The Omnipotence Paradox
Friday, August 06, 2010
"Can God create a stone that he will fail to lift?"
This is a question that is often used by non-believers to argue against the existence of God. It is actually a particular form of The Omnipotence Paradox illustrated by the argument that if an omnipotent being exists, then it is capable of creating a task that it will fail to perform and is therefore not really omnipotent.
So does this debunk the existence of God? here are my two cents ...
Disclaimer: this post is meant to discuss the subject from a philosophical point of view only. Any apparent bias towards any set of beliefs, should any exist in the post, is completely unintended. The views presented here are the author's and do not by any means represent facts. Expression and discussion of religious beliefs on this post is not welcome, will not be tolerated and should rather be redirected here.
The question form of the argument can be rearranged into the statement "God can create a stone that he will fail to lift" to which we require a boolean evaluation; either true or false. The answer is trivial but is the source of a lot of confusion: there is no valid logical evaluation!
Actually, there is an infinite number of statements that do not have valid logical evaluations. For example; this statement is false, which again can not be either true or false. This is why these statements are called paradoxes. The real question is; in case of the omnipotence paradox, what does "not having a logical evaluation" really mean?
Non-believers answer this by saying "hence there is no such thing as omnipotence and therefore God does not exist". However, this is not necessarily true. The non-existence of a logical evaluation can simply mean that the model we used to represent and solve the problem is not perfect. The model in this case being logic. Logic says that each statement can be either true or false, so how come such a statement that is neither true or false exist?
Many branches of logic and philosophical reasoning provide different interpretations to the contradiction presented by such statements. In all cases, we have to keep in mind that our science is based solely on observation and the preposition of axioms (statements that can not be proved but are considered true and the base for further inference, such as 1x1=1). Therefore our science is by no means absolute and its failure to capture or model any phenomena should not necessarily indicate the non-existence of the phenomena.
IMHO, when somebody says "Can God create a stone he can not lift?", I see both an argument against the existence of God and a proof of the failure of the science behind the argument!
P.S: the omnipotence paradox is the subject of ongoing heated discussions in the scientific community. For a better overview and understanding on the almost-infinite different stands, check the Wikipedia article on the subject.
20 Response(s) to "The Omnipotence Paradox"
Ehab said:
The idea that logic (or the scientific process) might be inherently flawed as a model to explain reality has been playing in my mind for quite a while. But how are you going to prove it?
You could say that axioms are put forth by imperfect humans, therefore the model is incorrect, but is that real proof?
Do we need to prove/disprove the validity of logic, anyway? Can we at least learn to use logic (and the scientific process) in their proper contexts (if there are any)? Lots of questions, few answers...
Ghaith said:
Models are used to interpret reality. If we accept that what we perceive is reality then simply a mismatch between a model and what we perceive is evidence of the imperfection of the model. Arguing with axioms is fruitless because axioms are essentially assumptions and you can't argue with assumptions.
I don't think that we need to question the validity of models as long as they provide a sufficiently accurate interpretation of reality. However, models might need adjustments, changes or complete reworks if they fail to interpret newly made observations (think Classical Physics to Quantum Mechanics).
Haitham said:
Gaith,
There are variants of this paradox that ask if God was omnipotent then can he give rise to a creature that is just as omnipotent or more? Can he cease to exist?
Logic is very different from Science! Science builds on logic, and logic is improved based on scientific feedback! Remember that quantum mechanics did not fit with our classical logic, so we came up with quantum logic! So what type of logic do we use here? In quantum logic, you can have two states, which is not allowed in classical logic
Anyways, I just do not think that the answer to this paradox will be decisive in this regard!
Ghaith said:
I disagree with Logic being different from Science. Logic (referring to the study of of prepositions, inference and proof, not the human ability to reason) is an attempt to provide a base for explaining reality through science, and so can be regarded as a scientific model on its own.
Science does indeed build on logic but whether logic should be reconsidered on the basis of empirical evidence is a point of debate.
People who argue against the logical validity of omnipotence using this paradox use classical propositional logic. Quantum propositional logic is a good example of an improved model that might provide a better explanation to this paradox where classical logic appears to fail :)
And yes, you are definitely right about the non-existence of a decisive answer.
Ehab said:
But I ask about a wider picture. When classical physics failed to encompass observations, quantum physics was born. Both were based on a process - logic/the scientific process, right? But how can one prove/disprove the validity of this process? Are we taking it for granted?
Ghaith said:
The process you're referring to is the scientific method. It is the tool we use to create science and build models from empirical evidence. I think we can only "be happy with it" but can never validate it.
Giulia said:
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just a quick "hello"! I'm leaving to the states in a week time!
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Giulia
Devil's Mind said:
I got few remarks:
(1) ...............
Quote: "For example; this statement is false, which again can not be either true or false. "
This is a different category of paradoxes which are called self-referential paradoxes. The solution of this paradox is that the complete sentence "this sentence is false" is considered false (a paradox is by definition false). However, the common mistake is that we can make conclusions from false statements, which is not correct.
Remember that: False=p ^ False=~p.
Or remember that:
p = q = ~p v q
which means that
False = q
= ~False v q
= True v q
= True
In other words, you cannot make conclusions based on false statements. So the logical deduction that, if the statement is false, then it must be true is invalid.
read more about the paradox of entailment: http://en.wikipedia.org/wiki/Paradox_of_entailment#Paradox_of_entailment
(2) ................
Quote: "It is actually a particular form of The Omnipotence Paradox illustrated by the argument that if an omnipotent being exists, then it is capable of creating a task that it will fail to perform and is therefore not really omnipotent."
That's one confusing way to look at it. The more understandable view is that the paradox is a study of the property of omnipotence. The paradox shows that omnipotence is an inconsistent property, and therefore no real being can have this property.
Now this argument goes on to show that the "description" of God is made up by man. It does NOT prove that God does not exist.
Its like someone tells me: "Ghaith can move faster than the speed of light." If someone makes the conjuncture: "Nothing can go faster than speed of light, therefore Ghaith does not exist." He is obviously mistaken. The only conclusion I can make is that either the person who told the story was outright lying, or at least was exaggerating.
However, if you include omnipotence in the definition of God, then God definitely does not exist. So it proves that God does not exist, if and only if, omnipotence is a definitive feature of God.
(3) ................
The omnipotence paradox is not science, it goes under philosophy. Handling the issue "scientifically" would certainly be an error.
Quote: "I disagree with Logic being different from Science. Logic (referring to the study of of prepositions, inference and proof, not the human ability to reason) is an attempt to provide a base for explaining reality through science, and so can be regarded as a scientific model on its own."
You my friend have a major flaw in your understanding. Logic and mathematics are a priori. They are analytical and theoretical. Science is a posteriori. It is empirical and based on evidence.
The basics of proof in math and logic are worlds different than the basics of proof in science.
Ghaith said:
Hi Zaid,
1) False can lead to either False or True: agreed indeed (I don't even know why this a paradox itself). However, how do you prove/explain that paradoxes evaluate to False? isn't the absence of a plausible evaluation the very thing that makes a statement a paradox?
2) God is defined as an omnipotent being. Like you said, it is possible that our description of omnipotence is inaccurate or even incorrect and that the omnipotence paradox is a proof of the inconsistency of this property as we define it. However, assuming we're sticking to the classical definition of omnipotence, how do you use a paradox to infer that an omnipotent being cannot exist if paradoxes are false statements?
3) I realized I have been vague in my response so I'll try to rephrase what I've been trying to say in more accurate terms. I have used the term "Science" as slang in reference to the collective work of the human mind. I completely agree that the analysis of paradoxes falls under philosophical reasoning and not the scientific method. However, my point is as follows:
Philosophical studies form the tools/means/semantics used by the scientific method in the final favour of providing an explanation to reality. If both are products of human intelligence, couldn't philosophical analysis be as much wrong as a scientific model?
Devil's Mind said:
(1+2) Paradox means contradiction. Take the example that I gave for "Ghaith can move faster than the speed of light." Here, scientifically we make the conclusion that this statement must be false.
"God exists and God is omnipotent." In this instance, we use logic to make the conclusion that this statement must be false. This type of conclusion is stronger than science-based conclusions, as we are excluding empiricism as a source of error.
The law of non-contradiction tells us that Paradoxes evaluate to False. However, the law of non-contradiction itself has no proof. It is an axiom of classical logic.
Quote: "how do you use a paradox to infer that an omnipotent being cannot exist if paradoxes are false statements?" - It falls under proof by contradiction.
Ghaith said:
I don't think paradoxes are the same as contradictions.
Consider this; "Statement A is True ^ Statement A is False" is a contradiction because the premises are opposite. However, this is different from saying "This statement is False" because this has only one premise and that infers the conclusion "This statement is true" which opposes the premise.
In other terms, while a contradiction is represented by "p ^ ~p" which evaluates to False, a paradox is more like "p => ~p" which evaluates to "~p v ~p" and hence "~p".
Therefore I don't think proof by contradiction is applicable here.
Devil's Mind said:
Indeed there is proof by contradiction.
For any statement "p = p", and in our particular case "p = ~p". So we have a case where "(p = p) ^ (p = ~p)" This is the exact scenario of proof by contradiction.
A paradox is a contradiction, the difference you describe is form, don't let the self-referential form of the paradox fool you away from the obvious.
Just as a teaser, I'll give you another form of the paradox:
"Statement below is true.
Statement above is false."
Ghaith said:
The commenting system is interpreting the '>' char as a tag suffix and taking it off your comments, making it difficult to tell whether you meant '=' or '=>'.
Can I ask you to repost your argument in the prepositional form again? Please use the code > to produce a '>' character.
Devil's Mind said:
Indeed there is proof by contradiction.
For any statement "p => p", and in our particular case "p => ~p". So we have a case where "(p => p) ^ (p => ~p)" This is the exact scenario of proof by contradiction.
A paradox is a contradiction, the difference you describe is form, don't let the self-referential form of the paradox fool you away from the obvious.
Just as a teaser, I'll give you another form of the paradox:
"Statement below is true.
Statement above is false."
Devil's Mind said:
And in my first comment, section (1):
Remember that: False=>p ^ False=>~p.
Or remember that:
p => q = ~p v q
which means that
False => q
= ~False v q
= True v q
= True
Ghaith said:
Even though paradoxical arguments can be arranged such that they are proven false by contradiction, I still don't think it's applicable to them. If paradoxes were false, they wouldn't be any different from other false statements, therefore having no need to coin the term 'paradox' in the first place.
Maybe this is what paradoxes are all about, they are arguments that lead to contradictions but are assumed or otherwise proven true. We can argue prepositions all day long but at the end of the day, a paradox is supposed to be a hole in logic and so logic cannot give a satisfying explanation to it.
The explanation that I personally find the most satisfying is that perhaps true paradoxes do not exist. Similar to your example about me moving at the speed of light, if somebody claims that "(A is True) ^ (A => False ^ True)" then either A is not really True or their (False ^ True) is not really a (False ^ True).
That's it! paradoxes are not false, they simply don't exist :)
Devil's Mind said:
I have to disagree. The word paradox is used loosely; that's to say, it has different meanings depending on context. So, I think we should address each "paradox" individually, without doing the fallacy of over-generalization.
Let me give an example: "Person X has balls, but he has no balls." This statement is usually refereed to as a pun. But it can be thought of as a linguistic paradox. On the surface it seems that we are asserting "A ^ ~A", but in reality the sentence should be interpreted as: "Person X has testicles, but he has no courage." Paradox solved!
Another example is the paradox of hedonism. The paradox states that if you set happiness as a life goal, and try hard to to achieve happiness, this would make you miserable. This paradox does not say that happiness does not exist, and it does not say that happiness is impossible. It does not say that happiness is not a worthwhile life goal, either. It is critical of the methodology of hedonism. It is a paradox of counter-productive behavior.
As an exercise that does not involve theology, try to think of (and maybe blog about) the autoinfanticide paradox and how it affects the possibility of time-travel as a philosophical plausibility. The paradox states that going back in time should be impossible, because a person might accidentally kill himself as an infant, or change events in a way that he would never get born (think of the butterfly effect here).
In conclusion, as I said paradoxes should be thought about on case by case basis, and being cautious of making generalizations.
Ghaith said:
These are some interesting points, thanks for sharing!
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