On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jasonre...@gmail.com> wrote:
> One thing I thought of recently which is a good way of showing how
> computation occurs due to the objective truth or falsehood of mathematical
> propositions is as follows:
> Most would agree that a statement such as "8 is composite" has an eternal
> objective truth.

Assuming certain of axioms and rules of inference, sure.

But isn't that true of nearly anything?  How many axiomatic systems are there?

> Likewise the statement: the Nth fibbinacci number is X.
> Has an objective truth for any integer N no matter how large.  Let's say
> N=10 and X = 55.  The truth of this depends on the recursive definition of
> the fibbinacci sequence, where future states depend on prior states, and is
> therefore a kind if computation.  Since N may be infinitely large, then in a
> sense this mathematical computation proceeds forever.  Likewise one might
> say that chaitin's constant = Y has some objective mathematical truth.  For
> chaintons constant to have an objective value, the execution of all programs
> must occur.
> Simple recursive relations can lead to exraordinary complexity, consider the
> universe of the Mandelbrot set implied by the simple relation Z(n+1)= Z(n)^2
> + C.  Other recursive formulae may result in the evolution of structures
> such as our universe or the computation of your mind.

Is extraordinary complexity required for the manifestation of "mind"?
If so, why?

Is it that these recursive relations cause our experience, or are just
a way of thinking about our experience?

Is it:

Recursive relations cause thought.


Recursion is just a label that we apply to some of our implicational beliefs.

The latter seems more plausible to me.


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