>Jonathan Colvin wrote:
>
>> >>Agreed. But some *worlds* we can imagine may be logically 
>impossible 
>> >>(inconsistent), may they not? I can imagine (or talk 
>about) a world 
>> >>where entity A has property X and property Y, but it may be 
>> >>logically impossible for any existing entity A to simultaneously 
>> >>have
>> >property X
>> >>and Y. For example, it seems that it would be inconsistent
>> >for there to
>> >>exist a world where simultaneously I am omniscinent and I
>> >consist of a single elctron.
>> >>Such a world seems inconsistent (not logically possible).
>> >Such a world
>> >>may not appear in the set of worlds generated by all
>> >instantiated programs.
>> >
>> >Omniscience is a problematic concept; one can argue that a single 
>> >electron does indeed have all possible knowledge encoded in 
>one bit. 
>> >But leaving that aside, why do you say that it is logically 
>> >impossible for an electron to be intelligent? To show that it is 
>> >*logically* impossible you would have to show that it entails a 
>> >logical or mathematical contradiction, such as 2+2=5.
>>
>>My point is not that it *is* logically impossible, but that it *may 
>>be*. It is obvious that 2+2=5 is a mathematical contradiction. But if 
>>we take Tegmark's radical platonism seriously, then such 
>contradictions 
>>must "scale up" into the categories of things and worlds. All 
>possible 
>>things exist; and all impossible things do not. How do we decide 
>>whether "an omniscient electron" is a possible thing? It 
>certainly does 
>>not appear to be; and the point is that it may *in fact* be an 
>>impossible thing. It is straightforward to show that 2+2=5 is 
>>contradictory under number theory. It is obviously not so 
>>straightforward to show that "an omniscient electron" is equally 
>>a-priori contradictory. It is not even obvious that "an omniscient 
>>electron" is in the same category of propositions as "2+2=5". But I'd 
>>argue that if we take Tegmark seriously, then it should be.
>>
>>Jonathan Colvin
>
>Stathis: OK, I agree with your reasoning. But, just for fun, can you 
>think of an example of a physical reality which is clearly a 
>priori contradictory?

That's a good question. I can think of a chess position that is a-priori
illegal. But our macroscopic world is so complex it is far from obvious what
is allowed and what is forbidden. That's why I can't consistently predict
what tomorrow's lottery numbers will be. So if I could answer your question,
I'd probably be out buying lottery tickets right now :).

Jonathan Colvin

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