Can an omnipotent being do anything?
Descartes famously answered 'yes'. That is, Descartes thought an omnipotent being could do literally anything at all - including making a stone heavier than he can lift, and lifting it and other apparently impossible things, such as creating oneself.
But many think that this is confused and that omnipotence actually involves be able to do anything logically possible (with perhaps a few more qualifications to boot). So, on this view an omnipotent being cannot, for example, create a stone heavier than he (an omnipotent being, that is) can lift, for that involves a contradiction and omnipotence does not involve being able to do the impossible.
I have to say, though, I am more sympathetic to Descartes' view. Surely being unable to do the impossible is a restriction? A being who is able to create stones too heavy for him to lift, and lift them, is surely more powerful than one who can't?
But many think that this is confused and that omnipotence actually involves be able to do anything logically possible (with perhaps a few more qualifications to boot). So, on this view an omnipotent being cannot, for example, create a stone heavier than he (an omnipotent being, that is) can lift, for that involves a contradiction and omnipotence does not involve being able to do the impossible.
I have to say, though, I am more sympathetic to Descartes' view. Surely being unable to do the impossible is a restriction? A being who is able to create stones too heavy for him to lift, and lift them, is surely more powerful than one who can't?
Comments (93)
You already discarded that old saw as logically impossible.
And, yes, an omnipotent being can, by definition, do anything logically possible.
Potentially, yes. The question is HOW do they do it...?
So god didn't create logic?
Right. Otherwise one would have to say that logic was primary to god and god has to obey it.
I think the problem with that is logical impossibilities such as square circles or whatever aren’t things - rather they’re “no-thing”. So what you’re really saying there is God is restricted by his inability to create nothing.
Much of Christianity, however, is informed by the idea of the compatibility of reason and revelation. In accord with this view, omniscience becomes logically problematic; as if God is constrained by reason.
Is this about the omnipotent being's abilities or our (human) abilities? There is no impossibility for an omnipotent being, not at any moment of such existence. Therefore, there could never be a time/moment when anything (a stone) is impossible (unable to lift). The premise is illogical and any conclusions in support of such can only express the deficiency in one's reasoning.
Question: Can an omnipotent being create a stone which he cannot lift?
Answer: SORRY, CANNOT COMPUTE. THE PREMISE DOES NOT CONFORM TO VALID LOGICAL PARAMETERS.
TLDR; It is a problem of logic as a tool.
You see, logic is not omnipotent. On the contrary, first-order logic is notoriously full of issues. You can easily say things in first-order logic language that are utmost paradoxical. (It is officially a "language")
For example, Richard's paradox (1905) created a serious problem in number theory. This paradox describes a number that cannot possibly have a decimal or other positional representation. The number is simply ineffable.
An even more famous example is Russell's paradox (1901). Does the set of all sets that do not contain themselves, contain itself? Both the answers "yes" and "no" are contradictory. This problem is known for causing the "foundational crisis" in mathematics.
At the beginning of the 20th century, they addressed the problem by hacking the axioms with several bug fixes that simply prevent you from expression the Russell sentence in set theory (Zermelo-Fränckel-Choice: ZFC). The axiom of restricted comprehension is specifically aimed at Russell's paradox:
This restriction is necessary to avoid Russell's paradox and its variants that accompany naive set theory with unrestricted comprehension.
In general, you can say that the axioms of regularity, pairing, and restricted comprehension are bug fixes to prevent you from asking questions that would throw ZFC into a tail spin.
This was the relatively stable situation in mathematics between 1908 (Zermelo's publication) and 1921 (Fränckel's late bug fixes). Was all of this bug fixing enough to solve all problems of that sort? No, not at all, and far from. The language itself causes problems too.
Gödel's incompleteness theorems (1931) are exactly about that problem. The language in which the typical mathematical theory is expressed, i.e. first-order logic, is full of issues, irrespective of what axioms you express in them.
You can trivially express Gödel sentences in first-order logic. Gödel sentences are yes/no questions that are not decidable from any theory. So, whatever theory you pick to try to solve your question, the theory will not be able to decide whether the answer to the question should be logically true or logically false.
That is how the entire field of computability came in to existence.
Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.
As a matter of fact, most problems have turned out to be undecidable:
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run.
It is a widespread misconception to believe that all problems would be decidable. The decidability of a question is, in fact, always the first question to consider. It is very, very naive and even ignorant to liberally assume decidability.
So far, I've made a circle with two sides, and I'm almost done with the third and fourth sides, and it will still be a circle, too.
No, it is an objection involving the limitations of knowledge itself.
With all knowledge necessarily constrained within the boundaries established by the Church-Turing thesis, on what grounds do you believe that your question would be decidable?
An answer is effectively calculable if its values can be found by some purely mechanical process.
With which purely mechanical process can your question be answered? If you cannot successfully propose such mechanical procedure, then the knowledge question must be declared undecidable.
Epistemology is about the existence of knowledge-justification methods. What method is it about? How do you know that the answer is within reach of the chosen method? Otherwise, the question can simply not be answered.
You are asking a question. On what grounds do you believe that this question is decidable?
I have made my position clear: I believe an omnipotent being would be able to do anything. And that's because I think an omnipotent being, to be truly omnipotent, would be able to make anything they want be true.
The first issue is always the decidability of the question. A good, historical example of an undecidable question is Russell's paradox:
Does the set of all sets that do not contain themselves, contain itself?
This question is undecidable. The bug fix was to make it impossible to ask this question in set theory (ZFC), by adding an axiom, i.e. restricted comprehension, that strictly prevents asking this question. That is how it was solved.
OK, it's done. How do you think it looks?
Again, logic isn't created, it is an expression of a relation between points of reality (truths). If something exists (in or as a reality), then logic is how we express that existence with respect to that reality. For example, in this argument's parameters, we have an omnipotent being who creates a stone (that can't be lifted). By definition, omnipotence implies absoluteness/ultimate. Therefore, such a stone could not exist because it would imply a certain degree of impotence (limitation) by the supposedly omnipotent (absolute) being. And that would not be logical because any impossibility with respect to an omnipotent being automatically negates the designation of omnipotence. Unless your 'omnipotence' has another significance which I'm not aware of and which allows a degree of impotence (because that's what you would be suggesting).
And before anyone argues that by the fact that he's an omnipotent being means it can do everything/anything including create such a stone, then I should remind them that absoluteness negates every/any relativity (limitation). Also, this omnipotent being would not be subject to human parameters of existence or interaction e.g. possibilities/probabilities and impossibilities/improbabilities. In this argument, the premise is beyond human parameters and we should adjust our reasons accordingly. This also means we have to analyse the significance of 'lift' in 'a stone that can't be lifted'. If we are not limiting the meaning to the human circumstances - which includes muscles, moving against gravity, etc - then, by creating anything we could just as well infer the fact of the power to lift it (more specifically, absolute power over all creations). Then, the supposed paradox becomes a matter of misrepresentation.
On the other hand, an omnipotent being can choose not to lift a stone but that's another story for another day.
And I’d say something that isn’t a possible thing is no-thing: impossible thing = impossible to be a thing = no thing = nothing.
But I think that may be beside the point, since God is omnipotent by virtue of the fact that everything that exists derives its being/powers from him. If a burning torch was the only logically possible thing that could exist then its being (which entails the powers to give heat and light) would be derived from God, who would be able to create them infinitely and so be all powerful. Or, come to think, I guess he would be omnipotent even if only one burning torch was the only logically possible thing that could be created - since all the power in existence would all the same be derived from him.
What I am saying is that how one answers the question depends on what assumptions one brings to the answer. Do logical limits point to the limits of what is possible or to limits of our thinking? Is a omnipotent being constrained by logical limits?
Logic is a formal language.
There is a mismatch in power between what we can say (formal language) and what we can solve (system). The solution in the development of set theory was to add constraints to restrict formal language as such to prevents particular questions from being asked. ZFC was extended with three "hacked" axioms for that. They have no other function than to restrict what can be asked. Still, the strategy ultimately failed because you can still do it (Gödel's incompleteness).
Well, I am only pointing to the history of "smartass" questions in mathematics.
After adding a rule to fix Bertrand Russell's "smartass" question, simply by making it impossible to ask (by introducing the axiom of restricted comprehension), another genius, Dmitry Mirimanoff, discovered a new way of asking "smartass" questions, because hey, "look, the system is full of bugs", and "look at this", and "look at that", and "Is this normal?", "Didn't I tell you so!?" ...
So, between 1917 and 1920, Mirimanoff published his endless rant, in a long series of articles, showing that there are "non-well-founded" sets that can cause all kinds of mischief in set theory. It is actually simple. The expression:
A = { A }
will easily cause havoc, because it means that you can replace A by { A }. Therefore:
A = {{ A }}
A = {{{ A }}}
A = {{{{ A }}}}
...
... ad nauseam ...
...
So, what did they do to get rid of Mirimanoff "smartass" questions?
Well, they (=Zermelo and Fränckel) introduced a new rule, titled "the axiom of regularity", which explicitly forbids asking this kind of "smartass" questions by making it impossible to do so. Problem solved.
Well, not really.
In 1928, Hilbert asked: If we forbid asking "smartass" questions, simply by outlawing them, can all yes/no questions be answered with a yes or a no?
Das Entscheidungsproblem. As late as 1930, Hilbert believed that there would be no such thing as an unsolvable problem.
In 1931, the first blow came with Kurt Gödel's incompleteness theorems. It is the language of logic itself that is the problem and that allows for asking "smartass" questions. So, fixing the system, by adding new rules, will not help. In 1936, Alan Turing and Alonzo Church then independently proved that a yes/no question is answerable only if there exists a purely mechanical procedure that can answer it.
Given the history of "smartass" questions in mathematics, and the 1936 conclusion, my position is:
I do not know of a purely mechanical procedure that can answer your yes/no question. Unless you can point out the existence of such procedure, your question must be deemed unanswerable.
Note: Computability, computation, and computer systems propel epistemology to the forefront. Knowledge-justification methods are truly key now.
Where is the purely mechanical procedure that would answer your question?
You see, a machine must be able to come to the same conclusion as you do. So, the very first part of the answer must consist in the description of an algorithm. I am just applying Alan Turing's and Alonzo Church's conclusions here, with regards to David Hilbert's question concerning the decidability of yes/no questions.
Reason says that to be maximally powerful is to be able to do anything. Reason says that if you can't do something - anything - then that's a restriction on your power. Therefore, a maximally powerful agent is not in any way restricted in what they can do. Thus, a maximally powerful agent is not bound by logic. They are the author of logic.
So, do you believe that Alan Turing's and Alonzo Church's answer to David Hilbert's question is not reasonable? On what grounds would you then believe that?
We're talking at different levels. my question is about whether or not an omnipotent agent would have control over logic. What you're doing is talking about the content of logic. What you're talking about it is irrelevant. Whatever you say about the content of logic, my point is that an omnipotent being isn't bound by it.
If you say no question can be given a yes/no answer, the omnipotent being can give you a definitive answer to any question you ask. And so on.
If an omnipotent being created a stone they could not lift, and then created a means to lift it, it would no longer be a stone they could not lift, and therefore not impossible. An omnipotent being has the capacity to make anything possible - even what is considered impossible from a certain perspective.
Wouldn’t any constraints on this being then be irrelevant to what is created?
Well, everything you are saying, is simply not decidable, unless you manage to point out a purely mechanical procedure that calculates your conclusion as its conclusion.
This requirement is simply part of the limitations of formal knowledge. You have never demonstrated that your yes/no question would fall within the boundaries of Turing-complete decidability/computability. If you do not demonstrate this convincingly, the only conclusion left, is that it falls outside these boundaries, and that formal knowledge-justification methods cannot reach it.
I am pointing out the issue of the addressability of the question. You seem to have pre-1936 views on this matter. Unlike what you seem to believe, disregarding the entire issue of decidability/computability will not help solving your question.
By the way, I am not answering Russell's and Mirimanoff's questions either. These problems were not solved by answering the question but by declaring them unanswerable.
Yes indeed, that is my point. From the POV of the game-world character, the fact that the programmer needs a comfort break. or occasionally cannot work out what will happen if he inserts this code, does not limit him, because he can always wind things back and do things over in another way until [s]it goes just as he wants[/s] He sees that it is good. his potency over the game world is unconstrained even by the limits of the computer, because that will affect the speed the game runs globally but will be unnoticable to the game characters. Even the logic of the computer does not constrain the physics of the game.
That is one concept of logic, but certainly not the only one.
Quoting Bartricks
Yes, omnipotence has, as the term indicates, to do with power. But the question is whether logical constraints are a limit on power, whether a logical contradiction limits what is possible or merely limits our understanding of what is possible.
Quoting Bartricks
And so, the paradox has to do with logic and not just power.
Yes, agreed.
It is a formal language along with transformation/rewrite/inference rules. The EBNF grammar of a particular language of logic does not capture its rewrite rules, but can/must be used to express them. So, a logic is indeed a complete formal system. There are, of course, numerous variants of different expressive power.
Still, the problem of computability/decidability is not caused by these inference/rewrite rules. These rules are just axioms, while it gradually (historically) became clear it is not the axioms causing (or solving) the problems. They are caused by the excessive, expressive power of universal quantifiers; which is a language problem.
The case is analogous to mathematics. There are fundamentally different views of their ontology. And, of course, there are different views of the ontology of language and thought. Are thinking and being the same? Is the logos a human activity or fundamental to being? Is it merely a human invention that attempts to give an account of what is or is it that which shapes and determines what is? That is, is logic merely descriptive or causal in the Aristotelian sense?
[Added: That is, the logos is regarded by some as an active, organizing principle that is prior to and and make possible formal languages and make possible the connection between thinking and being.]
I will not attempt to answer these questions, for any answer is based on certain assumptions that are not held in common by those who offer a contrary view.
Well, yes, the ontology of logic and of mathematics are up in the air, and will probably remain so for the foreseeable future.
I was only referring to what causes the problem of undecidable questions in logic. According to Gödel incompleteness theorems, they are not caused by the axioms, or lack of axioms, and cannot be fixed by the axioms (including the axiomatic inference rules).
It is the language of logic itself that causes the issue. It occurs when propositional logic gets extended to first-order logic, by adding existential quantifiers. The decidability damage is caused by introducing just two symbols: ? and ?.
I regard the paradox as a pseudo-problem since an omnipotent being is a hypothetical, but I do not think the problem of logical contradiction here is a language problem. I do, however, think the problem is compounded when one attempts to solve it on the basis of an abstract symbolic system.
This is good, as a circle perpendicular to the 2D square, like a rainbow.
Here is my 4-sided circle: O.
Sides one and two are the inside and the outside; sides three and four are the perpendicular top side and bottom side.
I also made an infinitely sided polygon circle: O.
The Creator of the real, physical world cannot be existentially contained in it. So, it is not a question of about the real, physical world. The question then becomes: Can human knowledge even reach outside the universe in order to answer questions about what we would observe there?
Furthermore, how are we supposed to ascertain that any purported answer really is the answer? We cannot try to inspect anything outside the universe. This objection would indeed involve the semantics of the question. But then again, if there are already syntactic issues, why even involve semantics?
Quoting Fooloso4
Yes, the abstract symbolic system will already fail on the bureaucracy of formalisms involved. They have limitations which prevent us from answering a whole range of questions about abstract, Platonic worlds, i.e. mathematical ones. Inasmuch as theories about the real, physical world -- in this case, even outside its boundaries -- make use of this bureaucracy of formalisms in order to maintain their own consistency, they will also start failing.
That is why the question, "Is it uberhaupt possible to address that kind of questions?", will automatically get propelled to the forefront. I wonder how anybody could take decidability/computability for granted, knowing that there is an entire field of investigation about just that issue?
Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.
This entire field would not even exist, if all possible questions were solvable ...
Some hold that there is only God and God's manifestations.
Quoting alcontali
It is a question of whether an omnipotent being exists. The question takes it as a given, even if only for the sake of the argument, that such a being exists. That is not a question that is reducible to the physical world, but it is also not a question for which we have a common agreed upon answer. Hence, it is a pseudo-problem about a hypothetical.
Quoting alcontali
I would frame it differently: can a being that is not omnipotent comprehend a being that is? This leaves open the question of whether an omnipotent being exists as well as the question of the limits of the "real" world.
The point, though, is that an omnipotent being would have to be the author of logic. That is incompatible with some concepts of logic. Well, either those concepts are the ones that have something answering to them -in which case we can conclude that no omnipotent being exists - or we have good evidence that an omnipotent being exists, in which case we can conclude that the alternative concepts do not have anything answering to them.
So we can learn something about the nature of logic from this kind of inquiry.
One could base a logic on such an assumption, but to require logic to conform to such an assumption is not something many of us would support.
Quoting Bartricks
Okay, but we do not know what such a logic would look like. Do we? How would this logic resolve the problem of contradiction?
Quoting Bartricks
The logical problem exists whether such a being exists or is simply posited.
Quoting Bartricks
I do not think that what you come away with from this inquiry is the same as what regard the problem to be. I do not think the problem is with logic, but rather what one expects from it.
Do you have such a demonstration?
Quoting Bartricks
Well, I think we can agree that logic exists in some form or other. If we accept a logic that forbids contradiction then we must then address the contradiction or apparent contradiction present in the paradox.
You posit an imaged God-given logic without saying how it resolves the paradox.
I have never said that I think that your answer is false. I am saying that I am absolutely sure that your answer is not even false.
1. If God can perform both actions in the boulder paradox, then he is omnipotent.
2. God can perform both actions in the boulder paradox.
3. Therefore, God is omnipotent. (1,2 MP)
It seems that you want to find this argument to be true because accepting anything otherwise would make God incapable of certain abilities, and therefore fail in the category of omnipotence (as per your definition of omnipotence), which could potentially discredit his Godlike nature.
However, Descartes’ argument nonetheless seems ridiculous. So in order to make sense of that, you offer the following modus ponens argument:
1. If God can do anything logically possible, then he is omnipotent.
2. God can do anything logically possible.
3. Therefore, God is omnipotent. (1,2 MP)
This argument seems to be the more relevant view of what you are trying to decipher. So I will make my objection in terms of this modus ponens argument.
The key issue here is your definition of omnipotence. You seem to have a good attempt to define it, but it falls short for the following reason. I object to premise 2, that God can do anything logically possible. My modus tollens argument is as follows:
1. If God can do anything logically possible, then he is omnipotent.
2. There are some logically possible things that God can’t do.
3. Therefore, God is not omnipotent.
There are some logical possibilities that God cannot do. An example of this would be lying. Lying is objectively logically possible. But God cannot lie, because it goes against his nature. Therefore, that presents a contradiction. A similar example would be the logical possibility of making a mistake – God can’t do this either.
So it seems that you need to redefine omnipotence. In my argument, my conclusion claims, “Therefore, God is not omnipotent,” only in terms of your definition of omnipotence, specifically, that an omnipotent being can do anything logically possible. I would also like to accept that God is omnipotent. But to do this, you need to redefine omnipotence, not just using the ability do any logically possible things as the basis for the definition. It’s more than just logical possibility.
For example, you can maintain the claim that God is omnipotent if you alter the antecedent in your original premise to “God can do anything that is logically possible for God.” This narrows the scope of what is logically possible to whatever is both logically possible in general and what does not contradict God’s nature (e.g., lying, erring).
A final important note – The fact that there are logically possible things that God cannot do does not undermine him as God. We wouldn’t want him to lie or make a mistake. So the fact that he is unable to do some of these logically possible things is actually a good thing, as it preserves his good nature.
Imagine a person who can do anything logically possible. Well, that person has a lot of power, to be sure. But they do not have as much as one who can also do the logically impossible. So I think true omnipotence involves the latter.
Yep, agreed!
By definition, it assumes that a Deity can do or be, both logical and illogical or possible and impossible things.
Those unresolved paradox's are clues to the probability of that description or idea, and can be reasonably inferred as such. Good points!!
What escapes me is why people who ask that kind of questions stubbornly refuse to learn from the history of Russell's paradox.
1) They are incredibly ignorant but they always know everything better.
2) They draw utterly dumb conclusions about religion.
Some people are simply beyond repair ...
Yep, I agree. Everything else is changing the definition of omnipotent (adding "limits" to something that is, by definition, "unlimited").
Quoting philorelkook
Ideas like this suggest that the "omnipotent" being under discussion has no will. Why can't an all-powerful being be wrong? Don't we need to include "all knowing" before that is an issue? Even all-knowing, couldn't it choose to be wrong?
Also when you mention "his nature" you are claiming much more knowledge of god than I think belongs in this discussion - I think many of the people involved in this thread are agnostic or atheist, and most religious people will disagree on god's "nature" (I am not saying you are wrong, just that what you are describing is a whole 'nother debate).
Also, isn't the concept of "omnipotence" in religion the result of the thousands of years of an arms race that claimed "my god is more powerful than yours"? Well if "your" god is limited by logic and having to tell the truth, then "my" god is more powerful.
Quoting BrianW
How exactly do you mean this? I view the idea of an omnipotent being as problematic, but if the premise starts with the omnipotent being existing, I don't see a problem with the rest?
It seems that you are giving an argument similar to the one as follows:
1. If God is truly omnipotent, then God must be able to successfully perform both the logically possible and the logically impossible.
2. God is omnipotent.
3. Therefore, God must be able to successfully perform both the logically possible and the logically impossible.
While this argument is valid in form, I do not think this argument is sound because of premise 1. I think we both agree with premise 2 that God is omnipotent, but I think our definition of what "omnipotence" means and looks like for God are different.
I think this difference comes from your abuse of the term "logically impossible." It is clear that you argue that a being who can do both the logically possible as well as the logically impossible is more powerful and omnipotent than a being who cannot. However, I think that to say that God cannot perform the logically impossible is not infringing on His omnipotence.
The definition of "logically impossible" is something that is contradictory or contrary to the laws of logic, such as a round square or a tall man not being tall. Your misuse of the term is seen when you claim that an omnipotent being can create a stone so heavy that it cannot lift it and then proceed to lift it, because if it can lift the stone then the stone was not too heavy for the being to lift it after all, and thus would fall into the realm of "logically possible" rather than "logically impossible," because logical impossibilities simply cannot exist. Logical impossibility infers that one cannot perform both action "x" and action "not x." Thus, God could not create a stone so heavy that He could not lift it and then lift it because it would be logically impossible, e.g. performing both "x" and "not x."
On another point that I will not dive too deeply into but think is worthy of bringing to light, do we even want to say that God can perform logical impossibilities? I think not, as this would have absurd implications, such as God being able to be both maximally just and unjust, loving and not loving, omnipotent and not omnipotent, etc.
In conclusion, I think what you are arguing to be unsound due to the misuse of the term "logically impossible," for it is not infringing upon the omnipotence of God to say that what is logically impossible, i.e. what is contradictory and therefore cannot occur, exist, or be done, cannot be done by God; if it could be done by God, then it would not be impossible but rather possible, because logical impossibilities cannot exist.
So rather having God be something like this:
1. If God is an omniscient being that can do anything, he should be able to make a stone heavier than he can lift.
2. God cannot make a stone heavier than he can lift.
3. God is not an omniscient being that can do anything.
I would argue for it to go more like this:
1. If God is an omniscient being, he is infinitely powerful to do anything that is possible/doable.
2. God cannot make a stone heavier than he can lift.
a. But there is no being that can exist that can do this task as it is impossible for any being to make a stone heavier than it can lift.
3. God is still an omniscient being.
God as an omniscient being that has created this universe, including what is possible and impossible, would also have to abide by the rules he set for the universe. I also believe that God would be able to do the impossible outside the realms of this universe, but it will in be in ways where we cannot comprehend because we are beings that live and die by the rules of this universe.
My understanding of the “being unable to do the impossible” argument is a little different. I understand the argument as something like this:
If God has perfect qualities, God does not fail.
If God does not fail, God’s actions necessarily do not cause God’s failure.
If God has perfect qualities, God’s actions necessarily do not cause God’s failure. (1,2 MP)
God has perfect qualities.
God’s actions necessarily do not cause God’s failure. (3, 4 MP)
If we apply this argument to the boulder case (or the Jesus microwaving a burrito case as so many memes have been parodying recently), it implies that God cannot create a boulder that God cannot lift. It is impossible not simply on a logical basis, that being that an omnipotent being cannot create something it cannot lift. God cannot perform the action of creating the boulder because God’s actions cannot cause God to fail because that jeopardizes God’s other perfect qualities.
I do not have to conclude that God is not omnipotent; I have to shift my understanding of omnipotence. Omnipotence means God can do all things except the one thing that would jeopardize God’s perfection: fail. If God could do all impossible, it seems like argument would allow for God to do other impossible things. What other things might we initially consider impossible for God? Considering God’s perfect nature and qualities, we could imagine it is impossible for God to not know something. It is impossible for God to kill God’s self. It is impossible for God to sin. Are we okay with saying that God can be perfect, in the sense that God cannot sin, and still say God is entirely capable of sinning despite God’s perfectly good nature? That might imply that God is only arbitrarily good, which seems like a very unsatisfactory conclusion for theists. I am content to view God as incapable of imperfection, of failure. Here is a potential argument that may come from the “God can do the impossible” train of thought:
God is perfectly good (in the sense that all of God’s qualities necessitate perfect goodness).
If God is perfectly good, then it is impossible for God to commit evil.
It is impossible for God to commit evil. (1, 2 MP)
God can do the impossible.
God can commit evil. (inferred from 3, 4)
If someone wanted to object to say that that gives humanity an ability that God does not have, I would say “I sure hope so! I can envy and lie and cheat and all manner of evil things if I am not trying to live a good life.” All of those things lead to my failure to be a perfect being. God is a perfect being. God cannot fail. If God could do the impossible, God could do all manner of things that contradict his perfect qualities.
You say, “But they (one “who can do anything logically possible”) do not have as much [power] as one who can also do the logically impossible.”
First, I would like to clarify the definition of logical impossibility. This doesn’t mean just anything that would seem illogical to achieve — for example, me eating ice cream before working out might seem illogical. But when we refer to logical possibility, we really mean anything that does not cause a logical contradiction to properly think of it. For example, claiming that both “P” and “not P” are true at the same time and in the same way would be a logical contradiction. Another example would be asking someone to think of a square circle. These contradictions are instances of logical impossibilities.
So referring back to your claim, then, that a being that could do the logically impossible has more power than one that cannot, is in and of itself a contradiction. By definition, what is logically impossible is that which one cannot do (my first and second premises below). There is no reason to think omnipotent beings are not included in this (my fourth premise below). So when you assert that there is a being that can do something which, by definition, no one can do, I think it fails to grasp the definition of omnipotence correctly.
My argument takes the following form:
1. If a being can do the logically impossible, then that being can make a contradiction true.
2. No one can make a contradiction true.
3. Therefore, no one can do the logically impossible (1, 2 MT).
4. An omnipotent being is someone.
5. Therefore, an omnipotent being cannot do the logically impossible (3, 4, MP).
So since no one can do the logically impossible, then it is not a decrease in anyone’s power to not be able to do the logically impossible. So, an omnipotent being still maintains the highest possible level of power without being able to do the logically impossible. Because there is no contradiction between an omnipotent being and a being that cannot do the logically impossible, then, I think your argument, and your conclusions regarding Descartes’ paradox, fail to succeed.
I believe the boulder case does not depend on whether God can or cannot create the heavy stone but the argument merely focuses on a dilemma where either choice tries to convince you that God is not omnipotent. Probably, the flaw is in the premise itself, which defines God as not omnipotent if God cannot create such a stone.
Moreover, the definition of omnipotence plays a big role in each's perspective. As God who has infinite power can create infinitely heavy stone and has infinite strength to lift the stone.
I think, our definition of omnipotence in terms of a deity goes beyond logical and illogical possibilities as God is not bounded by these limits.
1. Either god can create a stone so heavy that God cannot lift, or God cannot create such a stone
2. If God can create such a stone, then God is not omnipotent
3. If God cannot create such a stone, then God is not omnipotent
4.Omnipotence is not bounded by human's logic
5. We cannot know whether God is omnipotent or not
It seems to me that what you're doing is treating the idea of 'logical impossibility' as synonymous with the idea of 'something no-one can do'. However, for something to be 'logically impossible' is for it to be inconsistent with the laws of logic. My point is that those are not equivalent - that being an act that is inconsistent with the laws of logic is not one and the same as it being an act that no-one can do.
For example, as you yourself note, it is a basic law of logic that no proposition can be true and false at the same time (the law of non-contradiction). And thus making a proposition true and false at the same time is logically impossible, but that does not necessarily mean that it is not possible for someone to do it. If they did it, their act would violate the laws of logic. But it would still be something they did.
To illustrate, consider this proposition: "What I am saying now is false". Well, that proposition is true if it is false, and false if it is true. In creating that proposition, then, I seem to have done something that violates the law of non-contradiction. Creating that proposition was something I did. Yet what I did - if I did what I seem to have done - violates the law of non-contradiction because the proposition I created is both true and false at the same time (precisely what the law forbids).
I myself seem to be a counter-example to 2, then. And as what I just did anyone can do, we can all violate the laws of logic - we can all do something that is logically impossible, namely create propositions that are true and false at the same time.
Now, perhaps I did not violate a basic law of logic in creating that proposition. There's a debate to be had about that. The point is just that being logically impossible does not seem to be one and the same as being something no-one can do.
This is reasonable. But it suggests an understanding of "omnipotent" that I don't think we can ever have. Omnipotence is like saying black holes have INFINITE density. It means something in the abstract, that doesn't match reality. Why can't it be perfectly possible for an omnipotent being to do ANYTHING? Even if it contradicts physics, or logic, or human language...so what?
I will agree with @Bartricks on this one.
If it can be done then it is possible. So what you are saying just amounts to saying that an omnipotent being can (in some unfathomable way) do things which are, by our limited definitions, impossible.
An omnipotent being could, for example, according to your argument, create an object that is both black all over and white all over, or even every possible colour (as well as all the impossible ones) all over.
It's just silly vacuous nonsense, in other words.
What/who is 'one' ... (X)? OP's question fits under the hypothetical that omnipotent being exists.
Let's let X represent: 'omnipotent being' and as used in the OP.
If X denotes an 'omnipotent' being that exists,
If X denotes that such 'being' belongs to existence,
If X denotes that such a being has the power to do any thing at all.
Than it will follow that, X being does any thing at all, and this 'any thing at all' will be unique to such a being and detectable without in depth knowledge of 'how it works' because there is no such thing as X being capable of doing 'no such thing.' (Non-omnipresence, non-existence, etc..)
If X is not doing 'anything at all' .. then it follows that X cannot do 'anything at all' .. and X is not omnipotent and does not exist. So it seems clear to me that X cannot do anything at all, because it does not exist.
"How" he does any thing at all is not readily apparent how that is at all relevant. Thoughts?
My point was that if you had a clear understanding of how X does things, of what is involved in the doing, then you could determine whether or not such a thing was done or could be done, regardless of whether you were aware that it has been done.
But we don’t have any idea how X would do anything at all, let alone do things that we are unaware of. All we can do is assume based on what we are aware of that has been done, and how we might do things that we are unaware of being done.
FWIW, I don’t think X exists either, but I do think the potential to do anything at all exists. It’s just not a being.
But instead: How can anyone have a 'clear understanding' of any thing X does, if X has not done any thing at all, and because X does not do any thing at all, does not exist.
Your question of "how" being a relevant question does make sense to me. Demonstrating/knowledge that an omnipotent being cannot do anything at all does not require it to exist.
Quoting Possibility
This is a concern for after the fact: ... in the case of X, first, doing any thing at all. X cannot do any thing at all, so it is not at all (currently) necessary to have a 'clear understanding' about how X does any thing at all.
I am aware X cannot do any thing at all, and also (know) such because X does not do any thing at all, because there is "no such thing" of 'nothing that X cannot do'.
Quoting Possibility
Sure we do.
Quoting Possibility
What exactly are we 'assuming' if not all things 'possible' > any thing at all.. and 'known' things, that X should be knowingly doing.
Quoting Possibility
...? Sorry I'm not following.
'Potential' implying a probable, by necessary existing attributes = belong to existence ... "any thing at all..." including, every thing at all, correct?
If it's just a possible you're talking about, I'm not sure what point you're trying to make.
It's the same to say: "The possible is impossible." It's a trick language doesn't do.
It may be possible for an omnipotent being to do the impossible. But it's not possible for us to talk about it.
Potential: anything that can happen
Probable: anything that is likely to happen
Most discussions like this fail to make the distinction between potentiality and possibility. To actually do something, one needs to be aware (although not necessarily conscious of that awareness) that the something can be done.
There are plenty of things we can think of that we say cannot be done, because we are unaware of any potential for it to be done. We often say these are ‘impossible’ - but sometimes what we once thought impossible we soon discover to be possible. So in reality it was always possible, but we were only unaware of the potential.
One doesn’t have to do anything to be considered omnipotent - it only requires the potential. And you can only prove potential after the fact, so one cannot actually be omnipotent until everything is already achieved. So the concept of an ‘omnipotent being’ is a subjective perception at best, and in my view can only refer to the potential of the unfolding universe itself, of which we are a part.
So "potentiality" denotes any necessary existing attributes present & unique to X (omnipotent being), correct?
Quoting Possibility
I disagree. Any thing 'possible' is not just 'possible' because we imagined them to be so. Any thing 'possible' is 'all things possible.'
I can’t say I agree with that interpretation. I don’t believe an ‘omnipotent being’ exists to present unique attributes, let alone necessary ones.
Quoting Swan
You can’t clarify the meaning of a term by applying the term.
Well, I don't know then. We don't really have to agree/disagree with each other. I have nothing else to say.
In asking, “Can an omnipotent being do anything?” you side with Descartes’ view and argue that an omnipotent being can truly do anything at all, regardless of logical possibility. I have outlined your argument below:
If God is omnipotent, then He can do anything at all without regard to logical possibility.
God is omnipotent.
God can do anything at all without regard to logical possibility.
Although I do agree that omnipotence grants God a wide range of power that is otherwise unattainable to other beings, I would disagree with the argument that an omnipotent being can do anything, namely disagreeing with the first Premise of the outlined argument. I would argue that logical possibility is the greatest, and only, limit on the omnipotence of God.
For example, many incompatibilities exist within aspects of our world, such as the creation of a square circle or a married bachelor. Based on their definitions, a circle cannot have corners like a square and a bachelor cannot be married. These examples are simply things that God cannot create because they are logically impossible. Now you may argue that these definitions are merely constructs we have developed as a society to help us perceive the world around us and that God, being omnipotent, may have the power to create what, in our minds, would be impossible. To this, I would argue that God, also being omnibenevolent, would create a world we could comprehend, one that does not contain impossibilities by definition like that of a square circle. For, if God created a world like that, we would have a much harder time understanding the world we live in and an even greater struggle conceptualizing God. God’s creation of a world we can understand allows us to spend more time discussing the relevance of its creation.
Cases like God creating a stone heavier than He can lift also poses a logical impossibility. God’s omnipotence cannot be tested against two infinitives. To create a stone that has infinite weight and for God to have infinite strength cannot be compared as different amounts of infinity cannot be compared. It’s wrong to say that a being could be “able to create stones too heavy for him to lift, and then lift them” because if God created a stone that was too heavy for Him to lift, then He would not be able to lift it. As a result, comparisons of infinite value pose a logical impossibility of the omnipotence of God yet do not devalue His omnipotence.
Finally, regarding God’s creation of himself, I think it is safe to say that this is not a question of omnipotence. I would like to say that God has existed limitlessly throughout time, never requiring the necessity to be created, to begin with. This, as a result, would not require any omnipotent powers to lend to His creation although, this may be a personal preference in questioning how God has existed throughout time.
As a result, I do not believe God's omnipotence can do the logically impossible. This is based on impossibilities such as incompatible definitions we have created and the comparison of infinite values.
My argument was that a being who is not constrained by the laws of logic is more powerful than one who is. As there can be no one morepowerful than an omnipotent being, an omnipotent being is not going to be constrained by the laws of logic. Thus, an omnipotent being can do absolutely anything and not just the logically possible.
Again, a being who can do the impossible and the possible is more powerful than one who can do only the latter. The latter is constrained, the former is not.
You then say I said that logic is a social construction. No, that is absolutely not my view and you won't find it expressed in anything I have said.
Logic is robustly external in that there is nothing we can do to alter it.
Logic must be determined by an omnipotent being for that is the only way a being would not be constrained by it. Logic, then, is internal to them.
So far from being a social construction, logic is a divine construction. What is or is not possible is determined not by me or you or some group of us, but by a person, Reason, who by dint of this is omnipotent.
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And as for God creating himself - well, it is more impressive to have created oneself than not done so. Thus God has created himself. And if God existed of necessity - as you are claiming - then God would not be omnipotent for he would lack the power not to exist. God is omnipotent and thus has the power not to exist which in turn entails that he exists contingently.