Questions about omnipotence paradox
- Iundrah
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Questions about omnipotence paradox
- Alec Smart
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Re: Questions about omnipotence paradox
- Shanor
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Re: Questions about omnipotence paradox
As long as time counts as an acceptable barrier, then this question has a very simple answer, but without it this question is quite the paradox.
- LuckyR
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Re: Questions about omnipotence paradox
It's been a busy week.Alec Smart wrote:I was beginning to think we weren't going to get a God creating a stone he cannot lift thread this week.
OP, do a search...
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Re: Questions about omnipotence paradox
That is part of the paradox which we are trying to solve.Iundrah wrote:And if God is omnipotent, how can a stone be so heavy that He cannot lift it?
I think that it isn't, and here's why. By definition, omnipotence is the ability to do anything at all. From this it follows that, in particular, omnipotence includes the ability to transcend logic. Therefore, omnipotence is not restricted by logic. Interestingly, we have thus proved that omnipotence is beyond the laws of logic using the laws of logic.Iundrah wrote:Is omnipotence restricted by logic?
According to the above, we actually appear to know that omnipotence is not restricted by logic. How? Well, by applying logic to omnipotence. However, this creates another problem. By applying logic to omnipotence, we have come to the conclusion that logic does not apply to omnipotence. But if logic does not apply to omnipotence, then how did we apply logic to omnipotence in the first place?Iundrah wrote:If so, how do we know that
Let us examine what we did above more closely. We realize that for every logical argument, logic has to be assumed to apply to everything that is an object of that argument (axiom Axi1). It appears rather absurd to reject Axi1, since talking about an object in a logical argument means applying logic to that object, which requires logic to apply to the object in order for the argument to be logical in the first place. Our argument from above therefore runs as follows:
Argument Arg1:
1. Logic applies to omnipotence. (Premise) (Because omnipotence is an object of this argument Arg1, logic has to be assumed to apply to it by Axi1.)
2. Omnipotence is the ability to do anything at all. (Definition)
3. Omnipotence includes the ability to transcend logic. (Follows from 2.)
4. Omnipotence is not restricted by logic. (Follows from 3.)
5. Logic does not apply to omnipotence. (Follows from 4.)
I am aware that this argument is not formal, but I cannot see any flaw in it. Therefore, it is (hopefully) valid. However, if it were sound (valid and having only true premises), then it would prove the falsehood of one of its premises, in contradiction to its assumed soundness. It follows that Arg1 is not sound. So, it can't be used directly to prove that omnipotence transcends logic. Nevertheless, it follows from the validity of Arg1 that we have proved that if logic applies to omnipotence, then logic does not apply to omnipotence, and thus that logic does not apply to omnipotence. At least that is how it seems. But we face a problem here, too, which we can see in the following clearer formulation:
Argument Arg2:
1. Logic applies to omnipotence. (Premise) (Because omnipotence is an object of this argument Arg2 too, logic has to be assumed to apply to it by Axi1.)
2. If logic applies to omnipotence, then logic does not apply to omnipotence. (Follows from the validity of Arg1.)
3. Logic does not apply to omnipotence. (Follows from 2.)
Arg2 is valid like Arg1 (at least I can't see anything wrong with it), and again like Arg1, it is not sound out of the same reason as Arg1 (if it were sound, it would disprove its own soundness). Therefore, Arg2 cannot directly prove that omnipotence is beyond logic either.
In fact, the following argument appears to show a more general result:
Argument Arg3:
1. Logic applies to omnipotence. (Premise) (Because omnipotence is an object of this argument Arg3, logic has to be assumed to apply to it by Axi1.)
2. Arg is an argument which proves that logic does not apply to omnipotence. (Premise)
3. Omnipotence is an object of Arg. (Follows from 2.)
4. It is a premise of Arg that logic applies to omnipotence. (Follows from 3. and Axi1.)
5. Arg is not sound. (Follows from 2. and 4.)
This shows that, given that logic applies to omnipotence, then it is impossible to prove the contrary, which is a tautology given the correctness of logic and not worth the whole effort. However, we have learned that it is in fact senseless to try to use logic to decide whether logic applies to something or not, since a logical argument would cease to be one if one of its object were beyond logic. In particular, it is not fruitful to try to solve the omnipotence paradox using logic, since we have to know whether logic applies to omnipotence or not in order to solve the paradox, or do we?
I suggest a generalization of our above realization that logic is useless in some situations. That would be that language as a whole could be incapable of handling some situations. For example, maybe every sentence containing the word "omnipotence", including this one, is meaningless.
Therefore, we might be well-advised to take Proposition 7 of Wittgenstein's Tractatus to heart:
"What we cannot speak about we must pass over in silence." (from the Stanford Encyclopedia of Philosophy)
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Re: Questions about omnipotence paradox
This is quite interesting and creative.ChanceIsChange wrote:Argument Arg1:
1. Logic applies to omnipotence. (Premise) (Because omnipotence is an object of this argument Arg1, logic has to be assumed to apply to it by Axi1.)
2. Omnipotence is the ability to do anything at all. (Definition)
3. Omnipotence includes the ability to transcend logic. (Follows from 2.)
4. Omnipotence is not restricted by logic. (Follows from 3.)
5. Logic does not apply to omnipotence. (Follows from 4.)
I see a problem in 3. If omnipotence includes the ability to transcend logic, then your argument (which relies on logic) is also irrelevant.
If the omnipotent being can transcend logic, then the non-omnipotents can't use logic to analyze omnipotence, or analyze anything else for that matter, using logic.
But we do use logic to establish logical validity.
Therefore 3. is not acceptable.
(I'll continue reading.)
-- Updated December 15th, 2016, 5:44 pm to add the following --
4. if logic does not apply to omnipotence, then the premise 1. is acceptable as true. (As it was logic that was used to show 1. was false.)ChanceIsChange wrote: Argument Arg2:
1. Logic applies to omnipotence. (Premise) (Because omnipotence is an object of this argument Arg2 too, logic has to be assumed to apply to it by Axi1.)
2. If logic applies to omnipotence, then logic does not apply to omnipotence. (Follows from the validity of Arg1.)
3. Logic does not apply to omnipotence. (Follows from 2.)
5. Logic applies to omnipotence (Follows from 1.)
Infinite loop of flip-flopping values (true state of a true paradox.)
Here 3. is not a final conclusion. The final conclusion can't be reached. This is the nature of the paradox as defined.
-- Updated December 15th, 2016, 5:52 pm to add the following --
With all due respect, I suggest a different generalization. It is not that logic is useless; it is that "omnipotence", as a concept, is a paradox, and as such, it has no truth value. Omnipotence, as a quality, can't fulfil its own meaning. This is the conclusion I draw from the exercise.ChanceIsChange wrote:
I suggest a generalization of our above realization that logic is useless in some situations. That would be that language as a whole could be incapable of handling some situations. For example, maybe every sentence containing the word "omnipotence", including this one, is meaningless.
Therefore, we might be well-advised to take Proposition 7 of Wittgenstein's Tractatus to heart:
"What we cannot speak about we must pass over in silence." (from the Stanford Encyclopedia of Philosophy)
My conclusion has nothing to do with omnipotence being a quality of the Christian god. Omnipotence in and by itself is an ill-thought up concept.
To counter the quote by Wittgenstein, in order to show agreement to it, please consider: "Fish pass over all topics in silence."
- Felix
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Re: Questions about omnipotence paradox
I see a couple of possible logical solutions to this problem....Why cannot God create a stone so heavy He cannot lift it, but He can lift it? Is omnipotence restricted by logic?
Solution no. 1 is that the Omnipotent One is an immaterial being, and thus transcends physical laws. However, it is reasonable to assume that material manifestation must be, for the most part, logically consistent in order to remain stable, i.e., not collapse into utter chaos. Therefore the size and weight of a stone will be be limited by material laws. And if the Omnipotent One were to assume the form of a material being, his physical size and weight would also be limited by physical laws. Conclusion: no stones unlimited in size or God unlimited in power may have material existence (but the omnipotent God may have immaterial existence).
Solution no. 2 was referenced by Shanor (post #3). We must first assume that solution #1 may be false, i.e., we must leave the bounds of logic and assume that both gods and stones can have umlimited size/power. So then the Omnipotent One could create a gigantic stone that he could lift while he is omnipotent, and then assume a restricted form of himself that could not lift that stone (in his restricted guise).
Really though, there is a huge problem (no pun intended) with the premise of this paradox, and it is that one cannot define the physical properties of "the stone too big to lift." What form would it take? - A gigantic asteroid? A universe unto itself? You see the problem: the question itself is illogical.
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Re: Questions about omnipotence paradox
I believe the answer is that mortal beings with limited technology (such as ourselves) have little to no chance it understanding matters involving 'God' since it is pretty much a given that any God-like being (or other more resourceful/technologically advance beings) could claim that they are THE actual 'God' and if multiple beings try the same thing we wouldn't be able to tell the difference. Something that is either an angel or demon could for one reason or another appear as the other, as well as 'God' and false Gods could be mistaken for each other.Iundrah wrote:I have questions about omnipotence paradox. Why God cannot create a stone so heavy He cannot lift it, but He can lift it? Is omnipotence restricted by logic? If so, how do we know that, or are we ourselves determining limitations of omnipotence? And if God is omnipotent, how can a stone be so heavy that He cannot lift it? Is it not like asking what is north of north pole? Or am I wrong?
Also it is unclear if "God's" omnipotence comes from either magic or technology. If it is technology it is unclear how he is really better than the rest of us (and technologically advance aliens) enough for us to call him 'God'' if it is possible for other God-like being to also be powerful through highly advance technology. If it is from 'magic' than it is required for us to know how this so called 'magic' works, how it works differently from advance technology, and again how this 'magic' makes him 'God' if it is possible for other God-like beings to also use this 'magic'. I understand that some people might think it is best not to bother with such questions, but it is possible for any devil, demon, or other false God to trick people into serving them just because they can either perform some display of power or do some miracles; but just because a being can do such things conclusively prove that they are actually 'God'. In a nutshell knowing whether something is 'God' or anything about 'God', including anything about what his will is is a non-trivial problem and it is a given that anyone claiming that know for sure anything about such thing hasn't done enough due diligence (even if they work for the church) to talk about such things with any certainty. Or in short, it is a given both the church and the priests that work for it can at best guess about anything when they talk about 'God'.
From what I know from talking to some theists, how the people working in the church decipher the word of God between the lies and gibberish is that the church the 'authority' to certain priest to make the choice as to what is one and the other and they are supposedly guided by the 'divine word' to choose what is right. IMHO the fact that the church blessing their priest doesn't change things much (since they are merely as mortal as the rest of us) and if you choose to guess what is true and that which is not, you'll likely be as correct as whatever the church says is right. Plus if you make the effort to even guess what may be right you be at least thinking for yourself which in philosophy usually leads to the best results.
As I said before whatever 'God' is a nearly unsolvable problem, but that may not be a satisfactory answer to your question. In any case, if you don't agree with the doctrine from the church, with my post, or any other post just think about it enough until you come up with something that is good enough for your own curiosity and I'm pretty sure it will be about as good anything anyone else can come up with since we are all equally ignorant about such things so any reasonable guess is should be hardly any worse than another.
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Re: Questions about omnipotence paradox
True. In fact, the primary purpose of arguments Arg1, Arg2 and Arg3 was to show the irrelevance of logic regarding omnipotence by being irrelevant themselves. But that is not the only reason which I wrote them for, and you have indicated that there might be more to them than irrelevance, e.g. paradox in Arg2.Renee wrote:I see a problem in 3. If omnipotence includes the ability to transcend logic, then your argument (which relies on logic) is also irrelevant.
If 3. in Arg1 does not follow from 2. in Arg1, then, firstly, omnipotence would not include truly all powers, contradicting the definition 2., and secondly, it would become subject to the original omnipotence paradox. The latter fact would imply that omnipotence is logically impossible, which would support your quite reasonable position (if I have understood you correctly).
That is exactly what I wanted to say.Renee wrote:If the omnipotent being can transcend logic, then the non-omnipotents can't use logic to analyze omnipotence
Why? How does the "hyper-logicality" of omnipotence affect the applicability of logic to, say, the natural numbers? If the answer to the second question is 'not at all', then the hyper-logicality of omnipotence would not contradict the fact that we use logic to establish the logical validity of 1 + 1 = 2, for example. But then again, have we really found out anything at all using logic, or are we just deceiving ourselves?Renee wrote:or analyze anything else for that matter, using logic.
But we do use logic to establish logical validity.
To be honest, I do actually have a feeling that hyper-logicality would render the whole of logic useless in all situations, but I'm not sure how to express the reason for that yet. How would you justify the claim that hyper-logical omnipotence would make logical analysis totally useless? I feel that this claim is true, I even think that the very thought of hyper-logicality makes logical analysis impossible, but I can't yet justify that using ordinary language because I cannot answer the questions at the beginning of the last paragraph in a satisfying manner.
In my opinion, that is only the case if hyper-logicality would actually preclude logical analysis and logical analysis is possible. As I said, I cannot express justifications for doubting the former, but there are good reasons to doubt the latter. Firstly, logic as we know it might be flawed. For example, an incorrectly programmed calculator will produce incorrect results in spite of using "electronic logic". Now, how do we know that the "neuron logic" of our brains is correct? Secondly, all logical laws would have to be logically derived in order to be rigorous, leading either to infinite regress or to circular reasoning, both of which are unattractive. Much more could be elaborated on this, but I don't want to drift too far away from the topic.Renee wrote:Therefore 3. is not acceptable.
I have a problem with 4. It is true that if logic were used to show 1. was false, then logic would have to apply to omnipotence, showing 1. to be true and causing a (new?) paradox. However, this paradox can be escaped by realizing that Arg2 is not a logical argument at all. In that case, logic was not used to show that 1. is false, and no paradox arises. This demonstrates the irrelevance of logic to omnipotence. (We are now at an irrelevance stage, see below.)Renee wrote:4. if logic does not apply to omnipotence, then the premise 1. is acceptable as true. (As it was logic that was used to show 1. was false.)ChanceIsChange wrote: Argument Arg2:
1. Logic applies to omnipotence. (Premise) (Because omnipotence is an object of this argument Arg2 too, logic has to be assumed to apply to it by Axi1.)
2. If logic applies to omnipotence, then logic does not apply to omnipotence. (Follows from the validity of Arg1.)
3. Logic does not apply to omnipotence. (Follows from 2.)
5. Logic applies to omnipotence (Follows from 1.)
Infinite loop of flip-flopping values (true state of a true paradox.)
Here 3. is not a final conclusion. The final conclusion can't be reached. This is the nature of the paradox as defined.
Wait! Haven't we just used logic to show that irrelevance? Doesn't that make logic relevant again? (We are now at a contradictory stage, see below.)
It would, and therefore, we see that logic is not only irrelevant to omnipotence, but also to the irrelevance of logic to omnipotence. (Now, we are again at an irrelevance stage, but one of a higher order, see below.)
The above sequence could probably be continued ad infinitum. Interestingly, the sequence itself appears to be a paradox, but one that spirals up to ever higher orders of irrelevance rather than one that goes in circles. It is somewhat similar to a sequence of ever stronger Liar's Paradoxes rather than a single Liar's Paradox.
As I admitted above, the solution you propose is one of the most plausible solutions to the omnipotence paradox, as the latter is resolved entirely within logic. Also, that solution does not have any apparently problematic consequences, since it is not very difficult to accept the impossibility of something as fantastical as omnipotence. Importantly, the solution points out and makes use of the fact that not every linguistic expression necessarily refers to anything.Renee wrote:With all due respect, I suggest a different generalization. It is not that logic is useless; it is that "omnipotence", as a concept, is a paradox, and as such, it has no truth value. Omnipotence, as a quality, can't fulfil its own meaning. This is the conclusion I draw from the exercise.
My conclusion has nothing to do with omnipotence being a quality of the Christian god. Omnipotence in and by itself is an ill-thought up concept.
Still, I do not favor it. That is because it appears to be among those solutions which attempt to solve a problematic entity by simply saying that it doesn't exist. This has already been done with the Liar's Paradox and Russel's Paradox. I prefer to think of some paradoxes as logical phenomena that compel us to think beyond logic. After all, philosophy makes use of logic, but it isn't logic and it isn't confined to it. Therefore, I propose that an extra- or hyper-logical philosophical solution of the omnipotence paradox is needed, but I have not yet devised any such solution.
Very good indeed. I agree, and I think that that there is no fundamental difference between fish and philosophers. Both have intelligence, one of a very basic kind and one of a hopefully not so basic kind. On the other hand, with what right do I judge the intelligence of a fish? Regardless, fish pass over all topics in silence because they cannot talk, and philosophers pass over many topics in silence although they can talk. What I just said is not meant sarcastically at all but rather illustrates my not rigid belief that many differences are ones of degree and not of kind.Renee wrote:To counter the quote by Wittgenstein, in order to show agreement to it, please consider: "Fish pass over all topics in silence."
- Felix
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Re: Questions about omnipotence paradox
It's actually quite simple: it is only an apparent paradox created by language, which is in reality nonsensical: "Create something that cannot be created," "Lift something that cannot be lifted." Even omnipotence cannot make the physically impossible become possible.ChanceIsChange: Therefore, I propose that an extra- or hyper-logical philosophical solution of the omnipotence paradox is needed, but I have not yet devised any such solution.
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Re: Questions about omnipotence paradox
That is an interesting solution. In fact, even if time were no acceptable barrier, God, being omnipotent, could turn it into one. So, the solution would apparently remain valid even without an initially privileged role of time.Shanor wrote: Because a Omnipotent being has unlimited power, could he not limit his power for a short time and then create that rock? After then, he could raise it to unlimited power once again.
As long as time counts as an acceptable barrier, then this question has a very simple answer, but without it this question is quite the paradox.
However, the omnipotence paradox could be strengthened as follows:
Can God create a stone so heavy that even he cannot lift it, without limiting his power at any moment?
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Re: Questions about omnipotence paradox
That would be a direct violation of the definition of omnipotence and would therefore rule out the possibility of omnipotence based on physical laws. However, the omnipotence paradox is a logical paradox and concerns the logical possibility of omnipotence, not whether omnipotence is physically possible or even actual.Felix wrote:Even omnipotence cannot make the physically impossible become possible.
Those two phrases are contradictions and thereby violate logical laws, not just physical ones. You pointed out correctly that they are part of the paradox, but as you can see, they illustrate its logical nature. It is only coincidental that the omnipotence paradox is formulated in a physical context; it could just as well run as follows:Felix wrote:"Create something that cannot be created," "Lift something that cannot be lifted."
Can God create a power that even he does not possess?
This question is equally problematic to answer as the original one with the stone but is not related to the physical world.
I understand this to be the refutation of omnipotence by logic, and although there are good reasons to accept such a refutation (see my previous post), I personally prefer to go beyond logic as I also pointed out in my previous post.Felix wrote:It's actually quite simple: it is only an apparent paradox created by language, which is in reality nonsensical
I do not see how that solves the logical problems associated with omnipotence. Firstly, it has only been found out empirically that the laws of physics forbid the existence of stones and other entities with unlimited size/mass/weight etc. The paradox, on the other hand, does not arise only after one possesses certain empirical knowledge. Secondly, if the Omnipotent One is really omnipotent, he could alter the physical laws in such a way as to admit the existence of stones of unlimited weight and material manifestations of unlimited strength. Thirdly and most importantly, even if the first two points were not an issue, Solution #1 would only shift the omnipotence paradox from the material world to the immaterial world and not solve the logical problem at the heart of the paradox. In particular, it would not give a satisfactory answer to the alternative omnipotence paradox question I presented above.Felix wrote: Solution no. 1 is that the Omnipotent One is an immaterial being, and thus transcends physical laws. However, it is reasonable to assume that material manifestation must be, for the most part, logically consistent in order to remain stable, i.e., not collapse into utter chaos. Therefore the size and weight of a stone will be be limited by material laws. And if the Omnipotent One were to assume the form of a material being, his physical size and weight would also be limited by physical laws. Conclusion: no stones unlimited in size or God unlimited in power may have material existence (but the omnipotent God may have immaterial existence).
This is an interesting solution but has a problem of its own, please see my relevant post.Felix wrote: Solution no. 2 was referenced by Shanor (post #3). We must first assume that solution #1 may be false, i.e., we must leave the bounds of logic and assume that both gods and stones can have umlimited size/power. So then the Omnipotent One could create a gigantic stone that he could lift while he is omnipotent, and then assume a restricted form of himself that could not lift that stone (in his restricted guise).
It is true that according to the laws of physics I know, such a stone cannot exist. However, as I pointed out above, the problem runs deeper, down to the level of logical laws, since even if the laws of physics admitted the existence of stones with infinite weight, the omnipotence paradox would not be resolved due to logical issues.Felix wrote:Really though, there is a huge problem (no pun intended) with the premise of this paradox, and it is that one cannot define the physical properties of "the stone too big to lift." What form would it take? - A gigantic asteroid? A universe unto itself? You see the problem: the question itself is illogical.
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Re: Questions about omnipotence paradox
Obviously, this thought suggests the following solution to the omnipotence paradox:ChanceIsChange wrote:Secondly, if the Omnipotent One is really omnipotent, he could alter the physical laws in such a way as to admit the existence of stones of unlimited weight and material manifestations of unlimited strength.
If God is really omnipotent, he could alter the logical laws in such a way as to admit the existence of stones which he cannot lift without violating his absolute omnipotence.
This solution goes beyond logic and seems to solve the paradox, apparently supporting my stance on the subject that the paradox could and should be solved in an extra- or hyper-logical way.
However, it suffers from a similar problem as Shanor’s solution, for the paradox could be strengthened as follows:
Can God create a stone so heavy that even he cannot lift it, without manipulating the laws of logic?
The problem is that both in the case of Shanor’s solution and in the case of the above solution, God had to do something that logic necessitated. In the above solution, God transcended logic, but he still had to do so in accordance with logic. Consequently, the paradox could be strengthened in both cases to a form in which the solutions proved inadequate by asking whether God could perform the paradoxical feat without whatever it is that logic would require of him in order to allow him to accomplish it.
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Re: Questions about omnipotence paradox
-- Updated December 21st, 2016, 11:28 am to add the following --
In mathematics, "infinity" is often treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as natural or real numbers. ... And since, neither infinity-infinity=0, nor infinity/infinity=1 you could say that infinity is not equal to infinity. (Google search)
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Re: Questions about omnipotence paradox
My point is that it is not logical. Logic can only evaluate definite terms. "Omnipotent Being" is itself a logical contradiction, because to be a being is a limitation on omnipotence.ChanceIsChange: the omnipotence paradox is a logical paradox
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