> In other words the Mandelbrot Set is consistent with the axioms of
> mathematics, the axioms themselves have no proof but they just seem so true
> they must be, I mean, they're really obvious, as obviously true as the nature
> of reality is transparent.
>
...........
***** In my point of view (and in lots of mathematics' too) the set
of axioms that are the basis of a theory, do not need even to seem
true. The mathematical concept of "truth" just appears after (and
based on) the existence of the axioms... For example, being
formal, the Euclidean or Riemmanian Geometries do not need to having
anything to do with truth or reality. Just with its own axioms...
Just a comment.
> I talked about consistency because that's as precise and objective a concept
> as any known, truth on the other hand is as murky as reality. I also find
> there is very often a disturbing circular element. What is truth? That which
> is (exists). What is existence? That which is true.
***** Mathematically is not that... Repeat that "truth" depends on
the local axioms...
> I can't explain what truth is without using the idea of consistency, and
> I can't use the verb "to be" either because that implies existence and
> existence is what I'm trying to define. All these restrictions are too much
> for me, that's why I don't talk about truth.
>
> John K Clark johnkc@well.com
>
***** But if we consider as one of the axioms of the universe that
the universe is real, we could begin to think what would be the other
minimal set of axioms (consistent with the existence, at least,
of what would continue on existing if, for example, all the
mankind would die...). After that we could try to define what is
real and true, or not.... in other case I think we will be
rationally lost and will begin to inventing mathematical religions...
Gomes
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Prof. Gomes
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http://www.geocities.com/ResearchTriangle/Lab/1065
emails: gomes@cnen.gov.br
profgomes@geocities.com
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Thanks for visiting my web site.
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