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Lester Zick wrote:
> On 30 Aug 2006 17:24:44 -0700, "MoeBlee" <jazzmobe@xxxxxxxxxxx> wrote:
> Who cares? We have it from Virgil that axioms and definitions in
> modern math aren't true.
You're circling closer to what Virgil (and everyone familiar
with axiomatic mathematics) is saying, but not there yet.
A definition is a shorthand. It is a name given to a concept,
generally because the name is shorter than the description
of the concept.
"Definitions aren't true" sounds like they have a truth value
of "false". In fact they don't have a truth value. They're just
symbolic substitutions.
Axioms do have a truth value. They are true by assumption,
if consistent. I would say they are true by assumption even
if not consistent but in that case there may be some room
for different conventions.
- Randy
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