On 08 Nov 2012, at 01:38, Stephen P. King wrote:

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On 11/7/2012 12:44 PM, Bruno Marchal wrote:On 07 Nov 2012, at 17:13, Stephen P. King wrote:On 11/7/2012 9:41 AM, Bruno Marchal wrote:Arithmetic explains why they are observers and how and why theymake theories.Dear Bruno,This is a vacuous statement, IMHO. Absent the prior existence ofentities capable of counting there is no such thing as Arithmetic.Your belief to the contrary cannot be falsified!In the same sense that "2+2=4" cannot be falsified.Dear Bruno,You are missing my message. "2+2=4" is universally true onlybecause there does not exist a counter-example that can be agreedupon by 3 or more entities. You continue to only think from thepoint of view of a single entity. My reasoning asks questions fromthe point of view of many entities

`But even with that criteria, your point will not go through, as it is`

`obvious that nobody will find any counterexample to the fact that`

`observer exists in arithmetic (assuming comp). In the same "sense"`

`that 2+2=4.`

It just mean that you have never grasp the proof of Gödel'sincompleteness theorem, which does that, almost in passing. This isproved in all good introduction text to logic.Ha! OK, but you are wrong.

`If you stiudy and grasp by yourself Gödel's prrof, you should see why`

`the prior existence of comp-counting entities is a theorem of`

`arithmetic, and have the same reality as 2+2=4. You would not have the`

`remark above.`

We can prove, in Peano arithmetic, that there exist entitiescapable of counting.If we follow the orthodox interpretation of Tennenbaum theoremthere can only be one entity that can count; the standard model ofPA. I am thinking of the uncountable infinity of non-standard modelsof PA that have a condition imposed on them: each thinks that italone is the standard model as it cannot know that it is non-standard. In this way we can get an infinity of standard models ofPA instead of just one. I think that this gives us a modal logicalform of general relativity!By Gödel's completeness those entities exists in the standard modelof arithmetic (arithmetical truth), and in all model, and thusalso in all non standard model.Yes, but each model must be able to truthfully believe that italone is the standard model; it cannot see the constant that definesit as non-standard from inside itself.

It is confusing to use models for modeling thinking entities.

So arithmetic assures the prior existence of entities capable ofcounting.Sure.

Ah? But it is a key point that you seem to avoid in many of your post.

You have the Matiyasevich's book. A (more complex) proof is giventhere. It is more complex as it proves this for a much more tinyfragment of arithmetic.It is impossible for me to write my ideas in Matiyasevich'slanguage. :_(

`I am not sure why. I have taught computer science to disabled people,`

`and unless severe disability, it is always possible to overcome any`

`technical limitations.`

Forgive me, but I need to let others explain my argument as I haverun out of patience with my inability to form sentences that youwill understand. This article (which I cannot asses completely dueto the paywall) seems to make my claim well: http://www.springerlink.com/content/052422q295335527/Nomic Universals and Particular Causal Relations: Which are Basicand Which are Derived?"Armstrong holds that a law of nature is a certain sort ofstructural universal which, in turn, fixes causal relationsbetween particular states of affairs. His claim that these nomicstructural universals explain causal relations commits him tosaying that such universals are irreducible, not supervenient uponthe particular causal relations they fix. However, Armstrong alsowants to avoid Plato’s view that a universal can exist withoutbeing instantiated, a view which he regards as incompatible withnaturalism. This construal of naturalism forces Armstrong to saythat universals are abstractions from a certain class ofparticulars; they are abstractions from first-order states ofaffairs, to be more precise. It is here argued that these twotendencies in Armstrong cannot be reconciled: To say thatuniversals are abstractions from first-order states of affairs isnot compatible with saying that universals fix causal relationsbetween particulars. Causal relations are themselves states ofaffairs of a sort, and Armstrong’s claim that a law is a kind ofstructural universal is best understood as the view that any givenlaw logically supervenes on its corresponding causal relations.The result is an inconsistency, Armstrong having to say that lawsdo not supervene on particular causal relations while also beingcommitted to the view that they do so supervene. The inconsistencyis perhaps best resolved by denying that universals areabstractions from states of affairs."I don't assume nature. And comp refutes naturalism, that's the point.You are thinking too literally about that I am writing. compassumes Platonism, no?

`No. Just arithmetical realism. Platonism is a consequence of comp.`

`Comp itself is neutral. It is just the belief that our brain can be`

`replaced by a computer (so we assume a Turing complete physical`

`reality, but tis agnostic on the precise nature of it (primitive or`

`not).`

Why can we not see Platonism and Naturalism as just opposite or"polar" views on Reality? Platonism looks Top-down and Naturalismlooks from the bottom-up.

`Because it violates the facts derived from comp. Nature or the`

`physical world is only a surface of a "non natural" (but arithmetical)`

`volume.`

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.