[Serious Phil] phil of math.

[Eray Ozkural]

On Tue, Jun 12, 2012 at 5:55 PM, larry_tapper_2 <
Philscimind at undergroundwiki.org> wrote:

> EO> Imaginary numbers have an, IMO obvious, geometric interpretation. It
> might
> > be an accident of history this was not evident in the first formulation,
> > but that's how evolution works, not everything that is invented in an
> > evolutionary system is immediately put to maximum use. So, in this sense,
> > the imaginary number was probably thought of as an investigation into the
> > properties of the roots of negative numbers first, then the a-ha, this is
> > geometry, moment comes.... So, this is an investigation into the
> properties
> > of a formal system, that's why it's confusing, it really is a theory
> about
> > certain programs (in this case, squareroot(number) where number is
> > negative), so it's a predictive theory that predicts properties of
> > programs. That's why it's not comprehensible to anybody who does not grok
> > the computational turn.
> >
>
>
> W> I hope you realize that you have turned what was originally an
> empirical claim into a non-falsifiable axiom (if math produces it, it must
> someday have a use). Not good.
>
> Yes, that would be the gist of my complaint too. Except we could also read
> Eray as making a stronger claim which is true but trivial: If we define
> math as that which can be realized by a computer program, any mathematical
> theory whatsoever *already has* a predictive use: predicting what will
> happen when we run the program!


No, *you* have trivialized it but that's not what it does. The semantics of
all meaningful mathematics is computational, this is the strongest
statement of constructivism, and that's because thought itself is
computational, and mathematics is an abstract form of thought.

So, for instance, the theory of arithmetic allows us to predict the
outcomes or properties of certain programs (i.e. whether they would halt)
without running them. Think of it like a shortcut.

When you get it, you will realize it is ANYTHING but trivial. Is the
halting problem trivial? It is NOT!

In other words, the halting probability of a universal computer (any given
one) is the golden standard of mathematics. There is nothing more to
mathematics than that. That formalizes all the information that can be
present in any mathematical theory.

Not too difficult, that was what metamathematics was for, but of course
Platonists made the stupidest interpretation of it. I presented to you the
correct interpretation, before everyone else comes to realize it (like 50
years later). You should be thankful, but alas, I hear only petty
complaints :)

Best,


-- 
Eray Ozkural, PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
http://groups.yahoo.com/group/ai-philosophy
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