If he doesn't exist, he necessarily doesn't exist in any possible worlds. (I wonder if io9 meant to write "all" instead of "any?")
In any case, the point Gödel seemed to be working from was, "If we can prove God does not exist in any possible world, then we can prove that God does not exist." But since we can not prove God does not exist in our world (the only one we have data about), we can not prove that God does not exist...but that renders the non-existence of God an unknown, not an impossibility.
Or, in simpler terms, "Proven Not Possible" can not be assumed from "Not Proven Possible."
Under the circumstances, "proven not possible" and "not proven possible" actually are the same thing.
The first supposition is that a condition of being the greatest imaginable being is that the being "is." It has to actually "be." If you imagined something greater that had no existence, then that would not by definition be a "being," and therefore isn't as good as something with existence. Since it is possible to imagine a being that can exist everywhere/everywhen, that becomes part of the "greatest" characteristic.
It follows that the greatest imaginable being, an omnipotent, unlimited entity, would by definition exist in all possible frames of reference, including all possible worlds. If said being doesn't exist somewhere, that implies a limit, which defies the whole concept of "greatest being" as presented. If you could somehow prove a negative (which can't really be done), and could through that method prove that said being is NOT part of a single world, what you'd have there is a clear indicator that the being in question isn't God as defined as the "greatest being." You might still have an entity, one that exists some places but not all places, but that entity wouldn't be God, definitionally.
But that doesn't follow. My ability to imagine a thing does not make that thing necessarily exist. I imagine many things that I know are untrue.
This chain of logic seems to not move in the direction St. Anselm intends. Instead, this seems to be an argument that Bob, who works down in Marketing, may very well be God.
Assume that Bob is the greatest being that I personally know to exist. I can imagine something greater than Bob, but by that argument those greater imagined things therefore cannot definitively be said to be "beings". Therefore Bob is (potentially) the greatest (existing) being imaginable. Therefore Bob is God.
The first supposition is that a condition of being the greatest imaginable being is that the being "is." It has to actually "be."
Well, yes. But that doesn't mean that, "God can either necessarily exist, or necessarily not exist," covers all the possibilities. God can be an unknown, or there wouldn't be any need for Gödel to do all this work.
"It follows that the greatest imaginable being, an omnipotent, unlimited entity, would by definition exist in all possible frames of reference,"
True enough. But he proceeds to claim that because we can't prove God doesn't exist (God's non-existence: Not Proven Possible), God's non-existence is therefore not an option (God's non-existence: Proven Not Possible).
The breakdown isn't the definition of God. It's getting from
"It is not possible to say that God does not exist in any possible world. No matter how slim the chance is, God might exist."
to
That means that God can't necessarily not exist."
that I don't like. I don't see how he gets from the first part to the second without breaking logic.
My college freshman philosophy courses dealt with this, but Gödel's name wasn't attached to it. This was the 2nd half of the 70's -- perhaps it was too new to have been digested yet?
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branchandroot
(no subject)
Date: 2011-05-27 07:59 pm (UTC)(no subject)
Date: 2011-05-27 05:39 pm (UTC)(no subject)
Date: 2011-05-27 06:07 pm (UTC)If he doesn't exist, he necessarily doesn't exist in any possible worlds. (I wonder if io9 meant to write "all" instead of "any?")
In any case, the point Gödel seemed to be working from was, "If we can prove God does not exist in any possible world, then we can prove that God does not exist." But since we can not prove God does not exist in our world (the only one we have data about), we can not prove that God does not exist...but that renders the non-existence of God an unknown, not an impossibility.
Or, in simpler terms, "Proven Not Possible" can not be assumed from "Not Proven Possible."
(no subject)
Date: 2011-05-27 10:18 pm (UTC)The first supposition is that a condition of being the greatest imaginable being is that the being "is." It has to actually "be." If you imagined something greater that had no existence, then that would not by definition be a "being," and therefore isn't as good as something with existence. Since it is possible to imagine a being that can exist everywhere/everywhen, that becomes part of the "greatest" characteristic.
It follows that the greatest imaginable being, an omnipotent, unlimited entity, would by definition exist in all possible frames of reference, including all possible worlds. If said being doesn't exist somewhere, that implies a limit, which defies the whole concept of "greatest being" as presented. If you could somehow prove a negative (which can't really be done), and could through that method prove that said being is NOT part of a single world, what you'd have there is a clear indicator that the being in question isn't God as defined as the "greatest being." You might still have an entity, one that exists some places but not all places, but that entity wouldn't be God, definitionally.
(no subject)
Date: 2011-05-28 02:46 am (UTC)This chain of logic seems to not move in the direction St. Anselm intends. Instead, this seems to be an argument that Bob, who works down in Marketing, may very well be God.
Assume that Bob is the greatest being that I personally know to exist. I can imagine something greater than Bob, but by that argument those greater imagined things therefore cannot definitively be said to be "beings". Therefore Bob is (potentially) the greatest (existing) being imaginable. Therefore Bob is God.
(no subject)
Date: 2011-05-28 03:56 am (UTC)Well, yes. But that doesn't mean that, "God can either necessarily exist, or necessarily not exist," covers all the possibilities. God can be an unknown, or there wouldn't be any need for Gödel to do all this work.
"It follows that the greatest imaginable being, an omnipotent, unlimited entity, would by definition exist in all possible frames of reference,"
True enough. But he proceeds to claim that because we can't prove God doesn't exist (God's non-existence: Not Proven Possible), God's non-existence is therefore not an option (God's non-existence: Proven Not Possible).
The breakdown isn't the definition of God. It's getting from
to
that I don't like. I don't see how he gets from the first part to the second without breaking logic.
(no subject)
Date: 2011-05-28 01:04 am (UTC)(no subject)
Date: 2011-06-01 02:59 pm (UTC)