🚀 go-pugleaf

In article <TORKEL.92Nov20160605@lludd.sics.se>, torkel@sics.se (Torkel Franzen) writes:
>   You don't have to accept anything. You are free to develop whatever
> mathematics you like and put it forward for general consideration. What
> I am objecting to is only the idea that e.g. the distinction between
> countable and uncountable sets can be seen to be a "relative" one in
> the light of results in logic.

Everything in mathematics is "relative" to some formal system. To talk
about what is absolutely true independent of a foral system is philosophy
not mathematics. It is not something that can be derived from results
in logic. Perhaps I do not understand what you mean by relative. 

It would be awkward, but not necessarily unreasonable, to define a formal
system in which the reals are countable. One could add an axiom that allows
one to see from within the system that all the reals namable in the language
of the system are countable. This would have to be done with care so that
one could not use this model of oneself to construct paradoxes, but I do
not think there is any fundamental problem in doing this.

Paul Budnik