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

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?

--Stathis Papaioannou

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