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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