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
>> > 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.
> 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"?

Perhaps there is just 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".

>> 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
> minds.

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

>> 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.
>> OR:
>> Recursion is just a label that we apply to some of our implicational
>> beliefs.
>> The latter seems more plausible to me.
> Through recursion one can implement any form of computation.

But, ultimately, what is computation?

> 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?


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