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