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


Torkel Franzen wrote:
> anzaurres1@xxxxxxxxxxx writes:
>
> > You can pick any axiomatic system you want. In some the statement
0=1
> > will be true. In others - false.
>
> There is no concept of a statement being true or false "in an
> axiomatic system" in logic.

Torkel,

When we, mathematicians, say that a statement is true in a given
axiomatic system, we mean that one can logically derive this statement
from the axioms.

If you don't know what an axiom is, ask your mommy.

.

Relevant Pages

  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... It's the *axioms* ... Otherwise it's not an axiomatic system. ... generator to compare to a proof checker in the first place. ... The program was to be able to rewrite all mathematics starting using ...
    (sci.logic)
  • Re: Relativity as an axiomatic system
    ... > What Einstein describes is an axiomatic system which, by definition, ... > can be presented as a sequence of propositions with the axioms at the ... the path from the axioms ... quantum mechanics and relativity". ...
    (sci.physics.relativity)
  • Re: Help in answering news story on refutation of fermats last theorem
    ... >> When we, mathematicians, say that a statement is true in a given ... > axiomatic system" when they mean that it is provable in that system. ... > observation that there are theories with false axioms. ...
    (sci.math)
  • Re: Natural deduction?
    ... introduce what amounts to additional axioms in the middle of a proof. ... If you want to openly declare them separate from all of the theorems, ... You then have an axiomatic system: ... The Premise Rule alone invalidates the claim that it is an axiomatic ...
    (sci.logic)
  • Re: abundance of irrationals!)
    ... >>> The basic truths are the axioms. ... within an axiom system the axioms are basic truths. ... >> reasons OUTSIDE of the particular axiomatic system. ... There are no reasons OUTSIDE an axiomatic system for either of the ...
    (sci.math)