On 04 Jun 2011, at 20:03, Rex Allen wrote:

On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <jasonre...@gmail.com> wrote:

On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen <rexallen31...@gmail.com> wrote:

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
propositions is as follows:

Most would agree that a statement such as "8 is composite" has an
objective truth.

Assuming certain of axioms and rules of inference, sure.

Godel showed no single axiomatic system captures all mathematical truth, any
fixed set of axioms can at best approximate mathematical truth.  If
mathematical truth cannot be fully captured by a set of axioms, it must
exist outside sets of axioms altogether.

Then perhaps the correct conclusion to draw is that there is no such
thing as "mathematical truth"?

No theories nor machine can reach all arithmetical truth, but few people doubt that closed arithmetical propositions are either true or false. We do share a common intuition on the nature of arithmetical truth. I have doubt on any notion of global mathematical truth. Sets, real numbers, complex numbers, etc. are simplifications of the natural numbers. They are convenient fictions, I think. If we are machine, it is undecidable if ontology is more than N.

Perhaps there is just human belief.

Jason said it. If you follow that slope you may as well say that there is only belief by Rex. You can also decide that there is nothing to explain, no theories to find, and go walking in the woods. Science, by definition, assumes something beyond (human) belief.

The fractal is just an example of a simple formula leading to very complex
output.  The same is true for the UDA:
for i = 0 to inf:
  for each j in set of programs:
    execute single instruction of program j
  add i to set of programs
That simple formula executes all programs.

Following those instructions will let someone "execute" all "programs".

Or, alternatively, configuring a physical system in a way that
represents those instructions will allow someone to interpret the
system's subsequent states as being analogous to the "execution" of
all "programs".

Do you need someone observing your brain for you to feel something?
Why would the physical UD execution differ?
Indeed, why would the arithmetical UD execution differ?

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

I don't know what lower bound of information or complexity is required for

Then why do you believe that information of complexity is required for minds?

If you accept that the brain is Turing emulable, then it is easy to explain that matter/consciousness is arithmetical information as seen from inside. That is certainly easier than explaining consciousness by physical attributes.

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

The latter seems more plausible to me.

Through recursion one can implement any form of computation.

But, ultimately, what is computation?

Any mathematical transformation which is Turing emulable.
Assuming Church thesis this is a very general definition.

Recursion is
common and easy to show in different mathematical formulas, while showing a Turing machine is more difficult. Many programs which can be easily defined through recursion can also be implemented without recursion, so I was not
implying recursion is necessary for minds.

Then what do you believe is necessary for minds?

A universal system, or universal numbers. Now they can be proved to exist from logic + non negative integers, so we don't need a lot.

Jason answered "An informational process". That's OK, especially in his context (that computation exist in math), but the word "process" is frequently interpreted by "primitively spatio-temporal process", when we need only (sigma_1) arithmetical relations.



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