Re: Am I a crank?

In article <1lugf2hnqivjk9jpitvd0k062hhihq77hb@xxxxxxx>,
Lester Zick <dontbother@xxxxxxxxxxx> wrote:

On Thu, 31 Aug 2006 23:08:10 GMT, "*** T. Winter" <***.Winter@xxxxxx>
wrote:

In article <1g6ef29j95erganm4b51kteh5ab6d7pcdf@xxxxxxx> Lester Zick
<dontbother@xxxxxxxxxxx> writes:
...
Zick claims that mathematicians claim their axioms to be true.
What evidence does he have of this claim?
Like most of his claims here, none!

Actually Zick claims that modern mathematikers claim their axioms are
not true.

Mathematicians do not claim axioms to be either true or false. They are
non-provable basic assumptions. And when reasoning within a certain set
of axioms they are assumed to be true.

Okay. So how exactly can they be assumed true if their axioms are not
assumed true?

In an axiom system anything deducible from those axioms, including the
axioms themselves, is deemed "true in that system", but not necessarily
true outside it.


The problem is that they're routinely assumed true

Only with in some system of axioms, but not outside that system.

and referred to as true without regard to assumptions of truth for
their axioms.

Very much with regard for these assumptions.

So are definitions.

Definitions are generally only useful within certain axioms systems.
There is no use in defining a triangle if there is not going to be
anything geometrical involved. But there is nothing tha would prevent
one from making useless definitins in any axiom system.

All that is really demonstrated of
theorems is the absence of logical inconsistency between them and
their axioms and not truth.

Precisely. But that allows theorems of the form
"if these axioms are all true then that proposition is also true",
which is the form all mathematical theorems take.
.

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