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 physicalresources 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 isjust that we agree that for all x, there is a y with y > x. It istrivial. PA proves AxEy(x < y & x ≠ y)Dear Bruno,My claim is that the phrase that you used above "...we agree thatfor all ...." is just another way of thinking of my definition ofreality as "That which is incontrovertible for some collection ofobservers that can communicate with each other". It is the mutualagreement between all participants, be they electrons or amoeba orhuman 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 mindsand their mutual statistics. It allows us to derive many propertiesand conditions that have to be just assumed to be the case ofpostulated in single mind theories. What I am proposing is a way tobridge between Universals and Nominals to eliminate what I believeto be a false dichotomy in ontology.This is not a matter of choice or contrivance. We see somethinglike this in any system of interactions between many entities. Forexample, if I find the local valuation of currencies to beinconsistent with my goods and services then I will not be able tointeract in a local economy. If I do not find the Doctors in auniverse to able to determine the proper level of functionalsubstitution of my brain then my ability to be independent of aparticular 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 arithmeticalrelations implement all computations, but this is the big thingdiscovered by Post, Church, Kleene, and others and which is thebase of computer science.My problem is that I do not understand how you stratify the manylevels 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 thingsfrom 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 asfundamental, but you seem intent on keeping your ontology asChangeless.

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) butnever 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 theTuring universality, the diophantine polynomial of degree four areenough.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), ...}.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.