Re: Preface: Going Further
Mathematicians assume the Axiom of Choice, which is based
on "faith"; of course, mathematics isn't exactly logic.
There are compelling reasons to accept it as an axiom in
professional mathematics; many proofs depend on it and some
intuitively compelling theorems are equivalent to it.
Very few mathematicians have less "faith"; e.g., for
Constructivists, mathematical objects have to be
constructed.
In this world, we make some assumptions. Some have faith
that there is truth in some absolute sense and some have
faith in G-d.
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