>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. > >Hal wrote: 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.
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. >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. As a Platonist, I would disagree. In *all* possible worlds, 2+2=4. So we do live in a world where 2+2=4. > 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. Sure; it is the other way round: our world is contingent on the truths of mathematics. > >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. Yes; but this is begging the question as to how we decide whether any description we come up with corresponds to a logically possible world. Or are you saying that any description necessarily corresponds with a possible world? Is there a world where A AND ~A? Jonathan Colvin