On 11 Jun., 22:31, Virgil <virg...@nowhere.com> wrote: > In article > <1348b29b-3f39-40a7-be0e-5bd24a4e3...@s21g2000vbb.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > I need no axioms. > > Then there is absolutely nothing that you take to be true? > > There are absolutely no truths from which you can deduce other things?
There are truths, like 1 + 1 = 2, or, for linear sets, ExAy <==> AyEx, but they cannot be chosen by free will.
Incorrect are such lies as the axiom of infinity or the axiom of choice. > > That makes for a very simple mathematics in which nothing need be true. > > Consider axioms like in the American Declaration of Independence: > > "We hold these truths to be self evident..." > > Unless WM can list the things he "holds to be self evident", he does not > have anything to build on.
There is no necessity to list them in mathematics. Every sober mind knows them.