I agree with Brent's comment:

> I essentially agree.  If we say, "2+2=5" then we have failed to describe
> anything because we have contradicted our own semantics.  Logic is not a
> constraint on the world, but only on our use of language to describe it.  But
> that doesn't mean that any world for which we make up a description can exist.
> Logic doesn't constrain reality; either by prohibiting it or by making it
> "possible".

It's not that logically impossible worlds don't (or can't) exist; it's
that if we use a logical contradiction, we have failed to describe
a world.

Consider a specific example that captures some of the sense of the
proposed logically impossible world where an electron is omniscient.
Consider a 2-D cellular automaton world like Conway's Life.  Every cell
is either occupied or unoccupied.  It has one of two states.  Now let
us consider such a world in which one cell holds much more than one
bit of information.  Suppose it holds a million bits.  This one cell
is tiny like an electron; yet it holds a great deal of information,
like an omniscient entity.

This description is logically contradictory.  A system with only two
states cannot hold a million bits of information.  That is an elementary
theorem of mathematical information theory.

The problem is not specific to a world.  The problem is with the concept
that a two state system can hold a million bits.  That concept is
inherently contradictory.  That makes it meaningless.  Trying to apply
it to a world or to anything else is going to produce meaningless results.

Rather than say that such a world cannot exist because it is logically
contradictory, it makes more sense to say that logically contradictory
descriptions fail to describe worlds, because they fail to describe
anything in a meaningful way.

Hal Finney

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