Not directly related to my previous posts, but I think this is a somewhat clearer “omnipotence paradox”:
God: Anything you can do, I can do better. Anything you can do, I can do too.
Guy who isn’t God: Can you not be God? (It’s easy; I do it for days at a time.)
God: Er…
Guy who isn’t God: Well, looks like there’s one thing it’s possible for me to do but not for you to do. Ergo, re: your original assertion, “No you can’t”.
I stand corrected. I’m not THAT old.
Why can’t God stop being God? After all, he’s omnipotent. Both that and the OP’s question don’t include the caveat about maintaining omnipotence.
Here’s another approach to the same problem, from the flip side so to speak. You might like it, the mathematician wins in the end. And interestingly, it’s been referenced on the SDMB in the past.
I don’t see the paradox. Omnipotence doesn’t imply an inability to give up your omnipotence, does it?
If you don’t have a notion of metaphysical possibility to hand, how about a notion of logical possibility?
It would be possible. What I want is the widest, reasonable, scope of possibility you have; say the internally consistent worlds. And cash out “internally consistent” however you want (within reason). If you want to include among such worlds, worlds where there are objects that are red and green all over, that is fine, and if you want to exclude them, that is fine too; either way should be interesting enough.
I think it is non-obvious how we should interpret our own language. And I think it is non-obvious where problems will or won’t arise when we have these sorts of wide scope concepts (everything is blah, and substitute in for blah as you please). In that sense I don’t think of them as pseudo-problems.
Perhaps if I put things a different way. I like the idea of putting the first sentence in terms of another. But the second sentence lacks something the first has, namely any statement about an omnipotent being. (I presume an impossible task master could create an impossible task, and not be omnipotent.) So lets just add something about that to the second sentence, to have two sentences closer in meaning, and see what we have.
I don’t think the following is an important point, because a temporal puzzle is as good as any, but I didn’t mean to make it a temporal issue. I said “never existed”, which may have implied such, but what I had in mind was that “an omnipotent being brings it about that there are no omnipotent beings” is going to be impossible if we quantify a-temporally (because “there exists an omnipotent being” and “there exist no omnipotent beings” seem to both be implied).
Perhaps my wording was unclear. You both seem to be taking my use of “being God” as synonymous with having certain abilities. I was using “God” in that instance, however, as the name for a particular person’s identity regardless of their abilities.
My intent was this:
Alex: Anything you can do I can do better. Anything you can do I can do too.
Bob: Well, one thing I do all the time is not be you. Could you do that? Could you not be Alex? (I don’t mean in terms of changing your name… I mean in terms of just not being you)
Alex: Er…
OK. But I still don’t see why Alex, if he were omnipotent, could give up his Alexness.
Given a particular system of logic and a particular set of background facts (possibly empty), I can well enough talk about what is consistent in that system of logic with those background facts.
But this is highly sensitive to the system of logic and background facts. One might well imagine one wants this system of logic and background facts to include claims about concepts like “possible”; perhaps axioms/facts such as “If X holds, then X is possible” or “If it is possible that X is possible, then X is possible”.
But what that background theory of possibility should be is up in the air… there are different formalizations I might choose to look at. (E.g., S4 vs. S5-style modal logic)
Sorry, I should clarified, I think: is it possible, even now, given the history that has already occurred, for Abraham Lincoln to never have been assassinated in 1865? I should think that logically impossible; it would not be consistent with what has already been given. (But, at any rate, I realize now you did not intend to focus on a temporal paradox, as such)
I don’t think what I’m about to say is an important point either, but I feel like “brings it about that” generally carries a temporal sense; when we say that Q brings it about that P, we don’t mean that P is already true, or atemporally true. We mean that whatever truth status P has now, after Q performs their action, P will be true.
If we’re going to demand that “Q brings it about that P” implies “P is true”, atemporally, then we might as well identify “Q brings it about that P” with “P is true (and Q likes it that way)”. In that case, yes, it wouldn’t be possible for God to both not exist and like the fact that he doesn’t exist, making “God does not exist” something which God cannot “bring about”. But this is the sort of thing where I feel we’ve gotten caught up in analyzing some formalism and lost sight of the way language is actually used; normally, if we were to say something like “Can Bob bring it about that Bob does not exist”, we would mean something like “Can Bob commit suicide?”.
Did you mean to write “couldn’t” here? Because if not, I agree that Alex can’t give up his Alexness… Alex is always Alex, tautologically, no matter what he does to his name, face, or abilities. And therefore, there’s something Bob can do that Alex can’t.
But it’s also just sort of a linguistic trick… It doesn’t make me think any less of Alex. (Why should it? I’d be just as disappointed with Bob for not being able to not be Bob. Which is in some sense a different inability than the one Alex has, but also, in some sense, the same one). And that’s how I feel about most of the omnipotence paradoxes as well.
I did mean “couldn’t”. And - in my opinion, which I recognise as being as much nonsense as everyone else 's here, since we’re talking about magic - if Alex is omnipotent, he can stop being Alex. If he can’t, then he isn’t omnipotent.
Well, that’s a bit like saying “If Alex is omnipotent, he can create a triangle with 5 sides. If he can’t, then he isn’t omnipotent”. One might, if one were so inclined, take Alex’s inability to not be Alex as logical proof that Alex isn’t omnipotent; that would be the same sort of thing people do with the other omnipotence paradoxes.
Well, omnipotence is as fanciful as a triangle with 5 sides. In any scenario where I’m to suspend my disbelief and accept omnipotence as a concept, I have no problem with accepting 5-sided triangles, too.
It’s kinda like watching Doctor Who. It requires a certain buy-in. Buying into omnipotence but not 5-sided triangles doesn’t work - for me, at least.
So yeah, an omnipotent being can create a 5-sided triangle.
Obviously, there’s never gonna be any kind of agreement on this. The very subject is nonsensical. So it’s going to mean something different to everyone. What it’s never going to do, though, is make any kind of sense whatsoever.
I suspect that choice of modal logic shouldn’t make a difference. I set things up with “bring about any possible world”, so I suspect all I need is that there is a world without an omnipotent being, and I don’t think that is a question of accessibility relations. But if I am to pick, S5 (or classical FOL extended with S5).
Some things that are false are possible, and in that sense, it is possible. Call your sentence p, and I’ll use M for possibility. Mp is true now. Mp & ~p is also true now. And given that, we can never drop the possibility operator from Mp. Does that answer the question?
The way I see it as going is that we give a reasonable definition of omnipotence, or just some feature we think any God ought have. Whether my use of “bring it about that” corresponds to normal usage of that phrase doesn’t matter too much, what matters is whether (my usage) corresponds to a feature God ought have (or that prima facie we think it ought), or our concept of omnipotence. (And mine might not.)
The other thing is I think our natural language concepts can be put up to similar sort of scrutiny as our formal concepts. Take unrestricted comprehension, for example, it seemed a perfectly coherent formal concept, but it’s not, and we know so due to just this sort of trickery. Maybe our concept of omnipotence is just like that.
I guess my concern is that God’s inability to now (given what we already know about history) make it such that Abraham Lincoln was never assassinated in 1865, or God’s inability to make it such that God never existed, or such things, are as little concerning to me as the inability to make a 5-sided triangle or God(/Bob)'s inability to win the “Don’t be God(/Bob)” game.
These all seem to me of the same flavor, asking God to do something which is in some sense logically impossible, even though, in some other sense, one might say these are logical possibilities.
So I’ll back off my earlier apparent attitude that there is nothing interesting here (which wasn’t quite my position, but it could easily have come across that way), and acknowledge that it would be interesting to clarify the sense in which I feel all three tasks above are logical impossibilities; then, if we are to exclude the ability to make 5-sided triangles from the demands of omnipotence, then we might as well exclude the others too, on similar motives. The question is how to formalize the relevant criterion for the sense of logical possibility I have inchoately in mind, accounting for the fact that there are of course people who aren’t Bob and histories where Abraham Lincoln survived.
Also, just to clarify, I have no particular love for omnipotence or God. It’s just that the inabilities people construct as sophisticated omnipotence paradoxes generally strike me as ultimately not that different from the 5-sided triangle inability, which seems not to trouble most people that much.
I think I keep wording myself poorly on the point I was hoping to communicate with all that. If someone were to go up to God and say “Hey, could you please make it such that Abraham Lincoln wasn’t assassinated?”, God could only reply “Sorry, buddy, you already know that Abraham Lincoln was assassinated. I can’t change that aspect of this world’s history. Sure, there’s some other ‘possible world-with-history’ out there where Abraham Lincoln was never assassinated in the first place, but it’s logically impossible for me to take any action which results in Lincoln avoiding assassination in the history of this world (where he was already assassinated). Your request is impossible for me to fulfill.”
So this would be a request which God would be unable to fulfill, but one which is also in some sense logically impossible to fulfill, even though there are other "possible world"s in which Lincoln survived. And I would feel the same way about asking God to bring it about that God never existed.
I’m having a devil of a time communicating what I’m trying to say here, though… (Perhaps I’m not contributing very much to this thread and should just try to gracefully bow out)
He’s no more bound to follow them than Gary Gygax was bound to follow the rules of D&D.
I was there just giving the sense of possibility I meant.
If you want to call that logical impossibility, and say it’s a fair reason for even a God to refuse, I’d have no particular objection. (But I would still be interested in how to put the exact qualification on God’s power.)
Neither I.
To follow the analogy above, if I went to God and asked him to create a 5-sided triangle, God might ask me what I even meant “draw me a picture of your request” he might say, whereas if I asked for Abraham to be saved, he might just shrug and say “too late”. To me they seem different, in any case.
IMHO, this is the nub of the debate. No one, on either side, cares whether God can create a rock too heavy for himself to lift. The question is whether God can work miracles, i.e., do things which observation of nature doesn’t predict and science can’t explain. If yes, God is as close to omnipotent as we need to consider seriously. If not, well, not.
To me, the problem of omnipotence - given this less ambituous definition - isn’t so much whether it’s possible as whether it’s true. As an atheist and a skeptic, I have to say I don’t see any reasonable evidential basis to believe it’s true. Without such an evidential basis, I conclude it’s not. But that’s not proof. It’s induction.