Torgny Tholerus wrote:
> Brent Meeker skrev:
>> Torgny Tholerus wrote:
>>
>>> Mark Peaty skrev:
>>>
>>>> And next: what do you mean by 'exist'?
>>>>
>>> 'Exist' is exactly the same as 'mathematical possibility'.
>>>
>>> Our Universe is a mathemathical possibility. That is why our Universe
>>> exists. Every mathematically possible Universe exists in the same way.
>>> But we can not get in touch with any of the other Universes, so from our
>>> point of view does the other Universes not exist.
>>>
>> But what is "mathematical possibility"? Is it the same as "logically possible"? Does it rule out, "The book is green and the book is red."? Or does it only rule out, "The book is green and the book is not green."?
>>
> Yes, it is the same as logically possible. One simple Universe is the
> Game of Life, with some starting configuration. This simple Universe
> exists in the same way as our Universe, even if nobody ever tries this
> starting configuration.
>
But that doesn't answer the question. Can a thing be both red and green? Is that logically impossible or only nomologically impossible? It seems to me there is a problem with talking about logically possible. I can adopt some axioms including an axiom that says a thing can be any two different colors at the same time and then proceed with logical inferences to derive a lot of theorems and so long as I don't have another axiom that says a thing can only be one color at a time I won't run into an inconsistency. Does that mean it is possible for the a thing to be two different colors at the same time - I don't think so. But the reason I don't think so is an inductive inference about the physical world and the meaning of words by reference to it (as Bruno would say, the absence of white rabbits), not with logic.
Also, "logically possible" is the same as "logically consistent" (at least under most rules of inference). But except for simple systems you cannot know when a logical system is consistent. I think that's why Bruno builds on arithmetic; because he can ask you to "bet" it is true and you probably will even though it cannot be proven consistent (internally). If he asked you to bet on metric manifolds over the octonions you might bet the other way.
Brent Meeker
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Received on Wed Feb 07 2007 - 14:17:30 PST