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
