Hi John,
> > Digitality and its application is human invention and humans APPLY it to
>the
> > world.
OK, but then the difference between human and non human is also a
human invention, and humans apply it to what they see, or believe to see.
>With a different evolutionary setup of brainfunctions we maight
>have
> > a different idea of the "mathematical".
How different? Perhaps we might have discover the p-adic numbers first,
or we would have always worked in finite fields Z_p, or we would have
natural logarithmic capacities, or we would have quite different notions of the
continua. But I don't think any of this can change the status of
arithmetic, in which you can embed most of computer science proposition,
including consistent discourse on numbers and machine.
In a sense I agree with you for the large meaning of "mathematical", but
concerning arithmetical proposition of the form
It exists n such that P(n)
with P decidable, can depend of me our us.
>Would that change the world?
> > maybe someone could identify the "mathematical" in the sense as it
>"exists"
> > by itself. I think in "effects" not finding the "words" properly
>describing
> > them. If the 'mathematical' does describe them all properly, it is still a
> > description of something otherwise not identifiable, not the "something"
> > itself.
> > I have the idea that the esteemed listmembers consider "the mathematical"
>as
> > a god that created the world and rules its existence. By itself.
OK for me, with "mathematical" (a very fuzzy term) replaced by "arithmetical"
or better " computable".
Those terms are still fuzzy, for example the set of all completely
computable things
is not itself computable, but, with CT (Church Thesis), the set of
completely or not
completely computable things is computable! (This is a consequence of
diagonalisation closure see the diagonalisation post. It is what makes the UD
possible). So we get the less we need to
postulate if we hope being serious getting some explanation of us and the
worlds.
What is your god? What is the least you thing we should accept to get the rest?
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Tue Nov 11 2003 - 07:03:53 PST