Jonathan Colvin writes: > I didn't say that it *was* logically impossible for such a world to exist; I > said that it *might* be that such a world is logically impossible. Just > because we can talk about such a world does not mean that it is logically > possible.
It's important to understand that logical possibility is not a constraint on worlds as such; it is a constraint on our understanding of worlds. It's not like we could go to God and say, "God, please implement this world"; and God takes a look at the spec, and answers, in a deep, sorrowful voice, "No, I'm sorry, I can't implement this world, it's not logically possible. Go back and try again." And we say, "Okay, sorry, God, we'll try harder next time." If we think of computer programs as implementing worlds, all programs exist and are instantiated. It's not that some programs may be logically impossible and the universal TM refuses to run them. Where logical possibility arises is in our understanding of worlds. The mere concept of a world where 2+2=5, for example, represents an error of understanding. What 2+2 equals is not a property of a world! It is incoherent to speak of a world where 2+2 equals anything specific, whether 4 or 5. We don't live in a world where 2+2=4. That mathematical fact has no bearing whatsoever on the existence of our world. We live in a world with certain laws of physics: conservation of energy, quantum theory, Einsteinian gravitation. We may use mathematics to help us understand these laws, but the truths of mathematics are not contingent on anything about our world or any world. If a world is logically impossible, the problem is always in our description and understanding of the world. Worlds themselves exist (given the AUH) independently of our understanding of them. Logical and mathematical consistency are not properties of worlds, they are properties of our descriptions. Hal