On 13 Nov 2012, at 18:54, Stephen P. King wrote:

On 11/13/2012 10:46 AM, Bruno Marchal wrote:
There is a cost in resource utilization (or entropy generation) to gain knowledge.

I can still agree. Then the comp consequence is that the physical resources are derivable from a notion of arithmetical resource.

Dear Bruno,

  Could you explain this idea of arithmetical resource in depth?

Just imagine the universal dovetailer. It generates and implements, and execute all programs. The infinite resource of arithmetic is just that we agree that for all x, there is a y with y > x. It is trivial. PA proves AxEy(x < y & x ≠ y)

Dear Bruno,

My claim is that the phrase that you used above "...we agree that for all ...." is just another way of thinking of my definition of reality as "That which is incontrovertible for some collection of observers that can communicate with each other". It is the mutual agreement between all participants, be they electrons or amoeba or human or galactic clusters, that makes a reality "real".

OK. That is recovered in comp by the notion of first person plural (duplication of machine population)

This is a result of taking seriously the consequences of many minds and their mutual statistics. It allows us to derive many properties and conditions that have to be just assumed to be the case of postulated in single mind theories. What I am proposing is a way to bridge between Universals and Nominals to eliminate what I believe to be a false dichotomy in ontology. This is not a matter of choice or contrivance. We see something like this in any system of interactions between many entities. For example, if I find the local valuation of currencies to be inconsistent with my goods and services then I will not be able to interact in a local economy. If I do not find the Doctors in a universe to able to determine the proper level of functional substitution of my brain then my ability to be independent of a particular physical body in that universe cannot occur.

No problem with this.
The difference is methodological. I derive necessary propositions from comp, only.

May be you are still skeptical that the elementary arithmetical relations implement all computations, but this is the big thing discovered by Post, Church, Kleene, and others and which is the base of computer science.

My problem is that I do not understand how you stratify the many levels of significance of the numbers. You propose that {0,1, +, *} are ontologically primitive

I do not. I derive this from comp.

and then jump over what ontological process generates all things from that basis set of primitives.

? I use only the postulated laws (addition and multiplication, in case of numbers).

I have been considering a Heraclitean view that takes Becoming as fundamental, but you seem intent on keeping your ontology as Changeless.

I use comp, and no more.

I am baffled as to how you seem OK to use the language of Becoming (as you use verbs and discuss actions at the arithmetic level) but never discuss how the Becoming or Change comes to be.

That's the easy part. Computations are dynamical notion, even if they have simple 3p statical descriptions.

Matiyasevitch extended such result by showing that for getting the Turing universality, the diophantine polynomial of degree four are enough.

   Sure, but his work does not solve the ontological problem.

It does. The ontology with comp, is given by the terms of whatever logical specifications you give for some universal system you choose. We have chosen the numbers, so the ontology is given by N = {0, s(0), ...}.



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