On Sat, Jun 4, 2011 at 4:09 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 04 Jun 2011, at 19:06, Rex Allen 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.
>
> But everyone agree on the axioms of arithmetic.

I’m not sure what you mean here.  “Agree” in what sense?

Everyone agrees that the axioms of arithmetic are...what?  Interesting?  Useful?

Who is “everyone”?

Does everyone also agree that there are other axiomatic systems?


> And we could take any
> universal (in the Turing sense) system instead. The physical laws cannot
> depend on the choice of the "universal base".

What exactly are “physical laws”?

You’re really saying “the regularities in our experience cannot depend
on the choice of the universal base”?


>>> 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.
>>
>> OR:
>>
>> Recursion is just a label that we apply to some of our implicational
>> beliefs.
>
> I think you are confusing computability, which is absolute (assuming Church
> thesis), and provability, which is always relative to theories, machines,
> entities, etc.

What are your justifications for assuming the Church thesis?

Do oracles exist in Platonia?  In HyperPlatonia perhaps?  If not, what
precludes their existence?


> Jason is right, computation occurs in "arithmetical platonia", even in a
> tiny part of it actually, independently of us.

Ya, I have my doubts about that.


> This tiny part is assumed in the rest of science, and comp makes
> it necessarily enough (by taking seriously the first and third person
> distinction).

What is science in a deterministic universe?  What is science in a
probabilistic universe?  What other kinds of universes could there be?


Rex

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