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? — Bartricks

You already discarded that old saw as logically impossible.

And, yes, an omnipotent being can, by definition, do anything logically possible.

And, yes, an omnipotent being can, by definition, do anything logically possible. — PoeticUniverse

Potentially, yes. The question is HOW do they do it...?

So god didn't create logic?

What if, instead of being constrained by logic or creating logic, God is identical in some sense with it, being Truth itself, or some such?

No, exactly what omnipotence involves is the issue under discussion. I am saying that it involves being able to do anything, not just the possible.

yes, that would be my view - an omnipotent being would be the arbiter of truth and thus would be capable of anything as what's possible and impossible is now constitutively determined by their will.

I think an omnipotent being would be the creator of logic and thus they would have control over what is logically possible. Thus such a being could do impossible things bexcuse their being impossible was itself determined by the being.

Right. Otherwise one would have to say that logic was primary to god and god has to obey it.

Surely being unable to do the impossible is a restriction? — Bartricks

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.

The question is based on the underlying assumption that reason should underlie of understanding of God. The Jewish God was conceived of in terms of his will. In Ecclesiastes and Job there is a struggle to understand God. Both fail. This marks the limits of human understanding. A willful God need not be a god that acts in accord with reason and logic.

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.

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? — Bartricks

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.

Logic isn't created. It is an expression of the connection/relation between two points in reality (truth).

That seems question begging in this context, for if omnipotence involves being able to determine what is or is not possible, then the logic would be created if, that is, an omnipotent being exists (or, alternatively, if we know in advance that logic is not created, we could then conclude that no omnipotent being exists).

It is not clear to me what your answer to the question is. Are you saying that omnipotence involves not being constrained by the laws of logic?

Hm, a square circle isn't nothing, rather it is an object that is both square and circular. Their existence seems to be impossible. But I think a truly omnipotent being would be able to create one, for nothing is impossible for a truly omnipotent being.

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. — Bartricks

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.

Hm, a square circle isn't nothing, rather it is an object that is both square and circular. — Bartricks

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.

I am not entirely sure what you're saying - are you saying that even if an omnipotent being were bound by logic, this would not be much of a bind, or are you saying that an omnipotent being is not bound by logic, or are you saying that logic, as it is, shows evidence of being the creation of an omnipotent being?

I am not entirely sure what you're saying - are you saying that even if an omnipotent being were bound by logic, this would not be much of a bind, or are you saying that an omnipotent being is not bound by logic, or are you saying that logic, as it is, shows evidence of being the creation of an omnipotent being? — Bartricks

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.

I still don't know what your answer is to the question. Can an omnipotent being make a square circle or not?

I still don't know what your answer is to the question. Can an omnipotent being make a square circle or not? — Bartricks

You are asking a question. On what grounds do you believe that this question is decidable?

You can't answer a question with a question.

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.

You can't answer a question with a question. — Bartricks

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.

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. — PoeticUniverse

OK, it's done. How do you think it looks?

That seems question begging in this context, for if omnipotence involves being able to determine what is or is not possible, then the logic would be created if, that is, an omnipotent being exists (or, alternatively, if we know in advance that logic is not created, we could then conclude that no omnipotent being exists). — Bartricks

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.

Hm, a square circle isn't nothing, rather it is an object that is both square and circular. Their existence seems to be impossible. But I think a truly omnipotent being would be able to create one, for nothing is impossible for a truly omnipotent being. — Bartricks

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.

A programmer can create a level he cannot complete, and then a cheat that enables him to complete it. In relation to the game-world, the programmer is omnipotent. Any constraints he may have are 'otherworldly'.

Fooloso4 It is not clear to me what your answer to the question is. Are you saying that omnipotence involves not being constrained by the laws of logic? — Bartricks

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?

How about an Albert Einsteinian answer. I'm not a scientist or mathematician, unqualified basically, but I've heard people talk of flatland. A 2 dimensional person can be trapped inside a closed square but, according to how I understand it, a 3 dimensional being can just jump over the sides of the square. In other words impossibility is relative. What is impossible for us may be possible in higher dimensions and God arguably must have access to all dimensions right?

I would have to say that in the situation of an omnipotent being, he would have the knowledge of how to change the universe in any way, but only through science, I believe he could control the process of chemical reactions and forces even unknown to us now, but I don't believe that he could break the fundamental laws of the universe just because he knows all.