I just finished the book "God's Debris" by Scott Adams. Its a great book and you should definitly read it.
However, I don't agree with everything in it. In particular, I don't agree with his conception of an omnipotent being. In particular, he thinks that since there is nothing an omnipotent being couldn't know or do, nothing would challenge it aside from the possiblity of destroying itself.
I, however, have a different idea of an omnipotent being.
Side Note: I'll probably refer to the being an question as "he" for this post. In general, I don't think he or she works, and it sounds awkward. No offense to any other gender is intended.
An Old Paradox
Here's a familiar paradox. Can an omnipotent being create a burrito so hot that he can't eat it? It would seem that an omnipotent being should be able to create a burrito so hot that no being could eat it. It would also seems that an omnipotent being should be able to eat any burrito, no matter how hot. So which is it?
I would argue that there cannot exist a being that can do both things. Therefore, an omnipotent being cannot exist, at least not in the sense most people think of it, i.e. a being that can make any state of reality true. Lets call this a "super-omnipotent being."
Conclusion 1: A super-omnipotent being cannot exist.
Potency
To really talk about omnipotent beings, we need to be able to compare two beings in a relavent way. Lets say being A is "more potent" that being B (A > B) if A can do anything B can. More precisely, for all states of the world, X, if B can change the state of the world to Y, A can change the state of the world to Y. (Note: techincally we're dealing with equivilence class of beings that can do all the same things, not beings themselves).
So, lets take two beings, A and B. Is it necessary that A > B or B > A? Clearly not. Right now, I can tip over a chair in the coffee table I'm at. However, at the same instant[1], most other beings cannot. But, many of them can tip of a chair somewhere else where I cannot. So, > is not a full ordering on the set of beings. However, we can easily imagine two beings A and B where A can do anything that B can (even if A and B are not human). As a result, > is a partial ordering on the set of beings.
Maximally Potent
This allows us to create a new defintion for omnipotent beings:
A being is omnipotent iff they are maximally potent.[2]
I.e. a being is omnipotent if no other being is more potent than them. This may seem like the same as the original definition, but its not. Since its possible that A \> B and B \> A, we might be able to imagine two *different* omnipotent beings. We might be able to imagine this, but can we?
We can imagine a being that can eat any burrito no matter how hot. We can also imagine a being that create a burrito so hot that no other being can eat it. We can also "build" an omnipotent being with each of these skills. How? Just take a being with the ability to eat any burrio, and keep adding abilities that are not contradictory (such as being able to make any burrito) until you can't add anymore. You can do the same a being that can make any burrito. So this gives us two distinct omnipotent beings.
God's Personality
Here's the thing. We might be able to imagine an omnipotent being that can't move mountains or turn water into wine, but I'd bet that there are an infinite number of omnipotent benings who can and can basically do anything that we can imagine (including creating reality as we understand it). So this means, that traditional views of god allow for a whole range of omnipotent beings.
Why is this important? Becuse it means that there are things that god *cannot* do. What are these things? I have no idea. But three things come to mind:
Either god cannot create any burrito, or good cannot create any burrito.
Either god cannot lift any stone or god cannot create a stone that no one can life.
Either god cannot create an unstoppable force or god cannot create an immovable object (or god cannot create a force that moves towards an immovable object, etc...).
All of our desires come from things we cannot do. We can't guarantee food, we cannot love forever, etc... Maybe god's desires come from the same place. I have no idea what god can and can't do, and I don't even know if these are things humans can comprehend. But at least, this gives us a reason for god to *want* anything.
Assuming, of course, there is a god.
[1] Maybe if we take into account relativity things change, but I doubt it.
[2] Technically we have to prove that a maximally potent being exists. Generally, in a partially ordered set, there may not be any maximal members. E.g. if we take the integers and say "a is more awesome than b if they have the same parity and a is larger than b" then "more awesome" is a partial ordering on the integers withou a maximal integer. A large part of the difficulty in "potency" is in how we define "the power to do thing."
"If God did not exist, it would be necessary to invent him"
ReplyDeleteWhere to start?
ReplyDeleteCan God create a circle that is a also a square? I would argue no. This is a definitional issue. From the outset, I would argue that He can't accomplish feats which make no semantic sense.
Can God create a number such that no person could find a larger number? Again, the answer is no. Here we have a mathematical impossibility. I think you see where I'm going with this. It's not even clear what it would mean for the answer to this question to be yes. We wouldn't expect an omnipotent being to be able to do such a thing. At least I wouldn't.
Your paradoxes are eerily similar. If He creates a burrito so hot that no being can eat it, by definition, he cannot eat it. If you demand omnipotence to enable a being to enact logical contradictions, then such a being is beyond our abilities of reason. He would exist outside of our logical system.
I guess I always assumed that if there was a God, then He is not omnipotent. Or if He was omnipotent, then He would be an omnipotent intelligence or self-awareness. After all, it seems unlikely that He would have a physical form, which would already severely limit what He could do. He couldn't eat a burrito in that case, no matter how agreeable the temperature was.
Even in that scenario, however, omnipotence still causes issues. You could ask, "Can God create a thing which he cannot destroy?" and play the same game.
Hey skating girl :)
ReplyDeleteMaybe true... one could argue that its already been done. In fact, Christians would almost argue the same thing (i.e. that other religions are making up a god for whatever reason).
Matt
I don't think its unlikely that God has physical form. Or at least, physical form in addition to whatever other form. Eating a burrito shouldn't really be outside the scope of what God can do.
That aside, I think I can tweak the burrito paradox. Can an OB (omnipotent being) have the following two abilities:
1) Make the universe such that there is a burrito even He cannot eat.
2) Make the universe such that there is no burrito He cannot eat.
You can replace burritos with indestructible objects and get similar logic.
The whole point is that only one of these two abilities is possible. What I'm trying to show is that there are abilities which an omnipotent being wouldn't have that are not, in themselves, logically incoherent but are logically contradictory to other abilities it has.
My main concern is with the question, "Why would an omnipotent being do anything?" On the face of it, doesn't appear that an omnipotent being would want anything and as a result wouldn't do anything. So that begs the question, why is there something?
I'm guessing that one possible answer is that there is some action, X, that He can't take even though X is not (by itself) logically incoherent. So, not being able to do X would lead to some desire...
So:
1) There are pairs, (X, Y) where X is logically coherent, Y is logically coherent, but (X, Y) is logically incoherent.
2) There are things an omnipotent being cannot do.
3) Therefore the being may have some desire and therefore do something.
Or am I wrong? The logic is definitely not air tight as is.
Very interesting thread....
ReplyDeleteI like your question "Would an OB want to do anything?", but that makes me think of another question: 1) "Would humans comprehend the motives of an OB?".
Also, 2) does the God that you have in mind really need to be an OB in the strict sense? Could there exist a "wide-sense omnipotence," such that a WS-OB will have limitations but will *appear* to be infinitely knowledgeable and powerful to a subset of all beings.
Let's compare humans and ants. This might open up a can of worms because ants aren't sentient beings with imaginations, but for the sake of a simple model, let's imbue them with some small capacity for thinking (like in a Disney movie). Many of the tasks that an ant will perform in its life can be done more effectively by a human(let's stick to absolute changes to the world, like cutting up a leaf or killing another ant, rather than relative comparisons, like lifting an object of your own weight or the number of generations of offspring you can expect to see in your lifespan). Can humans be thought of as OBs? Humans can make objects they can't lift without mechanical help, and they won't be able to lift that object without mechanical help. In the world of humans, humans clearly aren't OBs. However, they can make objects that no ant can lift, and are able to lift any object that an ant would ever think of lifting (rocks, plants, ant colonies, with mechanical help, which ants can't imagine). In addition, if an ant could talk with a human, he would find that this human can predict all sorts of natural disasters far better than any ant (think tornados, floods, volcanic eruptions, or even mundane events like the commencement of construction in a previously unused lot). This human could even unleash these forces of nature against ants through use of magical objects like fans, fire hoses, dynamite (Note: I know that ants can predict weather, such as rain, to some degree, but I doubt it's more accurate than what humans can collectively achieve). In the world of ants, humans could be considered omnipotent, but I think it's more accurate to say that humans are WS-OBs with respect to ants. In this ant world, humans/WS-OBs could create heavy objects that cannot be lifted (as far as ants are concerned), which the WS-OBs can lift.
Returning to the human world, for humans to grant the "omnipotence" label, does God really need to be an OB in the strict sense, or just WS-OB with respect to humans?
And remember, I went out on a stretch by assuming ants could think the way we do. The sentience of an ant is upper-bounded by that of a human, and I just gave them the benefit of the doubt. (Yes, I realize there are things ants can do that humans can't do, like give directions with phermones and communicate with antennae. But I think we can agree that overall, humans are cognitively more powerful than ants (I have to admit cognitive power is hard to define)). In reality ants probably can't imagine all these hyopthetical situations about heavy objects or hot burritos, they would probably die trying to eat one that was too hot. They couldn't fathom the long-term motivations of humans, or even be aware that there was such a thing as motivations. This brings us back to 1) above, which was my question to follow Hari's question.
Could humans understand what an OB (or a WS-OB with respect to humans) really wants to do or what motivations are driving those actions? Humans have trouble understanding what other humans are doing. If you could travel back 5000 years, what kind of conversations would take place (ignore the language barrier)?
Back to the idea of comprehending an OB/WS-OB's motives, is it possible that we as humans just can't understand them? In the case of the WS-OB, who does have limitations, there would definitely be things that he could strive to do.
Haven't thought this through in detail, please point out the holes.
I think it was Mr Grey in the Library with the Logic book.
ReplyDeleteYou should watch "The Nines." Don't look up reviews or summaries, they'll ruin the movie...
Also, props for using nested parens in English in a natural way. Very nice.
To your points...
I'm 100% willing to go with the ants example. Even if we talk about ants++ like you are doing, its not much of a (conceptual) stretch to give ants some sentience and intelligence. For all we know, they have some (or do we know they don't?).
Also, its definitely true that there are levels of potence that we would not be able to distinguish from omnipotence. Given the examples of miracles throughout history (if taken at face value), we don't really have any evidence to believe that whatever being caused them is omnipotent, merely very very powerful.
However, I don't think that its (necessarily) impossible to understand a (WS-)OB's motives. There's a different analogy people use when talking about god - like an author writing a book (god is the author, we are the story in the book). By reading a book, you can get some idea of the author's motives. Similarly, by looking at reality as it is, we *might* be able to get an idea bout God's motivations.
Going back to the ants -if the ants keep seeing their society being improved by the human, they might say "humans love us!" Instead, if they keep seeing their best inventions destroyed on the brink of becoming useful, they would say "humans like to watch us suffer!" Finally, if human action seemed to do both at random, they might conclude "humans don't care about us. They are to us as we are to ."
This isn't to say that we *can* figure out a (WS-)OBs motives. But we might be able to...
For example, we can fall in love. Maybe god lost a lover and wants to live vicariously through us.
Or maybe not. Its just a random guess.
Or am I still being too human centric and am really off base?
Still haven't gotten to the Nines....
ReplyDeleteThanks for the props (even though I try to avoid nested parens (at least since my hs teachers told me they were abominations (I'm joking (really)))).
This is a very simulating topic, but I think we will eventually end up creating a bunch of conjectures and frameworks based on assumptions. I like that some interesting possibilities will come to light, and I know I'll get a nice mental workout out of all this, but I'm sure in the end I will be no more or less sure about anything.
Intention is pretty hard to discern, even for humans trying to guess other humans. Pigs/cows/sheep probably think humans are pretty cool up until the day they're slaughtered. My dog probably hates me for taking him to the vet, even though the visits extend the length and quality of his life.
I agree that you can figure out the author's motives by reading the book. I wonder if our universe was written as a comedy, a tragedy, a romance, a mystery, . Maybe it's just there for shock value. But to understand the motive behind this universe, won't you need a point of reference? That is, it's pretty hard to see what the motive of the universe is without seeing what other universes could be like.
How confident are you that God allows you the capability to love because he can no longer, and not because he still does? Couldn't it be the other way around? I suppose it's possible to actually guess the intentions based on existing evidence, but it seems like playing 20 questions without feedback. You could get it right on your first guess, but never be certain that your guess was indeed correct.
What does it mean if God has intentions but doesn't share them with humans and gives humans the ability to suspect that he could have intentions? In other words, what is the intention behind not revealing intentions? Is it to delegate power to the religious authorities, who then advertise the concept of "faith"?
Returning to your example of falling in love, could it be that God likes to contemplate things, and gives humans this most difficult of puzzles to ponder during their lives (if they so choose)? Or maybe God doesn't have the ability to doubt anything because he makes the truth, and wants to see how humans grapple with doubt?
I'm just making up stuff now, but let know what you think.
Two side points that I hope won't distract us from the central point:
1) I am very thankful that we can have this discussion without fear of being branded as heretics. I recall being told by someone at one point that I would burn in hell. I can only imagine what society's attitude to unorthodox thought must have been like a few hundred years ago.
2) I'm skeptical of miracles, and the only rational explanations that I can think of are that they are scams or statistical anomalies. What does it mean when someone is miraculously healed of a terminal disease? If there are truly driving forces behind this miracle, why are they absent in the other cases? What are their intentions, if any, and is the healing actually part of their intentions or simply a byproduct of another goal?