Hi Mindey,

On 29 Dec 2009, at 15:07, Mindey wrote:

> I was just wondering, we are talking so much about universes, but how
> do we define "universe"? Sorry if that question was answered
> somewhere, but after a quick search I didn't find it.

What do you mean by "universe"? Do you mean, like many, the physical  
universe (or multiverse), or do you mean the ultimate basic reality  
(the third person everything)?

I think that if we assume mechanism, then it is absolutely undecidable  
if there is anything more than positive integers + addition and  
multiplication. Ontologically, if you want.

All the rest belongs to the epistemology of numbers, or, put it  
differently, of the inside views of arithmetic. The physical universe  
becomes the sharable (first person plural) ignorance of the universal  
numbers. It is an open question if this physical universe can be  
captured by a program (a number) or even by a mathematical structure.  
It is not a primitive structure. It has a reason linked to a  
statistics on computations. Matter is sort of derivative of the  
(machine's) mind. Cf the UDA reasoning, if you have followed.

There is a Skolem like paradox. Arithmetic, from outside, is infinite,  
but it is a relatively small and simple mathematical structure. Yet,  
as seen from inside, it escapes the whole of mathematics, because it  
looks *very* big for inside. So big that such a bigness is not even  
nameable by any of the creatures which live there.

There is a need of some amount of mathematical logic and computer  
science to give sense on all this. Especially for expression like "as  
seen from inside", etc.

Bruno Marchal


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