Hal wrote: >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.

In what way are those two statements not equivalent? They both seem to make the same point, which is that logically contradictory descriptions "do not refer". Jonathan