On 18 Aug 2009, at 19:17, Brent Meeker wrote:

>>>> Some posts ago, you seem to accept arithmetical realism, so I am no
>>>> more sure of your position.
>>> I may have assented to the *truth* of some propositions...
>>> but truth is not existence. At least, the claim that
>>> truth=existence is extraordinary and metaphysical...
>> Mathematical existence = truth of existential mathematical statement.
>> The number seven exists independently of me, is equivalent with the
>> statement that the truth of the mathematical statement Ex(x =
>> s(s(s(s(s(s(s(0)))))))) is true independently of me.
> The above of course is a set of tokens symbolizing a set of  
> cardinality eight.

Er, actually it symbolizes the number seven (it is a detail, but set  
theory will never been formalized in my posts, except much later, for  
giving another example of Lobian machine).

> The fact
> that it symbolizes something depends on humans interpreting it.

I would have used the usual humans notation "7".
So I was referring to any "interpretative machine" (computer,  
universal number) which agrees on the usual first order axiom of  
arithmetic, talking in first order language,  together with the  
supplementary symbols "s", 0, "x" and "+".
We fix the notation, and, in the case of such machine we fix the  
semantic by the usual mathematical structure (N,+,x).

> This seems similar to the
> MGA and the idea that a rock computes every function.

I have already criticized this. Once sup-comp is accepted, the  
computation exists in arithmetic and are given by well defined  
relations among numbers, entirely defined with the language above, and  
they have the usual interpretation in (N,+,x). But those relation will  
define complex UD-like relationships describing relative observers in  
relative environment/universal machine, like "Brent deciding to send a  
mail", for example. Those internal interpretation will exist in a  
sense which is not dependent of the choice of any interpretation or  
even representation, once you assume the usual truth of the  
arithmetical relations.
In comp, like in QM, a rock compute only in the sense that "it is made  
of infinities of computations". Without comp, I have no clue of what a  
rock is, except that QM seems to agree on the fact that it is made of  
infinities of computations.

> They depend on being interpreted in
> some context or environment.

Right. The interpreter are given by the universal numbers, or  
universal machine. This is a bit tricky to define shortly, and I  
postpone it in the seven step series (but I am a bit buzy), so that  
more can uderstand.

In the third person way: a computation is always defined relatively to  
another universal number, or directly in term of number addition and  
 From the first person perspective we can only bet on the most  
probable universal number, among an infinity of them.

> I'm happy to abstract them from their environment to get a
> manageable model.

But once the "model" is a number that the doctor will send on Mars,  
where a reconstitution device has been build, you have to abstract  
yourself from the environment, for awhile. Saying "yes doctor" *is* a  
big theological step. Nobody should ever force you. The ethic of comp  
is the right to say "no" to the doctor.

> I'm not so comfortable to say that that abstraction doesn't need the
> environment and is what is really real.

Yeah ... I am sorry. But let us not be driven by wishful thinking, and  
if comp survives UDA, there is a sense in which matter becomes much  
more solid and stable. Observable environment emerge statistically  
from infinities of non temporal and non spatial computations/number  

Including (universal) environment does not help, because the UD  
generates them all (with their many variants), except some infinite  
diagonal "garden of Eden" which are evacuated through the comp hyp.



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