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'[OT]:Philosophy of Euclidean gemetry or Faith base'
2001\06\05@205741 by michael brown

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----- Original Message -----
From: "wouter van ooijen & floortje hanneman" <spam_OUTwfTakeThisOuTspamXS4ALL.NL>

> > Finally, math is great, science is great but is
> > only 99.9 (repeating but not to infinity)% accurate.
>
> You should make a big distinction between math and science.
>
> Math in itself has nothing to do with the real word, it is just deriving
> consequences from a axioms.

There in lies the whole problem.  Axioms have not been proven to be true and
they cannot be proven, therefore I pose the question, "How can we create
'proofs' based on 'ideas' (axioms) that are said to be self-evident
truths?".  Using this line of reasoning, couldn't I say that 'magic' is real
since it appears to be 'self evident' and it is repeatable?

>In math you can prove such a consequence. Sorth
> of an error in the proof in math "once proven is forever true". But note
> that there are a large number of mathematical systems, and what is true in
> one system (there is no x such that x*x=-1) can be false in another
system.
>
> Science is (simplified) applying math to the real world. One guy just
poses
> some theory, and when others can not disprove it in reasonable time it is
> said to hold. But that does not mean it is the truth, just that it is the
> best we have up to now.
>
> Wouter

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2001\06\06@010409 by Eric Smith

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michael brown <n5qmgspamKILLspamAMSAT.ORG> writes:
> Axioms have not been proven to be true and
> they cannot be proven, therefore I pose the question, "How can we create
> 'proofs' based on 'ideas' (axioms) that are said to be self-evident
> truths?".  Using this line of reasoning, couldn't I say that 'magic' is real
> since it appears to be 'self evident' and it is repeatable?

Yes, if you can come up with a set of axioms from which you can
consistently and repeatedly derive and explain the things that you call
"magic".

However, just because you can postulate some axioms and derive a system
from them does not mean that the system has any resemblance to the "real
world", even if the axioms seem to.

Mathematics does not require one to have faith.  Mathematics just starts
from a set of axioms, and derives various theorems.  It is when one
tries to apply the mathematical theorems to other systems (e.g., the
"real world") that one may want to have faith in one's axioms.

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2001\06\06@012407 by uter van ooijen & floortje hanneman

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> > Math in itself has nothing to do with the real word, it is just deriving
> > consequences from a axioms.
>
> There in lies the whole problem.  Axioms have not been proven to be true
and
> they cannot be proven, therefore I pose the question, "How can we create
> 'proofs' based on 'ideas' (axioms) that are said to be self-evident
> truths?

Math does no claim that its axiom set (or rather one of its many axiom sets)
is true. What is claims (and that is an "absolute truth") is that the whole
building of a certain math (there are more than one) derive from its axioms.
That is both the power and the weakness: you can not sensibly deny that the
whole thing derives from its axioms, yet that does not say anything bout our
real world (hence it can not be disproven by experiments).

Wouter

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2001\06\07@091921 by Lawrence Lile

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This brings up the difference between Mechanics, Physicists, and
Mathematicians.

A Mechanic, Physicist, and Mathematician were riding together on a train.
On the way they saw a black sheep standing in a field.

The mechanic said " All sheep must be black!"

The Physicist said  "Some sheep are black."

The mathemetician said "I observed a sheep, half of which I observed to be
black."

-- Lawrence Lile

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2001\06\07@134928 by Peter L. Peres

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> There in lies the whole problem.  Axioms have not been proven to be
> true and they cannot be proven, therefore I pose the question, "How
> can we create 'proofs' based on 'ideas' (axioms) that are said to be
> self-evident truths?".  Using this line of reasoning, couldn't I say
> that 'magic' is real since it appears to be 'self evident' and it is
> repeatable?

The proofs based on a set of axioms are valid in the space of the corpus
(or corpii or groups) where they are defined. Higher algebra explains
this. They 'fail' only people who try to apply them on some ill-defined
corpus instead.

Magic is very real if you believe in it. You know the saying 'sufficiently
advanced technology is indistinguishable from magic'. Perhaps this can be
extended to sufficiently primitive technology too.  As in DNA & co. There
is a philosophical idea about the knowledge horizon or volume of man being
a donut-shaped body in the space of knowledge (with as many dimensions
considered, as you please). Anything beyond that he should either not
comprehend, refute, ignore, or take as granted.

Peter

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2001\06\07@203154 by michael brown

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----- Original Message -----
From: "Peter L. Peres" <.....plpKILLspamspam.....ACTCOM.CO.IL>
To: <EraseMEPICLISTspam_OUTspamTakeThisOuTMITVMA.MIT.EDU>
Sent: Wednesday, June 06, 2001 2:02 PM
Subject: [OT]:Philosophy of Euclidean gemetry or Faith based mathematics


{Quote hidden}

You seem to have evaded my point.  Axioms have not been proven.  What makes
"proofs" based on them valid?  Are you saying that algebra explains that
"Everything needs to be proven except axioms, because we can't prove axioms.
Therefore, they deserve a special exemption within the rules.  So we will
wave our magic exemption wand and grant axioms the divine right to go
unquestioned".  How do we add some more axioms to the list?  Do we just wait
until something comes along that we "wish" to believe, but cannot prove, and
then just call it an axiom?

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2001\06\07@221455 by goflo

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michael brown wrote:

> Axioms have not been proven.

Bingo. They are assumptions.

> What makes "proofs" based on them valid?

A proof which is a logical extension of the set of axioms
is valid, by definition. Because we say so. Why? Because
it's useful to do it that way. That's all there is to it.

> How do we add some more axioms to the list?  Do we just wait
> until something comes along that we "wish" to believe, but cannot
> prove, and then just call it an axiom?

One often suspects mathematicians of just such behavior, but
us lowly scientists & engineers generally prefer the set of
axioms which allow us to most readily model the observed data.

One more thing, and I'm done. Usually in science, and almost
always in engineering - "Why" is the wrong question. If you
know "how" something works the "why" is usually superfluous,
and if you don't you're wasting your time asking why.

best regards, Jack

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