>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



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