Re: Help in answering news story on refutation of fermat's last theorem

Torkel Franzen wrote:
> anzaurres1@xxxxxxxxxxx writes:
>
>The points are, (1) truth and falsity are semantic
> concepts, unlike that of provability in an axiom system, and (2)
> a simple example of a consistent theory with a false axiom is
> PA+"PA is inconsistent".

And my points are:

1. The statement

"if all bananas are green then all bananas are green"

is TRUE.

2. The statement

"if all bananas are green then not all bananas are green"

is FALSE.

4. There are no theories, studied by any professionally competent
mathematician, which contain "false axioms", no mater how you
define this term.

Nor can there be one. Why? Because every theory, advanced in the
science of mathematics, is based on at least one example, which
satisfies all axioms of that theory.

Thus, when you replied to me

> > When we, mathematicians, say that a statement is true...
>
> People do indeed often speak... For example, it sometimes prompts
> them to contradict the simple observation that there are
> theories with false axioms

you were talking not about what professional mathematicians actually do
but you THINK professional mathematicians do. Your image of what
professional mathematicians is dead wrong.

While I cannot change all the false images that the general public all
over the World has of mathematicians, I will correct the false
misconceptions that the general public expresses about mathematicians
in sci.math. Moreover, I fail to understand why so many people, who
bother with visiting sci.math, refuse to find out what mathematicians
do and how and why they do what they do.

1. If you insist on "explicitely" defining your term "false
axiom" by

"A false axiom is an axiom that is false",

you will not be able to find any professional mathematician or a
mathematician-in-training (PH.D. studfents) - be it a topologist or a
logician - who will give your home-spun ideas more than 0.6 seconds
of their time. Moreover, they will think you are playing mind games
with them.

.

Relevant Pages

  • Re: Help in answering news story on refutation of fermats last theorem
    ... > concepts, unlike that of provability in an axiom system, and ... "if all bananas are green then all bananas are green" ... >> When we, mathematicians, say that a statement is true... ... but you THINK professional mathematicians do. ...
    (sci.math)
  • Re: Help in answering news story on refutation of fermats last theorem
    ... People have been known to study an axiom system before knowing ... |>> When we, mathematicians, say that a statement is true... ... But since we're talking about professionals, ...
    (sci.math)
  • Re: A puzzle for Cantorists
    ... not, upon accepting the Axiom of Infinity, transfinite cardinals ... axiom and begin with a new set. ... Those are excellent mathematicians. ... I say infinite sets are equivalent, ...
    (sci.math)
  • Re: Question about induction
    ... description of the claim that least number principle and the principle ... mathematicians who have not studied mathematical logic -- see below. ... If you do you will find similar logically sloppy/naive/erroneous posts ... that they also need to explicitly include that axiom (or another axiom ...
    (sci.math)
  • Re: Cantors Theory sucks
    ... >>> truth of its axiom systems is not presumed except as a convenient ... > ultimately mere verification of the correctness of if-then statements ... > Pure math only deals with correctness, ... > Pure mathematicians are sort of like the tool makers for those applied ...
    (sci.math)