God and the paradox of the stone

[Javi]

INTRODUCTION.

The Paradox of the Stone is a type of omnipotence paradox. Omnipotence paradoxes try to demonstrate that the idea of omnipotence results in contradictions, so implying that omnipotence is logically impossible. Consequently, the existence of omnipotent entities, such as God, is also logically impossible. In this context, omnipotence implies the ability to perform every act that is theoretically possible.

The Paradox.

The Paradox of the Stone is often presented as the following question:

Can God create a stone so heavy that He cannot lift it?

The paradox examines two possible answers:

1. Yes: If God can create such a stone, then He would not be omnipotent, as He would lack the ability to lift it.
2. No: If God cannot create such a stone, then He would not be omnipotent, as He would lack the ability to create it.

How to address this paradox.

I read intriguing comments and solutions to this paradox on the Internet. These are the two that I liked the most:

A Quick Solution To The Paradox of The Stone by Benjamin Tettü.

In my opinion, the simplest and most effective response to this paradox is to answer “No.” Although this may initially seem to limit God’s power, it actually reaffirms His omnipotence. By answering “No,” one is not actually saying that God lacks any power, instead, one is simply asserting that there is no such stone so heavy that God cannot lift it. It’s just saying that, in the set of possible stones, there is no stone that God can’t lift. This is because God, being omnipotent and therefore not constrained by any physical law, can lift any stone regardless of its weight.
Thus, saying “No” does not imply any limitation on God’s power. The “inability” to create a stone too heavy to lift is not a weakness but a necessary consequence of being omnipotent.

Aquinas:

It remains therefore, that God is called omnipotent because he can do all things that are possible absolutely; which is the second way of saying that a thing is possible. For a thing is said to be possible or impossible absolutely, according to relation in which the very terms stand to one another, possible if the predicate is not compatible with the subject; and absolutely impossible when the predicate is altogether incompatible with the subject, as for instance, that a man is a donkey.

Perhaps Aquinas is addressing this paradox out of the principal point. Yes, I understand what he meant: God is the subject and omnipotence the predicate. So, since these are compatible with each other, the paradox of the stone is resolved.

On the other hand, God is omnipotent, not bound by logic. So, it is not contradictory to say that yes, God can make such a rock. And yes, God can lift it. Perhaps this is another way to address it—using theology and not logic (philosophy).

In other words, I think I would use the argument of “God isn’t limited by logic” and sort out everything related to this. However, what if this paradox is a limitation of our language and not the being of God?

I know this an old and well-known debate. Some argue that this cannot be addressed using philosophy but theology. Others actually do an effort using logic. For example, I like this solution:

Yes, he can create such a rock, but because he doesn’t there’s nothing he can’t do. - Michael in the old TPF.

A further reading that I recommend is this paper by Jacek Wojtysiak: The Paradox of the stone and two concepts of omnipotence.

What is your take on all of this? I’m reading you!

[questioner]

@Javi

What is your take on all of this?

Well, of course, it’s not really about stones, but about the incoherence in the idea of omnipotence. I wonder if they who do say that God is omnipotent begin with that conclusion and craft their support of it to fit the conclusion.

The question of the omnipotence of God is often invoked in matters questioning human suffering. If God is omnipotent, why does he allow suffering? And then, if one does believe God is omnipotent, they are more likely to put their trust in him, believing that ultimately justice will prevail.

A scientific pantheist would say that the entire question is misframed, because God is not a supernatural being with individual will, but rather divinity consists in all existence in the universe. The universe does not have “power” but “process.” God is no more omnipotent than are matter, energy, space or time – all of it is “God” – operating within the constraint of physical laws.

The universe has no moral intentions. Human suffering is not controlled by some outside, supernatural choice. We are all liable to natural conditions. Our attention is best put on how we as humans respond to them.

[Javi]

Hello, questioner. Thank you so much for your reply.

Hmm, addressing the paradox of omnipotence is more complex than I thought at the beginning. I have read interesting arguments on both sides. It seemed to be a question to “prove Christianity wrong,” but it turned out to motivate theologians to argue about the existence of God with more emphasis.

I agree with you that God is not more omnipotent than are matter, energy, space or time, and perhaps this is God altogether.

However, I want to share with you an intriguing example that I watched a few days ago, and it is proposed by Alex O’Connor:

Imagine you are holding a glass by your hand; the hand works because it is held by your arm; and your arm is held by the shoulder; and finally, the shoulder works because it is held by the three bones. Therefore, something very simplistic like holding a glass of water entails a complex-mechanistic set.

Now, who or what is holding everything up the same way we do with our glass of water?

I’m in favor of omnipotence for this reason—perhaps God made a set of physical laws that work in our world, but he is out of them. Gravity, weight, space, etc. are concepts of how we understand the world we live in, but it is unnecessary to try to apply them to God as well.

Let’s say He can create a very heavy stone, but why does He need to lift it? Are we trying to reflect on God our weaknesses?

[questioner]

@Javi

Imagine you are holding a glass by your hand; the hand works because it is held by your arm; and your arm is held by the shoulder; and finally, the shoulder works because it is held by the three bones. Therefore, something very simplistic like holding a glass of water entails a complex-mechanistic set.

Now, who or what is holding everything up the same way we do with our glass of water?

That’s very interesting. But if we are asking “what is holding everything up?” - I’m not sure that an omnipotence needs to be ascribed to that. The concept of omnipotence suggest a “will” and that is where I get hung up on the problem. I do not believe there is a supernatural will controlling the events of the universe.

[AlveK]

So, I think omnipotence is defined in two ways, and even if those two definitions are equivalent, there is value in differentiating them for the sake of analysis, and then deriving if and when they are equivalent. And when they aren’t, there’s some further exploration to do. So, here’s the two definitions:

1. Omnipotence is the power to do anything.
2. Omnipotence is the power to do anything that is logically possible.

The first definition seems to capture the spirit of the notion of omnipotence best, because it places absolutely no constraints on the power.

It seems obvious that we can expand the first definition to be that omnipotence is the power to do anything, even if that thing brings forth a logical contradiction. I think this point is subtler than that, however. As such, I think we can divide this situation into a 2-by-2 matrix, where we look at all possible combinations of possibilities. Then I will explore each.

QUADRANT 1:

Quadrant 1 gives us two things. An utterly unlimited power for God, and the somewhat problematic idea that he can create contradictions.

In this quadrant, God could create a bachelor who’s married, and he could create an apple that is red all over, and also green all over. But, could he create the stone so heavy he could not lift it?

Well, if you are a classical logician, the stone scenario isn’t special. One contradiction implies all propositions, by the Principle of Explosion. So, God does not need to create the stone in order to contradict his own omnipotence. If he uses his omnipotence to create any contradiction whatsoever, reality would collapse into trivialism, and all propositions would be true, including the proposition that “God is omnipotent”, and “God is not omnipotent”.

And I think this leads into one of the principal objections to this whole problem. Some people subscribing to Quadrant 1 say that although God can create contradictions, he never will! They would say that a merely potential contradiction is not a contradiction at all.

Or, they would say that a potential contradiction is a contradiction… but that there are no potential contradictions, because God’s word is absolute. If God has decided that he never will bring forth contradictions, and he decided this at the start of reality, then God has used his own omnipotence to limit the possibilities of his omnipotence to exist safely within the bounds of non-contradiction. This does not restrict God’s omnipotence in an absolute sense, because self-imposed absolute restriction is not a proof of lack of omnipotence. To say otherwise would be to say that God being omnipotent and God being perfectly Good are logically contradictory, because God’s omnipotence means he must be capable of doing evil, but God’s perfect Goodness means he never will do evil: therefore, he cannot be omnipotent, using this reasoning.

So, if you are in Quadrant 1, and you uphold the Principle of Explosion, then you’ve got some options. You could say that a merely potential contradiction is not a contradiction, and so poses no issue. If you do that, you get to avoid actually committing to the claim above regarding what God won’t do, but in turn, you must commit to something else metaphysically (which might be fine, I haven’t thought too deeply about it), AND you also leave the door open to reality collapsing into trivialism at any point, because God may suddenly decide he wants a challenge at the rock-lifting gym.

…But what if you don’t uphold the Principle of Explosion? Well, then, you could still just say that God will never create contradictions (and thus never create the stone he cannot lift), but the argument for it is a bit weaker. If you believe that God creating a contradiction would make all of reality collapse into trivialism, that definitely seems like a not-good action, and most theists would therefore be able to prove from their axioms that God would never do that. It is not controversial to believe that God would not want a trivialist reality.

But if the principle is not true, then God can create a contradiction with no reality-collapsing consequences. And then, it is harder to argue that he never would… And also, in this scenario, since contradictions do not imply everything, then there is a material difference between the stone scenario, and other contradictions. Perhaps God may choose to create contradictions, sometimes. But would the stone scenario be one of the contradictions he never will create?

My point here is that Quadrant 1 gets a lot more complicated when you don’t have the Principle of Explosion. And I think all this has been a sufficient first analysis of Quadrant 1, so I’ll go to the next.

QUADRANT 2:

So this one is weird and tricky. It is the combination of the second definition with the claim that God… can create contradictions. That is tantamount to saying that contradictions are logically possible.

Now, most of us would agree that reality is not in a state of trivialism, so anyone in this quadrant would either believe one or both of the following assertions:

1. There are no contradictions.

2. The Principle of Explosion does not hold.

Why would they believe 1? Perhaps they are like some people in Quadrant 1, and they think God would never create contradictions, and therefore there are none. But then, why would they say that contradictions are logically possible? What does logic even mean in this scenario? In this case, they would reject the Law of Non-Contradiction (LNC from here) as a logical law, but they would not be a dialetheist (that is, believing some actual contradiction exists). They would say that logic (whatever that means to them) does not force the absence of contradictions, but that God does, and therefore there are none.

They could have one logic that describes all logically possible realities taken in isolation from God’s decree, and then they could have one logic for all possibilities in our actual reality, where this more specific (and more relevant) logic would be one that does contain the LNC. They would basically reject the LNC as a logical law, but accept it is a perfect, unbreakable scientific law. I call it a scientific law in this case for a lack of a better word.

Their logic without the LNC would be comparable to if we created a mathematical model of our universe without gravity: a logically possible reality, but just one that is not actual. And this logic without the LNC would either be trivialist (and so, not really a logic by anyone’s lights), or it would be a logic that rejects the Principle of Explosion (making it a paraconsistent logic). Maybe they would then use this paraconsistent logic to prove that God will never create contradictions, leading them to their classical sub-system that describes reality as it really is? In this final case, they’d not just believe 1., but both 1. and 2.

But what if they just believe 2., and not 1.? Then, they would be a dialetheist, and would also still probably use a paraconsistent logic. But, they would not then be able to go from that paraconsistent logic to a classical one (at least not a fully general, classical system), because they’d believe there’s at least one contradiction somewhere.

And that brings us back to the question that I ended Quadrant 1’s analysis on… what happens if you reject the Principle of Explosion? As I said in Quadrant 1, it perhaps gets harder to argue for the idea that God never creates contradictions. And in the specific scenario we are looking at right now, we take it as a premise that there IS at least one contradiction out there, which forces the issue.

If you are tolerant to some contradictions, then you cannot rule out the stone paradox merely on the basis that it is a contradiction. That means you must contend with it more specifically. If God allows for some contradictions, why does he not allow for the stone paradox? And if he does allow for the stone paradox, doesn’t that mean God isn’t omnipotent after all? I’ll return to this, but this seems like a good place to end the first analysis of Quadrant 2.

QUADRANT 3:

This quadrant may seem to be, ironically, the most contradictory one. God both can do absolutely anything, and God cannot create contradictions. Can \ne Cannot.

In Quadrant 1 and 2, we said that theists may say that God can in principle create contradictions, but merely that God will not do so. Some would counter them by saying that there is no difference between CANNOT and WILL NOT when the entity that won’t do something is God. There may be a debate to be had on that, but it seems to ultimately be a matter of the definition of to can, and so any disagreement in that debate is probably just people talking past each other.

But in Quadrant 3, we fly right past that debate by actually saying directly that God CANNOT create contradictions. It’s not that he never will… it is that he cannot, at all. And yet, he is omnipotent under definition 1, which states that “omnipotence is the power to do anything.” There’s no apparent qualification in that definition.

Well, I believe Quadrant 3 is necessarily the belief that the LNC and the Law of Identity are really exactly the same. God can create anything. A bachelor who is married is self-contradictory, which means it is self-non-identical, which means it does not merely lack existence… it lacks being. Unicorns don’t exist, but God can still create them. But married bachelors… not only do they not exist, they aren’t…

If they were, God could make them exist. But if they were, they would be identical to themselves, meaning their existence would imply no contradictions. This all may seem to kick the can down the road. God isn’t beholden to the LNC… but, he is beholden to the Law of Identity, which means God is beholden to something, and is not really omnipotent under Definition 1.

But I would argue that Definition 1, despite seeming utterly unconstrained, is in fact constrained by saying that God can create anything, where we may argue that anything is, by virtue of being something, self-identical. You cannot fault God for not being capable of creating self-non-identical things, because there are no self-non-identical things to create! It is not a limitation of God’s power, it is a limitation of being itself, a limitation that is equivalent to being being in and of itself.

I am discussing the idea of God in general here, but I think the concept of the Christian God is relevant here.

I am that I am.

-Exodus, 3:14

If God is everything, and God is himself, then everything is identical to itself. The Law of Identity is not a limitation on God’s power, it is the primitive being of God, perhaps the defining trait of God? There are many possible formulations in Quadrant 3 (all of them perhaps equivalent?), and I think this quadrant is the most profound and difficult to grasp of all four.

But I personally find it the most compelling. And it deals with the stone paradox the same way it deals with all contradictions, so one can really side-step the specifics of it (like in many of the other scenarios explored). The stone paradox is ruled out for the same reason as all other contradictions: because it is a contradiction. But in Quadrant 3, that is understood to be ruled out not due to God’s power, God’s will or anything like that… it is understood to be ruled out due to God’s very being: God’s self-identicality. To be anything is to be identical to oneself.

I don’t consider my analysis here to be perfect reasoning, and I think this topic is so profound that language starts to falter. But I think there might be something here.

QUADRANT 4:

This quadrant states that God is beholden to logic, and that God cannot create contradictions. I see two possibilities here:

1. God being “limited by logic” is nothing more than his inability to create contradictions.
2. God being “limited by logic” is more than just his inability to create contradictions.

So, a Quadrant 4 person believing in assertion 1 is materially in complete agreement with a person in Quadrant 3, and the only significant difference is potentially in how they define logic. A Quadrant 3 person who defines logic merely as the fundamental structure of reality, stemming solely from the LNC/Law of Identity, would actually agree with a Quadrant 4 person on everything. They would see Definition 1 and Definition 2 as completely equivalent, but Definition 2 would simply contain a redundant qualification. They only difference then is that Quadrant 3 people use the non-redundant definition, and Quadrant 4 people use the redundant definition.

But a Quadrant 3 person could have a more serious terminological disagreement with a Quadrant 4 person who believes in 1. A Quadrant 3 person could define logic as a more restrictive, specific structure than merely the LNC/Law of Identity, containing “extra laws”, whereas a Quadrant 4 person would, by the definition of this scenario, not do so. But they would still agree on the nature of God and reality, but a Quadrant 3 person would simply have a more specific, narrow definition of logic, one that is too narrow to describe God’s power. In either case, the only real disagreement between Quadrant 3 and Quadrant 4 people is terminological. Not too interesting.

But, if you are in Quadrant 4 and believe in the second assertion, then there’s is a material difference between you and Quadrant 3 people.

2. God being “limited by logic” is more than just his inability to create contradictions.

This means that you place those “extra laws” into logic, AND you think God is STILL beholden to logic. Perhaps there is only one extra law, eg. the Law of Excluded Middle (from here on called LEM). In this case, you would maintain that the LEM is not derivable from the LNC/Law of Identity, and you would say that God is nonetheless beholden to it. That is quite interesting because classical logic DOES contain the LEM, and if you think the LEM is not derivable from the LNC/Law of Identity, and you think God is beholden to classical logic, then you fall into this category. And this category is perhaps the category furthest from the spirit of the notion of omnipotence, where God is utterly unconstrained in his power.

Anyways, this quadrant, just like many of the other scenarios we’ve analyzed, solves the stone paradox by saying that it is a contradiction, and then blanket rejecting its possibility on the basis of it being a contradiction. No specifics needed.

Conclusion:

The above matrix is definitely a helpful taxonomy I believe, but when we sub-divided the first two quadrants, we saw that there’s another, very important question:

Are there any real contradictions? Because if there are, then we know two things:

1. The Law of Explosion does not hold (because reality is not trivial).

2. God allows some contradictions.

So, if God allows for some contradictions, then we cannot reject the possibility of the stone paradox on the basis of it being a contradiction… So then, is there a stone that God cannot lift? And if there is, doesn’t that mean God is not omnipotent? And if there isn’t, then why not? God clearly allows contradiction in this scenario, so why not allow the paradoxical stone? Why does he never will it into existence?

This shows that my post here is really a taxonomy (comprehensive and correct, I believe) for how to begin solving the stone paradox in different scenarios. But if you find yourself in Quadrant 1 or Quadrant 2, then you may need to deal with the stone paradox as a specific problem, as opposed to dealing with it as a mere contradiction, materially identical to all other contradictions.

[Javi]

Hello, AlveK.

Nice to meet you. I think we haven’t interacted in the old PF.

Wow! What a really elaborate reply! I appreciate the effort you put into it. Hmm… It is a bit complex to decide which quadrant to use because I think each of the four can help to address the paradox. Some with more solid arguments than others.

I actually believe that God can make contradictions, but it is not important whether He will or will not create a contradiction. He just can. It is that simple. This is very important—some people tried to prove Christianity wrong using this paradox, among others, because perhaps theological arguments end up with contradictions. However, paradoxically, thanks to this, some folks saw an opportunity to argue in favor of God’s omnipotence.

Given that Christianity allows for some contradictions, such as the Holy Trinity, it is expected that God might also engage in contradictions—such as creating a rock He cannot lift or break the rules of mathematics. If I were a believer, I would not say, “Yes, He can do contradictions, but no worries because He never will.” Instead, I would say he can create things, which I see as contradictions. Otherwise, denying Him the ability to create these things would be even worse than doing contradictions. Using this argument, at least, supports the claim that He is omnipotent.

This was just a short and simple addendum to your very well-written and elaborated post. I really appreciate your contribution.

[AlveK]

Thank you for the kind words! And no, I wasn’t active in the old PF.

Deciding which quadrant to go for is definitely complex, and I think the basis for the choice shouldn’t rest on how it solves the stone paradox, because other consequences of the choice are far more important, I believe. I think people should decide whether they believe in the LNC first before they delve into this issue. Because the truth or falsity of the LNC is a far more fundamental issue than the stone paradox, but the stone paradox is a very important issue that is affected by whatever we conclusions we come to regarding the LNC.

As was probably clear from my post, I am a bit of a Quadrant 3 guy myself; and not hypothetically, as I do believe in God. I think the LNC sometimes seems less fundamental than it really is, because of its abstract, technical formulation. But really, I genuinely believe that the distinction between the LNC and the Law of Identity is made up, and the Law of Identity is in fact hard to even believe in, because I cannot even fathom not believing in it, and to understand what something is, it helps (or is down-right essential) to understand what it is not.

The Law of Identity (LI from here) is so basic that I don’t even know what it means to believe in it. I don’t know what LI means. Not verbally, not logically. Perhaps I “know” it primitively, like a fish “knows” water.

Kant said the property of existing cannot be a predicate, because the negation of it does not exist, which means it is not a meaningful construct. In modern terminology, existence is often meant more narrowly than being. In fact, I echoed this differing usage in my post above. So, I will translate the older English translation of Kant into modern English philosospeak:

Let us say you have defined x. Then, to say “x is”, is to say nothing (new).

This pseudo-predicate, Is(), it seems a bit like self-identicality. When you say x=y, you are saying two distinct things are, to some degree, equal. But you are only capable of saying this because they are, to some degree, distinct. Even in mathematics, if you derive that two unknown numbers x and y are actually the same number, you have still equated two separate things. Because although those numbers were equal in quantity, equal in their extension, equal in their total definition too perhaps, they were unequal in their presentation to you, unequal in their partial (yet logically complete) definitions, and unequal in what signifier was capable of signifying them before x=y was derived.

These equalities that we derive, they are only identity up-to-a-point. Equality would not be a meaningful binary predicate if not for the fact that it pointed out an equivalence between two things that are unequal in some respect; their equality in the system is a reflection of that system’s inability to capture the subtle and higher-order way in which they are ultimately different.

True identicality then, is by definition, not even a binary predicate. It is not a relation between two separate things, but a relation between a thing and itself. In fact, it is no relation at all. It is a property, a unary predicate. It is an utterly uninformative property. x=x is really just Self-identical(x), and I think it means exactly as little as Is(x) does… I think it means exactly Is(x).

Self-identical(x) = Is(x)

They are the same predicate, presented differently… and this predicate is not really a predicate, because you are not making a meaningful assertion when you state it holds of something, because the alternative is not meaningful either.

As you can probably tell, I have trouble finding the right language to even describe this. It is more like the primitive, ground Truth upon which logic and language rests. Before things are something, they are. They are themselves. And it is at this level you find God. When you stare into the abyss, God stares back. It is not the abyss of pure nothingness, but the the abyss of pure isness. Of self-identicality. Before we are anything, we are; we are ourselves. God is, God is God, God is that God is, or in his words: “I am that I am.” Or even more telling…:

“I am I am.”

So, for now, that is as good as I can do as far as advocating for the Law of Identity. But I have yet to argue for why the LI is the same as the LNC. I am actively working on this topic as I build my philosophy/system, and giving this topic the attention it deserves here would make this post massive, and also quite technical. But I think there’s a rather simple, intuitive and strong argument for why the LI = the LNC, or at least equivalent to it.

We must begin by asking what negation even is, of what “not” means. The answer to this question is where a lot of the diversity between different formal systems arises. Adherents of classical logic, paracomplete logic and paraconsistent logic can often agree on basic ontological facts, but always disagree on epistemology. Because of that, they define negation based on what’s the most practical definition of negation given their differing epistemological stances.

But this discussion is more about ontology, about what is. You could think that no REAL contradictions exist, and nonetheless think the best logic is a paraconsistent logic (one that allows for P and not-P), because maybe you think that although only one of them is true in reality, a proposition and its negation may both be endorsable, provable or true-relative-to-the-human-mind, or something.

Since we are talking about ontology here, we won’t think of propositions as a strings constructed in some system and endorsed based on some process. No, propositions are strings that refer to reality: specifically, propositions refer to state-of-affairs, a somewhat abstract kind of component of reality (or perhaps the only kind of component…).

P is the assertion of the existence of the state-of-affairs that P. And not-P is the assertion of the inexistence of the state-of-affairs that P. I know this is vague, but I think it should be sufficient for now.

1. God = Everything that is (premise, often a part of theism in some shape or form)

2. P and not-P (supposition)

3. P is a state-of-affairs that exists (follows from 2)

4. P is not a state-of-affairs that exists (follows from 2)

5. Everything that is \ne Everything that is (follows from 3,4)

6. God \ne Everything that is (follows from 5 by substitution of the LHS)

From here, you really have some choice for what you want to be the reductio ad absurdum conclusion. 6 could be that. Or God \ne God could be it. Or even just 5. The fact is, if a theist accepts even just a single contradiction, then God is no longer what God is thought to be. God is no longer God. That reductio ad absurdum then allows them to reject the supposition, ie point 2. They can reject that P and not-P.

Another route to go from the LI to the LNC would be saying that objects have no being beyond the predicates that hold of them, and so equality is defined by those predicates, making a contradiction in those predicates the exact same thing as non-self-identicality.

Therefore, I don’t think God can create contradictions, because God cannot be non-identical to himself. But I am sure the last word has not been said on this very profound topic.

[Hanover]

What does an unliftable liftable rock look like? We need to ask that before we can ask anything about it. If we don’t know what it is, then the answer as to what God can do with it is not knowable.

Meaningless expressions are just that.

[AlveK]

So, something is meaningless/unknown if you don’t know what it looks like? Or more generally, something is meaningless/unknown if it cannot be perceived/felt? That is a pretty extraordinary claim, so I might be missing something here. But your response seems to be saying just that.

[Hanover]

I’m saying if you have words that are used to mean “that which is meaningless,” you can’t then discuss its hypothesized (yet non-existent) referent as if it has meaning.

If a Glurg is defined as an unliftable liftable rock, then “Glurg” is used to mean that which has no meaning. Can God create Glurgs? I can’t answer that because you have a term defined to be that without meaning.

It’s not as if Glurgs are within the set of “everything.” It’s that Glurgs have no referent in reality or imagination, nor is the word used to convey anything meaningful.

That is, a syntactically coherent phrase (square circle, 4 sided triangle, unliftable liftable rock) doesn’t obtain ontological status (actual or potential) by usage. If inherent in the phrase is semantic incoherence (e.g. a square circle), saying it cannot exist does not lead to synthetic truth (i.e. God can’t create it). It just repeats that it’s incoherent.

[AlveK]

Okay, now I understand what you mean.

Firstly, I agree that no contradictions exist, that a self-contradictory string of terms has no referent. My quadrant analysis above only investigates dialetheistic view-points as a matter of maximal generality and inclusivity, because this is a debate liable to bring in a lot of people who do believe in contradictions. I wanted a common framework for people with wildly different philosophies to compare their views on the topic.

As you can see in my posts above, I myself fall into Quadrant 3, which clearly holds the LNC in very high regard.

With that out of the way, we can continue our debate with the common ground that contradictions do not exist; a self-contradictory string has no referents.

Because even though we have that common ground, there seems to be a massive disagreement here.

@Hanover

Can God create Glurgs? I can’t answer that because you have a term defined to be that without meaning.

This assertion is completely missing the point of talking about contradictions. Can God create Glurgs? If so, then our current concept of God is self-contradictory and therefore wrong. Conclusion: Let’s return to the drawing board.

That is why people who do not believe in contradictions nonetheless talk about contradictions. It is called reductio ad absurdum, and it is extremely important.

If you assume P, derive a contradiction Q \land \neg Q, then you conclude \bot. That is, the assumption P must be wrong, because it leads to contradiction.

Let’s apply this to the Stone Paradox. Some people worry that the following argumentation is valid:

1. God is omnipotent (assumption 1)

2. God is omnipotent \implies God can create the unliftable liftable rock (assumption 2)

3. God can create the unliftable liftable rock (Modus Ponens 1,2)

4. The ability to create a contradiction \implies contradiction (assumption 3)

5. Contradiction (Modus Ponens 3,4)

We derived a contradiction here. That means that one, or more, of our assumptions must be false. That is the value of talking about a contradiction.

From there, the debate is about which assumption is incorrect. At least, that is our debate, as people who take the LNC to be true. For dialetheists, there is a fourth option, which is simply accepting the contradiction. Rejecting that, we can look at the options for resolving the Stone Paradox:

1. Some people reject assumption 1, arguing that that the Stone Paradox shows God cannot be omnipotent, at least not in the absolutely unrestricted sense that most people mean by that.

2. Some people reject assumption 2, arguing that God can be completely omnipotent, and yet he cannot make the unliftable liftable rock. That is my position, detailed in Quadrant 3 above.

3. Some people reject assumption 3, arguing that a mere potential contradiction is no contradiction at all. These people would also probably go one step further and argue that it can be proven that God will never turn this potential contradiction into an actual contradiction. That then entails it is no longer a potential contradiction, by virtue of God’s self-imposed limits.

The point is, even for people who uphold the LNC, there is great value in talking about contradictions. If you disagree, you’re simultaneously saying that we cannot have a contradiction, but also that if we assume P, and derive a contradiction therefrom, then we cannot conclude P is false. That would be philosophically incoherent.

[Hanover]

@AlveK

The point is, even for people who uphold the LNC, there is great value in talking about contradictions.

I’ve not suggested we can’t speak of contradictions. We obviously can and are right now, but we’re speaking of them analytically, not synthetically. That is, I can say in the abstract that a thing that is and is not cannot be, which is what LNC says. The “unliftable liftable” rock has analytic meaning, namely “X and not X.” Synthetically, it’s meaningless. It cannot be described because it cannot have ontlogical existence. You can’t find and show me a “liftable yet unliftable rock.” If I say there are no all white penguins, that is a synthetic truth, and you would look the world over for one to prove me wrong. If you find me one, but I deny it’s a penguin because penguins are defined as having some black in them, then “all white penguin is meaningless.”

So, when I say contradictions cannot exist, I don’t mean they can’t exist as propositions without referents on an entirely analytic level, but I mean they are meaningless as actual entities. That means when I say “God cannot lift the unliftable” I mean God cannot do something to a thing that isn’t a thing.

[Tom_Storm]

@Javi

I actually believe that God can make contradictions, but it is not important whether He will or will not create a contradiction. He just can. It is that simple.

The problem is that most attempts to disprove God are debunking a cartoon literalist figure like a giant Donald Trump in the sky.

My Christian friends would say something like God is not a being among beings but the infinite act of being itself, the transcendent source and ground of all that exists.

This is closer to a Neoplatonic account of The One. This is more like consciousness itself which doesn’t go about lifting stones.

Of course if you insist that God is a cartoon magic space wizard as per less sophisticated theists then the usual response to this is god can’t do what is logically impossible. The question is flawed. God can also not make a square circle.

[Javi]

@Tom_Storm

the usual response to this is god can’t do what is logically impossible. The question is flawed. God can also not make a square circle.

Hey, Tom. Nice to see you here.

I see it the other way around. I honestly believe that God can make things that are logically impossible. Thus, making a square circle or breaking the basic rules of math.

God and His omnipotence are not bounded by logic. If God were not omnipotent, the paradox would reemerge. Furthermore, if God doesn’t lift a heavy stone, it is because He is self-limiting Himself, but it is not limited by logic.

Aquinas argues that God (subject) and predicate are compatible, and furthermore, God is the perfect reality. Therefore, it is expected that He can do logically impossible things, even if He decides to not do so.

In other words, we may not ask God to do a square circle because we already expect that from Him. If we ask Him to do it, we will doubt His omnipotence and therefore His existence. Perhaps we are the ones who enter the paradox and not God.

[Tom_Storm]

@Javi

I see it the other way around. I honestly believe that God can make things that are logically impossible.

Bear in mind, this isn’t my view as I don’t believe in a god, so for me god can’t tie a shoelace, let alone do the impossible

My understanding of Thomas Aquinas is that he would say God cannot do what is logically impossible. In Summa Theologiae (I, q.25, a.3), he explicitly argues that divine omnipotence extends to all things that are possible absolutely, but that which implies a contradiction does not fall under omnipotence. A proposed undertaking like a square circle or a stone so heavy that God cannot lift it are not “difficult”, they are pseudo, they describe nothing real.

I’m curious what you think about the more sophisticated understanding of god I sketched above. I’ve always been more attracted to the apophatic tradition than to theistic personalism.

[Javi]

@Tom_Storm

I’m curious what you think about the more sophisticated understanding of god I sketched above.

Fair point, Tom!

Yes, it is another way of seeing it, and I can’t disagree at all.While Aquinas did make that statement, my point was focused on the work that Tettü actually quoted, not on Summa Theologiae.

Specifically, this quote of Aquinas:

@Javi

It remains therefore, that God is called omnipotent because he can do all things that are possible absolutely; which is the second way of saying that a thing is possible. For a thing is said to be possible or impossible absolutely, according to relation in which the very terms stand to one another, possible if the predicate is not compatible with the subject; and absolutely impossible when the predicate is altogether incompatible with the subject, as for instance, that a man is a donkey.

Perhaps I am wrong, but I understood it in the following way:It is predicable that God can do all things that are possible absolutely. In other words, God can do things that are compatible with Him. Therefore, these “things” must necessarily be logical, not Him. When the predicate is incompatible with the subject, that is when we have an impossible thing.

Is it absolutely possible to make a square circle? No.

Can God make a square circle? Perhaps because God is not limited by logic. Absolutely possible doesn’t equal logically possible, and therefore, there might be compatibility with God. What is impossible or not logical to us doesn’t apply to God. I can’t believe a donkey and a man at the same time, but it seems that God can.

[Chevron]

The paradox is inconsequential in negating the ability of an omnipotent being. I think gods power goes beyond the contradictions of human logic. But of course it doesn’t negate the questions tricky nature either

[Ripheus23]

Well, accidentally deleted my attempt to contribute to this conversation… I was trying to edit it anyway…

Maybe the word “omnipotent” is not clear of itself. Some interpretations of “having all power” or “being almighty” would be:

1. Having power over all things, including oneself.
2. Having power over all other things.
3. Having all powers in general; this doesn’t work if “the power to raise one’s hand” is a general term and if God doesn’t have literal hands.
4. Having all specific powers; this doesn’t work unless occasionalism is true.
5. Having the greatest kind of power (simplipotence or theopotence, following divine simplicity by essence or divine conceptual simplicity).

[Tom_Storm]

@Ripheus23

Maybe the word “omnipotent” is not clear of itself.

Sure. But the word God is not clear either. Are we talking about theistic personalism or an ineffable ground of being? Theists bon’t agree on this and god could be anything from magic sky wizard to being itself. The latter doesn’t do tricks. Which one are we referring to?

[Javi]

@Ripheus23

Maybe the word “omnipotent” is not clear of itself. Some interpretations of “having all power” or “being almighty” would be:

1. Having power over all things, including oneself.
2. Having power over all other things.

I don’t think omnipotence is related to power in that context. Power means the ability to do something, but when we talk about God, this goes beyond any kind of ability. Omnipotence is more related to possibilities—the ability to do all possible things.

@Ripheus23

• Having all powers in general; this doesn’t work if “the power to raise one’s hand” is a general term and if God doesn’t have literal hands.

Good point. Your argument reminded me of Divine Simplicity theory. God has no parts.

@Ripheus23

• Having all specific powers; this doesn’t work unless occasionalism is true.
• Having the greatest kind of power (simplipotence or theopotence, following divine simplicity by essence or divine conceptual simplicity).

I honestly believe that the theory of divine simplicity might be a solution to the stone’s paradox. According to this theological doctrine, God is not composed of parts, so His “power,” ability, matter, goodness, etc., are identical. Thus, the attributes are not separated; they are one. This means God is just one God, and He has no accidents (properties that are not necessary). Therefore, perhaps, creating a stone too heavy to lift it is just unnecessary to God. The question would turn into, “Why does He have to create such a thing?”