete or be
> The Discrete and the Continuous are two twin pillars of
> Mathematics, neither to be explained in terms of the other.
To disclude the possibility of explaining one in terms of the other appears
too dogmatic. We can see either as a special case of the other and in many
ways. It is sometimes more difficult to build mathematical models with the
discrete and then the easier continuous models are approximations.
So I accept about some of the first proposition only.
Member, Cal. Math. Soc
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