The 'omnipotence' paradox...

[Singular Intellect]

I was thinking about this the earlier today:

One of the logical arguements against the concept of omnipotence (ie: literally unlimited power) is the proposed question "Could an omnipotent being create a object it could not lift?" or variation thereof. A positive or negative answer always leads to said 'limitless' omnipotent entity being, well, limited. I've personally used this arguement myself.

Which made me think...suppose a human being had 'unlimited power', where their imagination is the sole limit to their capabilities. Let's say this person is you. You have unlimited power and can do absolutely anything your imagination desires.

Now, if presented with this question ('create an object you cannot lift' or similar natured concept), how would you apporach the concept?

Keeping in mind, you can do anything you can possibly imagine.

To me this suggests an interesting paradox...any human being can imagine an object they couldn't lift. They could also imagine the ability or means to do so.

So far, the only conclusion I've been able to reach is that such an omnipotent person (in this case yourself as the relevent example) would be both unlimited in power, but capable of limitations. The only trick being such limitations would be self imposed and could just as easily be overidden.

Thoughts? Logical flaws? Better explainations?

[ThatGuyFromThatPlace]

The Human mind is a fickle thing, the power of suggestion can cause disease symptoms or feats of super-human ability. I have no trouble imagining that someone gifted with this power could create something so big/heavy theu were psychologically incapable of lifting.

[SeeingRed]

I'd agree that an omnipotent being would not necessarily limit itself to creating things they were physiologically incapable of lifting (assuming that said omnipotent being had any concept of "lifting" things, and if it did, had some limitation as to what it could/could not lift). But if as you say I as the omnipotent being can do anything I can possibly imagine, I could give myself the power to lift this thing, could I not? It seems to me that the paradox here exists only theoretically and would quickly disappear in practice.

Scott Adams takes this idea one step further in his book God's Debris in which, among other things, he postulates that if a truly omnipotent being existed, the only question of any interest to it would be whether it could bring about its own self-destruction.

[Exonerate]

The standard reply would be that an omnipotent power would be not bound to the rules of logic, and could simultaneously lift it while being unable to lift it or some bullshit like that. It strikes me as a copout, but any attempt to refute that claim with logic would be essentially futile, since they would just claim logic doesn't apply over and over again.

[Surlethe]

The answer to this depends on how detailed the imagination has to be. For example, I can imagine something called the "set of all sets"; hell, I can write it down: {X : X is a set}. I cannot, however, visualize how I would go about making that set if I were omnipotent.

Perhaps I need only put it this way: Omnipotence (within the bounds of imagination) gives me any power I can imagine. I can imagine the power to make false statements true. Therefore, I will make a false statement true: specifically, I will continue to assume ZFC, but {X : X is a set} will now exist. We have reached a contradiction, since {X : X is a set} cannot exist within the framework of the ZFC axioms; therefore, one of my assumptions must be false. Clearly, I can imagine a false statement to be true (and, indeed, it's not difficult, even if one is not insane); thus, omnipotence, even within the bounds of my imagination, must be absurd.

The point here is that although it's tempting to wank omnipotence, the consequences are more than disastrous: you'd disappear in a puff of logic. Because we can imagine false things to be true, we're still capable of creating omnipotence paradoxes even if we only limit ourselves to powers which we can imagine.

[Enforcer Talen]

The Human mind is a fickle thing, the power of suggestion can cause disease symptoms or feats of super-human ability. I have no trouble imagining that someone gifted with this power could create something so big/heavy theu were psychologically incapable of lifting.

Interestign example: in highschool, we had a hypnotist visit, and one of the results was that an entire football team couldnt lift 5lbs.

[Keevan_Colton]

Often they take the cop out of defining omnipotence for the purposes of a god, that omnipotence means the ability to do anything that isnt logically impossible...which is pretty stupid.

[Rye]

Actually, that's pretty standard, a hypothetical omnipotent entity in a bit of logical discourse would automatically be limited to what is logically consistent. Instead of thinking of omnipotence as unlimited power, think of it in terms of the maximum amount of power it's possible to have.

The "heavier thing than you can lift" is essentially "can you trump your own power," which obviously, you can't, if you're omnipotent. It would be impossible as an omnipotent entity to weild more power than you yourself have.

The kind of ability in the OP that can do mutually contradictory things by either imagining they're possible or imagining themselves imagining they're possible. This might then end up with the person being permanently neutered by the nature of their own thoughts or the universe exploding or something.

[Surlethe]

I don't see how you can even consider the effects of "breaking the laws of logic"; if logic is no longer valid, then there's no way of finding the ramifications of statements -- in particular, there's no way of finding the ramifications of the statement, "Logic is no longer valid". Trying to visualize what would happen if the laws of logic no longer constrained reality is even worse than trying to visualize the laws of thermodynamics no longer applying.

[Rye]

The omnivore paradox:

If you are an omnivore, can you eat your own head?

[Sikon]

In mathematics, sometimes the way one understands the result of infinite terms is to consider a limit, where they are treated like variables each approaching infinity.

Such would seem to be the way the hypothetical concept of omnipotence could be considered.

For example, suppose a powerful entity can create an object half as heavy as what he can lift. If that trend continues, when he is ten times as powerful, he can create a heavier object but can lift even more, and so on up towards an infinite power level ...

Reverse the situation, and it could be the other way around.

To use an analogy, a fraction with some infinite terms in both its numerator and its denominator can be either more than 1 or less than 1 depending on the details; such can be evaluated by seeing the result when the infinite terms approach infinity.

The technique of evaluating the limit as power approaches infinity thus leads to the conclusion that the answer to the "paradox" is indeterminate without more information, as it could be either way.

Such doesn't practically matter because both creating power and lifting power are infinite, with no less than omnipotence to a finite observer.

[Singular Intellect]

Like I said, this scenario almost struck me as an effective counter to the 'create an object incapable of being lifted' arguement, since in my spare time I occasionally like to challenge my own arguements to see how they stand up.

While on the same subject, my OP could also be applied to the term 'omniscience', the definition of knowing anything and everything possible. The challenging question of course would merely be re worded to 'could an omniscient being know what it's like to not know something?'

If coupled with the omnipotent aspect, such an entity could indeed 'not know something', but such a limitation is, again, self imposed.

Indeed, from my personal point of view, an omniscient state would be extremely undesireable since it leaves no room for surprises, change or growth. Hence, existence would have nothing of value to offer.

[Sriad]

Now, if presented with this question ('create an object you cannot lift' or similar natured concept), how would you apporach the concept?

By creating an object that fills all of space and time; there would be nowhere to lift it TO.

By a separate act, I could make a place to stand, and a place to move it to, but would be unable to move the omni-object without taking some such enabling action.

...I definitely wouldn't be messing around with laws of logic until I'd set up a properly isolated pocket universe.

[Gil Hamilton]

The omnivore paradox:

If you are an omnivore, can you eat your own head?

Well, you can't eat all of your head, but you could probably eat a fair bit of it.

[anybody_mcc]

a bit OT : I was thinking about omniscience , does it logically follow from omniscience that the world is deterministic and there is no free will ? I think so , but still have some doubts about some of the inferences along the way.

I am pretty sure that it follows if you cannot use the outside of time trick , which is the standard copout , that the omniscient being is outside of time so he just sees all of the timeline and knows what you did , do and will do without really interfering with your free will. But then what does it even mean "to know something" when you are outside of time ? Messy topic )

[Rye]

a bit OT : I was thinking about omniscience , does it logically follow from omniscience that the world is deterministic and there is no free will ? I think so , but still have some doubts about some of the inferences along the way.

Yes, it does, it doesn't matter who is omniscient, how long they're omniscient for, nor how much they interact with things. If something knows everything that ever will be, it is impossible to deviate from that knowledge and so no true ability to choose a different path exists.

But then what does it even mean "to know something" when you are outside of time ? Messy topic )

It wouldn't mean anything, really. Existing "outside of time," is one of those dumb theological apologetic statements that means nothing. Omniscience as a concept sort of betrays the nature of knowing, implying that knowledge can exist without learning and I have a few rants on that that I will organise some day into some sort of essay. Being outside of time and yet being omniscient would mean you'd have to have some magical means of storing all that information without being able to change in any shape or form.

Apologists often don't understand that by asserting god exists outside of time, they're in effect freezing him in one instant and preventing him from interacting with the world. William Lane Craig and similar arseholes think that God became temporal with the big bang...it's all very lame and contrived.

[Surlethe]

a bit OT : I was thinking about omniscience , does it logically follow from omniscience that the world is deterministic and there is no free will ? I think so , but still have some doubts about some of the inferences along the way.

Well, follow the logic in its purest form, supposing some entity G is omniscient:

• Omniscience grants all knowledge.
• Everything which will ever be done in the future is a subset of all knowledge.
• If, given any person A, A will at any given point in time be faced with an arbitrary choice, and it is known to G that A will choose some option O, then it is absolutely impossible for A to choose any option other than O: for then G would not be truly omniscient, as he would have been wrong about which option A chose.
• Therefore, A does not have free will: he is constrained by G's knowledge.

I am pretty sure that it follows if you cannot use the outside of time trick , which is the standard copout , that the omniscient being is outside of time so he just sees all of the timeline and knows what you did , do and will do without really interfering with your free will. But then what does it even mean "to know something" when you are outside of time ? Messy topic )

It means absolutely nothing. It is impossible for anything to exist outside of space-time, since then it would not exist: everything is by definition inside of the universe, and therefore inside space and time. As we hammered out in a discussion oh, a year and a half ago, a God outside of space and time is a static God, unable to think, feel, or know; it is certainly not anything remotely like the Christian conception of God.

[Rye]

It means absolutely nothing. It is impossible for anything to exist outside of space-time, since then it would not exist: everything is by definition inside of the universe, and therefore inside space and time.

So if other hubble volumes existed independently of our own, they wouldn't actually exist? We wouldn't know of them, nor would they be knowable, but they would still exist, just inherently seperate from us.

[Surlethe]

So if other hubble volumes existed independently of our own, they wouldn't actually exist? We wouldn't know of them, nor would they be knowable, but they would still exist, just inherently seperate from us.

If they existed independently of our own, then of course they'd actually exist. However, we would conclude that they don't exist, if they're unknowable, by parsimony.

At least, that's how the universe is defined: containing everything which exists. So these partitions of the universe would still be in the universe, I think, although we would conclude they don't exist.

[Kuroneko]

• Omniscience grants all knowledge.
• Everything which will ever be done in the future is a subset of all knowledge.

The latter is not obvious. It's certainly not analytically true.

• If, given any person A, A will at any given point in time be faced with an arbitrary choice, and it is known to G that A will choose some option O, then it is absolutely impossible for A to choose any option other than O: for then G would not be truly omniscient, as he would have been wrong about which option A chose.

Yes, as a conditional statement, it is true, but its hypothesis might fail to hold.

• Therefore, A does not have free will: he is constrained by G's knowledge.

Not necessarily. If one takes a view of the universe as inherently quantum-mechanical, treating the wavefunction as fundamental, then exact knowledge of the future would be exact knowledge of the wavefunction. But classically, this would correspond to a probability distribution of "choices", so that, by virtue of knowing the future exactly, G would be aware of the exact probabilities of A's choice, but not the choice itself.

Of course, quantum mechanics isn't kind to the notion of free will either, but that's separate from the argument from omniscience. In the end, I don't see why the philosophical notion of free will should be considered important if it is distinguished from moral autonomy (which is, strictly speaking, compatible with determinism), or even what free will is actually supposed to be.

It means absolutely nothing. It is impossible for anything to exist outside of space-time, since then it would not exist: everything is by definition inside of the universe, and therefore inside space and time.

That's a bit strong. One could simply add another time dimension to the universe, etc.--it may not be physically justified (or perhaps even justifiable), but it's not the same thing as meaningless.

So if other hubble volumes existed independently of our own, they wouldn't actually exist? We wouldn't know of them, nor would they be knowable, but they would still exist, just inherently seperate from us.

Under many cases of cosmological parameters, it's possible for one to observe objects outside one's Hubble volume. You probably mean cosmological horizon rather than Hubble volume.

If they existed independently of our own, then of course they'd actually exist. However, we would conclude that they don't exist, if they're unknowable, by parsimony.

Again, not necessarily. We could be forced by parsimony into accepting a model that does have regions outside our cosmological horizon, in which case the proper conclusion would be that they exist. That's pretty much the state of affairs today--the evidence suggests an open, and thus infinite, universe.

The omnivore paradox: If you are an omnivore, can you eat your own head?

Beautiful.

[Surlethe]

• Omniscience grants all knowledge.
• Everything which will ever be done in the future is a subset of all knowledge.

The latter is not obvious. It's certainly not analytically true.

If you possess knowledge, you know things, correct? Therefore, it doesn't seem unreasonable to define "knowledge of G" as a set of facts which are known to G -- i.e., {p : p is a proposition whose truth value is known to G}. The sum total of the knowledge you have can be expressed as such a set, for example, can't it?

From that and the definition of omniscience, it follows that if G is omniscient, then for any proposition p, G knows the truth value of that proposition. Certainly, the statement "X will occur" is a proposition; thus, G knows whether or not it will occur. Universalizing, everything which will ever happen in the future is a subset of all knowledge.

• Therefore, A does not have free will: he is constrained by G's knowledge.

Not necessarily. If one takes a view of the universe as inherently quantum-mechanical, treating the wavefunction as fundamental, then exact knowledge of the future would be exact knowledge of the wavefunction. But classically, this would correspond to a probability distribution of "choices", so that, by virtue of knowing the future exactly, G would be aware of the exact probabilities of A's choice, but not the choice itself.

But doesn't that description contradict the omniscience of G? The proposition "A will choose X course" is certainly one which G ought to know the truth of, if G is omniscient. At best, the inherently quantum-mechanical description of the universe rules out true omniscience, which was the goal anyway.

Of course, quantum mechanics isn't kind to the notion of free will either, but that's separate from the argument from omniscience. In the end, I don't see why the philosophical notion of free will should be considered important if it is distinguished from moral autonomy (which is, strictly speaking, compatible with determinism), or even what free will is actually supposed to be.

How, exactly, is moral autonomy compatible with determinism? I suppose people tend to fixate on free will in and of itself because we like to think we have some control over our lives, instead of acting out a predetermined pattern.

It means absolutely nothing. It is impossible for anything to exist outside of space-time, since then it would not exist: everything is by definition inside of the universe, and therefore inside space and time.

That's a bit strong. One could simply add another time dimension to the universe, etc.--it may not be physically justified (or perhaps even justifiable), but it's not the same thing as meaningless.

True; I stand corrected.

If they existed independently of our own, then of course they'd actually exist. However, we would conclude that they don't exist, if they're unknowable, by parsimony.

Again, not necessarily. We could be forced by parsimony into accepting a model that does have regions outside our cosmological horizon, in which case the proper conclusion would be that they exist. That's pretty much the state of affairs today--the evidence suggests an open, and thus infinite, universe.

Ach, that's what I get for assuming I know what "Hubble pockets" are. I thought he was talking about a pocket universe completely outside our own; but even then, your objection holds in the general case. I guess, though, if it's not necessary to a broader theory, an unknowable entity is almost trivially sliced out by Occam's Razor.

[Kuroneko]

From that and the definition of omniscience, it follows that if G is omniscient, then for any proposition p, G knows the truth value of that proposition. Certainly, the statement "X will occur" is a proposition; ... .

"Certainly"? I agree with the ultimate conclusion that this is a genuine proposition, but I don't see it as either obvious or certain. At least, not in the sense you need it to work, i.e., a literal proposition about the future, thus treating "future" as an actually existing object/state. It's quite possible to self-consistently deny this. The interpretation of future contingents has a rather long history in philosophy, starting with Aristotle's distinction of "definite" and "indefinite" truth. Something analogous to this is present in moral philosophy as well--for example, some schools of thought interpret "murder is immoral" as a statement about the preferences of the one who stated it rather than a genuine moral proposition.

But doesn't that description contradict the omniscience of G? The proposition "A will choose X course" is certainly one which G ought to know the truth of, if G is omniscient.

As above, one could easily have a system of metaphysics in which that is not a genuine proposition of the future.

At best, the inherently quantum-mechanical description of the universe rules out true omniscience, which was the goal anyway.

Not if the wavefunctions are fundamental.

How, exactly, is moral autonomy compatible with determinism? I suppose people tend to fixate on free will in and of itself because we like to think we have some control over our lives, instead of acting out a predetermined pattern.

If one rids oneself of the traditional but unjustified dualistic conception of mind and body, thus identifying the "self" with the central nervous system of the body, "autonomy" simply means that the decision process behind "making a choice" is dominated by this system in some appropriate sense. There doesn't seem to be any inconsistency with this interpretation. A fortiori, it's possible to argue that determinism is necessary for true moral accountability (in complete reversal of employing this a defense of non-determinism), since then by punishing agents that have performed an evil action we are assured this was a genuine failure on their part, rather than their action being some sort of random fluctuation that simply happened to them. Determinism puts moral responsibility directly on the agent, while indeterminism, lacking a satisfactory account of what's behind the decisions, seems to treat moral choices as something that "just happens" to moral agents, rather than being genuinely formed by them.

[Kuroneko]

Actually, I think you misunderstood my objection regarding quantum mechanics. Having omniscient knowledge of the future means knowing the configuration of the universe at the relevant points in time, but if wavefunctions are fundamental, then this amount to knowing some sort of "universal wavefunction" in its exact form. This would be natural interpretation of omniscience regarding the future, but it classically corresponds to probability distributions of choices rather than choices. Put simply, there is no choice to know in the absolute sense under this interpretation (although the wavefunction would give a fair impression of it through decoherence).

[Rye]

I guess, though, if it's not necessary to a broader theory, an unknowable entity is almost trivially sliced out by Occam's Razor.

Well yeah, but tentative conclusions like "I don't believe x exists due to the lack of evidence for it," are different from "it definately does not exist because everything that exists must exist within the dimensions we exist within," which is what it looked like you were saying.

Under many cases of cosmological parameters, it's possible for one to observe objects outside one's Hubble volume. You probably mean cosmological horizon rather than Hubble volume.

Well, I meant in the way Surlethe interpreted it, different universes, different sets of dimensions distinct from our own, and things existing within them that we would never know of but would nevertheless exist despite not conforming to Surlethe's assertion of all existing things being within spacetime.

Beautiful.

I don't get told that nearly enough.

Also regarding determinism vs fate, even with confusing quantum jiggery pokery, I don't see how that would affect a deterministic universe that just so happens to behave in a difficult to understand way. I suspect determinism to be the case, but pragmatically, there would be no difference either way, I'd still feel in control and I'd still think and do the things I do.

[SWPIGWANG]

Kuroneko: I think you are talking about different things. Omniscience, when talked about in philosophy, generally means knowledges to the answers to "all possible statements" as opposed "all observable facts" or "all existing facts" which is what you seem to be talking about.

If we talk of the latter, it might be possible with some solipsist reasoning to concluded that any individual could very well be omniscient.