Infinity > Infinity?

[Uraniun235]

Now, this confuses me.

"If God can't make a rock bigger than he can lift, then he's not omnipotent! But if he can, then he can't lift it and he's not omnipotent!"

So... in effect, God is supposed to make infinity bigger than infinity?

[Nova Andromeda]

--Infinity can be larger than infinity (the limit of x is smaller than the limit of x^2). That is not the problem. The problem is that there is no such thing as omnipotent (see your paradox).

[Yogi]

There are diffrent values of infinity. For example, lim (x->inf.) of x and lim (x->inf) of X^2 are both infinity, but if you divide the second by the first, the answer is infinity, which means that the second must be greater than the first.

Heh. Simultanious post.

[Durandal]

Also compare the infinite continuum of real whole numbers to the one of all real numbers. The latter is clearly a larger infinity.

[IDMR]

The later has a larger cardinality.

And folks, I think we should stop turning this into a mathematicians' chat room.

[The Dark]

Now, this confuses me.

"If God can't make a rock bigger than he can lift, then he's not omnipotent! But if he can, then he can't lift it and he's not omnipotent!"

So... in effect, God is supposed to make infinity bigger than infinity?

That's a paradox used by people attempting to prove that there is no God. Within theology, God's omnipotence is defined as God's ability to do whatever is in God's will. Since God's will would not include either of those options, since they would lessen God's appearance (among those who would care), the question is meaningless.

[Durandal]

You presume to know God's will. The fact that he may not want to do it doesn't change the fact that he can't do it. Jesus said something to the effect of "For nothing is impossible with God," or something. Clearly, he was lying or severely delusional.

[IDMR]

You presume to know God's will. The fact that he may not want to do it doesn't change the fact that he can't do it. Jesus said something to the effect of "For nothing is impossible with God," or something. Clearly, he was lying or severely delusional.

You miss the point. You know what they say about theology? It was invented so people who no longer believe in God can stay within the church.

You see, something about an atheist no longer drawing a stipend...

[Durandal]

So, it's completely irrational. Thanks.

[Frank_Scenario]

Two answers to the God and a big rock question:
1. (The one I agree with) Omnipotence is the ability to do all things that are doable. That is to say that all logically possible feats can be accomplished by an omnipotent being. This would rule out things like drawing a square circle. The task is incoherent, because the definition of a square necessarily precludes it also being a circle. Similarly, the creation of a rock so big that it can't be lifted by a being with presumably-infinite lifting power is equally incoherent. So no, God can't make a rock that big, but that doesn't take away from God's power.
2. (The backup) If you don't buy that, then the answer is just yes, God can make a rock so big He can't lift it, even though such a rock is impossible. He can also lift that rock, because it's just as impossible as the initial creation.

All of this assumes you want to protect God's omnipotence; I don't see why He needs to be omnipotent (though the Bible does strongly imply that He is).

[Shinova]

God's omnipotence is an abstract concept that cannot be scientifically proven.

Some may say that it's beyond science's capability to prove. Others may say that it's just all made up.

My two cents for this debate.

[Durandal]

*sigh* One last time, science never proves anything.

[Shinova]

*sigh* One last time, science never proves anything.

Then why do they call them proofs?

[Darth Yoshi]

Because proof is supposed to work for any variable in that scenario. But I may have just stated the definition of a mathematical proof, which could be different from a scientific proof.

[neoolong]

Two answers to the God and a big rock question:
1. (The one I agree with) Omnipotence is the ability to do all things that are doable. That is to say that all logically possible feats can be accomplished by an omnipotent being. This would rule out things like drawing a square circle. The task is incoherent, because the definition of a square necessarily precludes it also being a circle. Similarly, the creation of a rock so big that it can't be lifted by a being with presumably-infinite lifting power is equally incoherent. So no, God can't make a rock that big, but that doesn't take away from God's power.
2. (The backup) If you don't buy that, then the answer is just yes, God can make a rock so big He can't lift it, even though such a rock is impossible. He can also lift that rock, because it's just as impossible as the initial creation.

All of this assumes you want to protect God's omnipotence; I don't see why He needs to be omnipotent (though the Bible does strongly imply that He is).

Have you actually read the definition of omnipotence? It is an abstract concept that is in reality impossible. It is infinite and all power. Both of your definitions imposes limits just so you can apply omnipotence to God. They are both wrong.

[Frank_Scenario]

Have you actually read the definition of omnipotence? It is an abstract concept that is in reality impossible. It is infinite and all power. Both of your definitions imposes limits just so you can apply omnipotence to God. They are both wrong.

How, precisely, does saying that God can do all things that are doable differ from claiming that God has infinte power? Some tasks, such as drawing a square circle, are not possible to do with any amount, finite or no, of power, because they're not coherent tasks. It's not logically possible to do it, and it's not a power issue. No limit is imposed on omnipotence here.

Further, defining omnipotence as the ability to do all things that are logically possible is the accepted definition in philosophy of religion and theology, and I know of no serious thinker in the field (off the top of my head, at least), going back as far as Thomas Aquinas, who has differed with it.

The second answer doesn't rely on the first at all. It's clear that it is paradoxical to say that a rock exists which cannot be lifted by a being that can lift anything. It's no more of a paradox to say that this being can also lift this rock that it can't lift. Assuming the definition of omnipotence allows for an omnipotent being to lift any object and make rocks of any size, this argument is fine. My definition allows that; so does saying that omnipotence is infinite power. Again, this argument places no limits on omnipotence; in fact, it allows God to do anything at all, even if it is incoherent to do so.

Finally, I don't particularly care if God is omnipotent or not, as long as it is possible for me to be saved through Him.

[Utsanomiko]

Human inventions don't save people; people have to save themselves.

Anywho, the main problem with the question, and more specifically with 'can god make a square circle?' is that it isn't really asking anything. By definition, it's just two contradictory concepts glued together. It's not a limitation to the laws of logic, just a inability to make things that aren't really anything.

but that's assuming the concpet of omnipotence actually exists in the real owrld. By all appearances, it's just a philosophical concept.

[Frank_Scenario]

Anywho, the main problem with the question, and more specifically with 'can god make a square circle?' is that it isn't really asking anything. By definition, it's just two contradictory concepts glued together. It's not a limitation to the laws of logic, just a inability to make things that aren't really anything.

Well, the limitation is a result of logic (specifically, the principle of noncontradiction, a thing cannot be both a and not-a). It's not a limitation on logic. You're right, though, the term "square circle" doesn't describe anything, and a square circle is not (and cannot be) a thing.

[neoolong]

Have you actually read the definition of omnipotence? It is an abstract concept that is in reality impossible. It is infinite and all power. Both of your definitions imposes limits just so you can apply omnipotence to God. They are both wrong.

How, precisely, does saying that God can do all things that are doable differ from claiming that God has infinte power? Some tasks, such as drawing a square circle, are not possible to do with any amount, finite or no, of power, because they're not coherent tasks. It's not logically possible to do it, and it's not a power issue. No limit is imposed on omnipotence here.

Infinite power has no limitations. It is an abstract concept. You impose limits by saying he cannot do certain things, does not matter whether they are impossible in themselves. As such, your definition of omnipotence is wrong.

Further, defining omnipotence as the ability to do all things that are logically possible is the accepted definition in philosophy of religion and theology, and I know of no serious thinker in the field (off the top of my head, at least), going back as far as Thomas Aquinas, who has differed with it.

That's because they want God to be as powerful as possible and just changed the definition of a word so that they can use it as a trait. It's like changing what a deity is so that somebody can "prove" that everybody believes in a deity. Or faith.

The second answer doesn't rely on the first at all. It's clear that it is paradoxical to say that a rock exists which cannot be lifted by a being that can lift anything. It's no more of a paradox to say that this being can also lift this rock that it can't lift. Assuming the definition of omnipotence allows for an omnipotent being to lift any object and make rocks of any size, this argument is fine. My definition allows that; so does saying that omnipotence is infinite power. Again, this argument places no limits on omnipotence; in fact, it allows God to do anything at all, even if it is incoherent to do so.

Finally, I don't particularly care if God is omnipotent or not, as long as it is possible for me to be saved through Him.

Your definition is wrong. You are just creating definitions so that you can say that God is omnipotent and really really powerful. Omnipotence is a paradox because the situation you described above is inherently contradictory. Infinite power is a concept. However, it is inherently pardoxical precisely because of situations like the rock. It doesn't work becuase you can just say, well he made a rock he can't lift, then he lifted it. But he can't lift it because he made it that way. If he could then he didn't do it in the first place and so isn't omnipotent.

You can't just change the definition to suit your own tastes just so you can say your deity is more powerful than the deity of the guy down the street.

[Frank_Scenario]

Infinite power has no limitations. It is an abstract concept. You impose limits by saying he cannot do certain things, does not matter whether they are impossible in themselves. As such, your definition of omnipotence is wrong.

Suggesting that an omnipotent being cannot draw a square circle (or create the rock in question) is not a limit on omnipotence. The tasks which are being discussed are not "things," in any significant sense because they are simply nonsensical.

Consider this nonsense word: galfurglestein. An omnipotent being cannot make a garfurglestein, because the word doesn't actually mean anything; it refers to nothing; it is nonsense. Similarly, a square circle, or the rock in question, refers to no 'real' object; it is equally nonsensical.

Further, defining omnipotence as the ability to do all things that are logically possible is the accepted definition in philosophy of religion and theology, and I know of no serious thinker in the field (off the top of my head, at least), going back as far as Thomas Aquinas, who has differed with it.

That's because they want God to be as powerful as possible and just changed the definition of a word so that they can use it as a trait. It's like changing what a deity is so that somebody can "prove" that everybody believes in a deity. Or faith.

Actually, the definition I'm using is, to my knowledge, the original definition; it's only relatively recently that it's come under dispute. At least, I'm not aware of any works on the subject earlier than the last 50 years or so. I could easily use this to make the accusation that you're changing the word's meaning to take power away from God. The accepted definition in theology and philosophy is, and has been for hundreds of years, my own.

Think of it this way: you wouldn't ask a creationist to define evolution, because, odds are, he'll get it wrong. You ask the people who spend their time studying it (biologists), because they know what they're talking about.

I'll hasten to point out that it's not a good definition just because it's accepted by theologians and philsophers. The fact that they accept it lends weight to it, but does not justify it.

Your definition is wrong. You are just creating definitions so that you can say that God is omnipotent and really really powerful. Omnipotence is a paradox because the situation you described above is inherently contradictory. Infinite power is a concept. However, it is inherently pardoxical precisely because of situations like the rock. It doesn't work becuase you can just say, well he made a rock he can't lift, then he lifted it. But he can't lift it because he made it that way. If he could then he didn't do it in the first place and so isn't omnipotent.

You can't just change the definition to suit your own tastes just so you can say your deity is more powerful than the deity of the guy down the street.

For the sake of argument, I'll concede your definition, because it doesn't matter. If an omnipotent being can do one thing that produces a contradiction (make a rock so big he can't lift), he can also do another (lift a rock that's too big for him to lift). You're applying the law of noncontradiction selectively. Essentially, you're saying the following:
1. An omnipotent being can do anything at all, and it is not bound by logic.
2. Therefore, an omnipotent being can draw a square circle, tell you what blue tastes like, and make a rock so big that the being can't lift it.
3. The last example shows that omnipotence is paradoxical because the being cannot lift the rock it created, but omnipotence is defined as being able to do anything.

However, the first part of your argument conradicts the third, because you've already ruled logic out of the discussion. If an omnipotent being is not bound by the laws of logic, it can lift a rock it's can't lift, even though this is contradictory, because it's not bound by the laws of logic.

So, in short, your position is incoherent, and you're changing the rules in the middle of the game.

This is one reason why philsophers and theologians accept my definition: once you've ruled logic out, you really can't say much more on the subject, and, well, that's useless.

[neoolong]

Infinite power has no limitations. It is an abstract concept. You impose limits by saying he cannot do certain things, does not matter whether they are impossible in themselves. As such, your definition of omnipotence is wrong.

Suggesting that an omnipotent being cannot draw a square circle (or create the rock in question) is not a limit on omnipotence. The tasks which are being discussed are not "things," in any significant sense because they are simply nonsensical.

Inconsequential. Infinite power is by definition infinite. Because there are things that cannot be such as a square circle, that just gives more proof that something cannot be omnipotent.

Consider this nonsense word: galfurglestein. An omnipotent being cannot make a garfurglestein, because the word doesn't actually mean anything; it refers to nothing; it is nonsense. Similarly, a square circle, or the rock in question, refers to no 'real' object; it is equally nonsensical.

Wrong. If I, as a pseudo-omipotent being, decide that a galfurglestein is a green rock and I make one, then a galfurglestein is a green rock and I just made one. On the other hand a square circle has a contradictory definition and therefore is impossible to make. Such omnipotence is not sufficient to make such a thing and so is impossible.

Further, defining omnipotence as the ability to do all things that are logically possible is the accepted definition in philosophy of religion and theology, and I know of no serious thinker in the field (off the top of my head, at least), going back as far as Thomas Aquinas, who has differed with it.

That's because they want God to be as powerful as possible and just changed the definition of a word so that they can use it as a trait. It's like changing what a deity is so that somebody can "prove" that everybody believes in a deity. Or faith.

Actually, the definition I'm using is, to my knowledge, the original definition; it's only relatively recently that it's come under dispute. At least, I'm not aware of any works on the subject earlier than the last 50 years or so. I could easily use this to make the accusation that you're changing the word's meaning to take power away from God. The accepted definition in theology and philosophy is, and has been for hundreds of years, my own.

Omni means all, as in all. Potent in this case means power. Thus all powerful or infinetly powerful. That is what the word breaks down to and what the meaning actually is. It is the original meaning.

Think of it this way: you wouldn't ask a creationist to define evolution, because, odds are, he'll get it wrong. You ask the people who spend their time studying it (biologists), because they know what they're talking about.

I'll hasten to point out that it's not a good definition just because it's accepted by theologians and philsophers. The fact that they accept it lends weight to it, but does not justify it.

If he wanted to debate it I would expect the creationist to get it right. Which is why here I have checked the definition of omnipotence.

Your definition is wrong. You are just creating definitions so that you can say that God is omnipotent and really really powerful. Omnipotence is a paradox because the situation you described above is inherently contradictory. Infinite power is a concept. However, it is inherently pardoxical precisely because of situations like the rock. It doesn't work becuase you can just say, well he made a rock he can't lift, then he lifted it. But he can't lift it because he made it that way. If he could then he didn't do it in the first place and so isn't omnipotent.

You can't just change the definition to suit your own tastes just so you can say your deity is more powerful than the deity of the guy down the street.

For the sake of argument, I'll concede your definition, because it doesn't matter. If an omnipotent being can do one thing that produces a contradiction (make a rock so big he can't lift), he can also do another (lift a rock that's too big for him to lift). You're applying the law of noncontradiction selectively. Essentially, you're saying the following:
1. An omnipotent being can do anything at all, and it is not bound by logic.
2. Therefore, an omnipotent being can draw a square circle, tell you what blue tastes like, and make a rock so big that the being can't lift it.
3. The last example shows that omnipotence is paradoxical because the being cannot lift the rock it created, but omnipotence is defined as being able to do anything.

However, the first part of your argument conradicts the third, because you've already ruled logic out of the discussion. If an omnipotent being is not bound by the laws of logic, it can lift a rock it's can't lift, even though this is contradictory, because it's not bound by the laws of logic.

So, in short, your position is incoherent, and you're changing the rules in the middle of the game.

Wrong. Read what I have typed again.

"It doesn't work becuase you can just say, well he made a rock he can't lift, then he lifted it. "

You can say he can do this, but it is still impossible. It's the same thing as me saying I can fly.

"But he can't lift it because he made it that way."

This goes to the second part of the definition of the rock. This part of the definition of the rock directly contradicts the lifting. Thus it is impossible.

"If he could then he didn't do it in the first place and so isn't omnipotent."

As a result, if he could, read could, make a rock he couldn't life that would make him really really powerful. However, it does not make him omnipotent.

This is one reason why philsophers and theologians accept my definition: once you've ruled logic out, you really can't say much more on the subject, and, well, that's useless.

Irrelevant. It still is a flawed definition.

[data_link]

No omnipotent God can ever do anything which is not logically possible. This is why:

1. If God can do that which is logically impossible, then He can have an effect on things when He doesn't exist. Therefore, the question of whether God exists is irrelevant, because He will have the same effect whether he exists or not.

2. A force (hereafter called THE FORCE) which is more powerful than God would also be able to have an effect if it doesn't exist.

3. Therefore, the fact that THE FORCE cannot exist because it is impossible to be more powerful than an omnipotent being is irrelevant, because THE FORCE will still be more powerful than Him even if it doesn't exist.

4. Because THE FORCE is more powerful than God, it will have the power to stop God from doing anything it doesn't like.

5. THE FORCE is created by all living things, it surrounds us, it penetrates us, it binds the galaxy together.

6. Because they create the Force, all living things are more powerful than God.

7. All living things do not have the power to do that which is logically impossible.

8. Therefore, God does not have the power to do that which is logically impossible.

[Darth Yoshi]

No omnipotent God can ever do anything which is not logically possible. This is why:

1. If God can do that which is logically impossible, then He can have an effect on things when He doesn't exist. Therefore, the question of whether God exists is irrelevant, because He will have the same effect whether he exists or not.

2. A force (hereafter called THE FORCE) which is more powerful than God would also be able to have an effect if it doesn't exist.

3. Therefore, the fact that THE FORCE cannot exist because it is impossible to be more powerful than an omnipotent being is irrelevant, because THE FORCE will still be more powerful than Him even if it doesn't exist.

4. Because THE FORCE is more powerful than God, it will have the power to stop God from doing anything it doesn't like.

5. THE FORCE is created by all living things, it surrounds us, it penetrates us, it binds the galaxy together.

6. Because they create the Force, all living things are more powerful than God.

7. All living things do not have the power to do that which is logically impossible.

8. Therefore, God does not have the power to do that which is logically impossible.

Not to be rude or anything, but what? You lost me around 3.

[data_link]

No omnipotent God can ever do anything which is not logically possible. This is why:

1. If God can do that which is logically impossible, then He can have an effect on things when He doesn't exist. Therefore, the question of whether God exists is irrelevant, because He will have the same effect whether he exists or not.

2. A force (hereafter called THE FORCE) which is more powerful than God would also be able to have an effect if it doesn't exist.

3. Therefore, the fact that THE FORCE cannot exist because it is impossible to be more powerful than an omnipotent being is irrelevant, because THE FORCE will still be more powerful than Him even if it doesn't exist.

4. Because THE FORCE is more powerful than God, it will have the power to stop God from doing anything it doesn't like.

5. THE FORCE is created by all living things, it surrounds us, it penetrates us, it binds the galaxy together.

6. Because they create the Force, all living things are more powerful than God.

7. All living things do not have the power to do that which is logically impossible.

8. Therefore, God does not have the power to do that which is logically impossible.

Not to be rude or anything, but what? You lost me around 3.

It's an indirect proof that God cannot do that which is logically impossible. Basically, logic dictates that that which results in a logical contradiction cannot exist (the principle of the indirect proof). Of course, if He can ignore logic, then not being able to exist does not stop God from having real world effects which are logically impossible. However, the same would apply to THE FORCE, which I have just defined as a force more powerful than God which is created by all living things. So, if it were possible for God to ignore logic, then THE FORCE should have observable effects and living things should be able to do things that are logically impossible. Since this does not happen, we can safely conclude that God cannot do that which is logically impossible. Granted, I could have made that point (that we don't see logically impossible things happening) with God, but I put in THE FORCE because one could use the counterargument with God that He could, but simply doesn't want to, whereas we know that if THE FORCE existed, then there would be a lot of people going around creating square circles just to see what they are like. Of course, the original argument was much more poetic, don't you think?

[Rathark]

Please bear with me here, since I don't hold my beer very well.

If God exists, then did It create the laws of mathematics? If so, then could it reshuffle a few details and make 1 + 1 = 3? Or would such an attempt collapse everything into zero, and thus "unmake existence" (to quote Dogma)? Is the existence of everything comprehensible and finite simply a "cosmic column" to seperate nothingness from infinity? If God is outside of the space-time continuum, then It is untouched by the "logic" of cause and effect. Therefore, the idea that God would create something that would allow It to exist in the first place would be both fallacious and obvious; since God, merely by existing, would be "constantly" generating the conditions (ie mathematics and logic) that allow It to exist in the first place.

Thus are God and Absolute Infinity one and the same, and the consistency of mathematics the lifeblood of Its being? Does God's own existence depend upon the consistency of mathematics? If so, does this make God inferior to mathematics, or are both concepts different sides of the same coin? Or is it fallacious to personify something as abstract and impersonal as the universe, logic, mathematics and infinity?

Am I making any sense whatsoever, or should I get some sleep quick smart and stop washing down those home-made honey mustard ham and cheese sandwiches with malt beer?

(PS: Maybe it might help if you ran a Google search on Georg Cantor).