Response to: Is God a Square-Circle?

Before I begin, I would like to thank Álvaro Marqués for pointing me in the direction of this video: Is God a Square-Circle? This is a YouTube video on a channel called Faded Pixels which is all about the omnipotence paradox. Given that this is something I’ve spoken about before (see this video and this video) which explains my response to the paradox in more detail, this is something I am more than familiar with. But maybe, just maybe, he can convince me I’m wrong about the definition of omnipotence being incoherent. So let’s hear what Faded Pixels has to say!

0:00 – 0:06

There’s a popular method that many think proves that God does not exist, it disproves the existence of God. 

Now I don’t want to be “that guy” (well… actually I do like being the guy who wants to get things right) but I don’t like disagreeing with literally everything someone has to say. But I have to disagree with this! While it is certainly true that some attempt to use arguments like the Paradox of the Stone as a method to prove that God does not exist, originally, it was historically used by theists to discern what their conception of God’s omnipotence would entail. It was developed prior to the Middle Ages when there were not many atheists running around trying to disprove God! So while to some, it may be an argument which disproves the existence of God, I think there is more utility to view the purpose of the omnipotence paradox is to promote the theist to come up with a definition of omnipotence which is complete and coherent. Therefore, the paradox can be used as a thought-experiment to see whether one’s definition of omnipotence is coherent and has utility. However in recent years, it has been used as an argument by atheists trying to claim that omnipotence is self-contradictory, rather than to merely hold theist’s feet to the fire to come up with a coherent definition of omnipotence and thus God.

… But anyway, you were saying…?

0:06 – 0:18

This method involves logical reasoning to prove that God is that of a square-circle. But is this really the case, is God really logically impossible and therefore non-existent in any possible world? Well let’s take a look at the arguments posed.

Just to fill everyone in with a bit of context, when he says that the method tries to prove that God is that of a square-circle, he means that the concept of God has a trait (or a number of traits) which are mutually exclusive and thus, cannot possibly exist. The reason being, if omnipotence is not coherent but God is necessarily by hypothesis omnipotent, then it soon becomes easy to disprove the existence of God. For instance, consider the following argument:

P1) Any entity which has a component of their nature which is incoherent cannot possibly exist

P2) Omnipotence is incoherent

C1) Therefore, any entity which is by hypothesis omnipotent cannot possibly exist

P4) God is by hypothesis omnipotent

C) Therefore, God cannot possibly exist

So yes, let’s have a look at these arguments and see his response to them!

0:18 – 0:28

God is all-powerful or omnipotent; he can do anything. Now many think this a trait which is logically flawed. Because of course, then comes the age-old question: can God create a rock so heavy that he can’t move it. It seems like any answer to this question just shows that omnipotence doesn’t make much sense.

Woah, hang on there! Let’s just make two things incredibly clear. The first, which is something I have spoken about in more detail here, the problem seems to be, is that the line of reasoning which theists typically base their argument on is that the omnipotence paradox is specifically about God (more on this below). The trouble is, the theist seems to already affirm the existence of God as a given, and then try to work backwards to come up with a definition of omnipotence which fits. Thus, the theist often attempt to respond to the paradox, not by really addressing the issue, but by working backwards from the belief that God exists and is omnipotent, rather than actually understanding what the omnipotence paradox is really asking.

Secondly, what he describes are at least two distinct concepts: being all-powerful and a being which can do anything and these are not necessarily referring to the same thing. While being all-powerful and omnipotent are generally seen as interchangeable terms, omnipotence and being able to do anything is a much more complicated story

The notion that omnipotence means able to do literally anything is one with a long history. In fact, the Christian Holy Scriptures seem to allude to a God which is able to do literally anything.

But Jesus looked at them and said, “With man this is impossible, but with God all things are possible.” (Matthew 19:26)

Jesus looked at them and said, “With man it is impossible, but not with God. For all things are possible with God.” (Mark 10:27)

For nothing will be impossible with God. (Luke 1:37)

Behold, I am the Lord, the God of all flesh. Is anything too hard for me? (Jeremiah 32:27)

I know that you [God] can do all things, and that no purpose of yours can be thwarted. (Job 42:2)

However, as is often the case, the story is not so straightforward, as there other passages within the New Testament which suggest that there are things which God cannot do, or are impossible:

God did this so that, by two unchangeable things in which it is impossible for God to lie, we who have fled to take hold of the hope set before us may be greatly encouraged (Hebrews 6:18)

In the hope of eternal life, which God, who cannot not lie, promised before the beginning of time (Titus 1:2)

Because of this, there has a been great deal of debate and disagreement between theologians for centuries regarding the precise nature of omnipotence, particularly; whether there are any limits to what an omnipotent being can potentially do and thus, whether such a concept is coherent and thus, could be a trait which any entity actually could posses.

Although this is perhaps the most fringe view in the contemporary literature, the first view is what is referred to as absolute omnipotence, the view that omnipotence means that such a being can do literally anything. The consequence of this, is that such a being, by hypothesis can perform literally any action, even if it violates mathematical law or the basic axioms of logic. As Earl Conee [1] observes: “to be omnipotent is to be all-powerful, where the “all” is utterly unrestricted. Omnipotence includes being able to do anything that could possibly be done, and being able to do the impossible. Omnipotence is absolutely unlimited power.” For instance, such a being could, by hypothesis make three larger than seven or draw a square-circle. Although these may sound ridiculous, one could not claim that an omnipotent being could not do these because such actions are impossible, given that such a being can do literally anything without restriction. Therefore, given that if one does not put at least some limit on omnipotence, this leads to absurd results like these.

While these may sound absurd, the paradox of this, is that if one assumes that an omnipotent being can do literally anything, then the omnipotence paradox soon disappears! The reason being, such a being could, by hypothesis create a rock so heavy they cannot lift it… and then lift it! As it states in the Philosophy of Religion: An Anthology [2] “the task of lifting a stone which He cannot lift—whose description is self-contradictory. But if God is supposed capable of performing one task whose description is self-contradictory—that of creating the problematic stone in the first place—why should He not be supposed capable of performing another—that of lifting the stone? After all, is there any greater trick in performing two logically impossible tasks than there is in performing one?” In other words, while it may sound completely absurd, if you say that an omnipotent being can do literally anything, then such an entity can create a rock so heavy they cannot lift it… and then lift it!

Now, the reason this is a fringe view, is that affirming that omnipotence is completely unrestricted appears to be a problematic position for logistic reasons, including perhaps the most the counter-intuitive conclusions of such a view, is that such a being could, by the fact they could do anything could remove their omnipotence at any moment, and then reinstate their original power or even create a being more powerful than themselves. Although these may sound ridiculous, one could not claim that an omnipotent being could not do these because such actions are impossible, given that such a being can do literally anything without restriction. Therefore, given that if one does not put at least some limit on omnipotence, this leads to absurd results like these.

Beyond this, there are also unpleasant theological ramifications for holding a view. For instance, one could equally imagine perhaps the most unpalatable conclusion that such a being could be offering eternal life while simultaneously not offering this or equally, torturing someone eternally, while at the same time rewarding them. Because of this, as Edward Wierenga [3] notes: “[w]hen people have tried to read into ‘God can do everything’… they have only landed themselves in intractable problems and hopeless confusions; no graspable sense has ever been given to this sentence that did not lead to self-contradiction or at least to conclusions manifestly untenable from a Christian point of view.”

The upshot of this, is that if absolute omnipotence is the “correct” way of viewing omnipotence (assuming that a correct definition is a thing) then this resolves the omnipotence paradox… kind of. But this creates more problems that it solves and hence, that is not the most widely used definition provided (more on that below). So the problem with this video, is that it the author seems to be incredibly sloppy with how he defines terms. He needs to make it clear what exactly his definition of omnipotence actually is.

Now that this has been made clear, let’s continue:

0:33 – 0:48

But that’s not the only problem that they claim. God is also described as all-good or omni-benevolent; incapable of doing evil. But then there comes a problem, if God is all-powerful, he can do evil. But if he’s all good, then he can’t. How can these co-exist in the same person?

Now I will do a specific post about the problem of omnipotence as it relates to moral perfection (although I will explain below). But, as alluded to above, these are separate issues to whether the concept of omnipotence is coherent. This is just another example of someone who seems incapable to seeing the trait of omnipotence as being separate from God. So to avoid any confusion, I will respond to this more fully elsewhere.

Anyway, carry on!

0:48 – 0:54

Now this is where many say God cannot exist because he’s logically impossible; he’s a square-circle.

Well, as I said above, that is certainly one way of looking at omnipotence paradox, but it is certainly not the only interpretation. One could equally look at this and merely say that omnipotence as currently defined has problems that we need to resolve. Or merely adopt the position of agnosticism or even theological non-cognitivism that we cannot meaningfully define the concept of omnipotence and thus, we cannot say whether any entity which has this trait can possibly exist. Either way, while it is certainly true that some use this as a silver-bullet argument against the existence of God, this is not the only way the omnipotence paradox is used.

But let’s continue:

0:54 – 0:58

Well this is only true if God’s power allows him to contradict his own nature. 

While I think I know what he means, what needs to be stressed is that omnipotence (if such a concept is coherent) is part of God’s nature. So it seems he is arguing that God’s omnipotence (or simply power) is in some way separate from his nature. However, what I can only assume he is trying to argue, is that omnipotence properly understood means that such an entity can only do anything consistent with the rest of their nature. But this is something we will consider in more detail below, as it relates to omni-benevolence.

But to help explain his overall goal of the video, he provides four points which are intended to guide the response to the omnipotence paradox. These are:

1:03 – 1:10

Anything is possible for God

Nothing is impossible for God

God can do anything

God can’t do nothing

He adds to this by saying that with these four points in mind, if we return to the omnipotence paradox, he responds by saying:

1:18 – 1:23

Can God create a rock too heavy for him to move? The answer is no because too heavy for an infinite being to move is logically incoherent.

There are two problems with this. The first is that he has spent the rest of the video talking about omnipotence and seems to have defined it as able to do anything. However, now he is talking about an “infinite being” which he does not specify the definition of. If he is using this term interchangeably with an omnipotent being, then surely the answer would be yes; an infinite being which can do anything can create a rock too heavy for him to lift. As noted above, there is no problem affirming that a being which can do anything such a being can create a rock so heavy they cannot lift and also lift it.

But let’s hear what he goes on to say:

1:23 – 1:42

Remember the points I made; everything is possible for God, nothing is impossible for God. Now listen closely, every thing is possible for God. No thing is impossible for God. Now God is eternally existent and because of that, he is incapable of doing nothing, it’s impossible for him.

I’ll ignore the fact that he did not actually say that “everything is possible for God” but that “anything is possible for God” but I think the same point holds either way but I have three problems with what he is saying here.

The first problem I have with this (and I promise this is the last time I’ll say this) but we are again talking about the concept of omnipotence not whether God is able to do everything. Now even I’m getting bored of saying this, but all I will say, is that the issue is whether omnipotence is coherent, not whether God’s whole nature is viable.

The second problem I have with this is, I’m not even totally sure what doing nothing even means; given that when we typically talk about “doing nothing” we do not mean this in a literal sense. For example, if someone asked you what are doing on Friday night and you reply nothing, this is only in the sense of you are not going out for a wild night of drinking (or whatever the popular kids are doing these days!). You are, of course, always doing something whether that being merely sitting in an armchair, breathing in and out, letting your mind drift etc. These are all instances of doing “something” so the notion of doing nothing seems to be a little perplexing. This is not to say that doing nothing is logically impossible but the issue is, the third and in many ways, related problem, is that I don’t see how the fact that God is eternally existent, necessarily entails that this therefore means such an entity must be incapable of doing nothing.

To explain this in simple terms (without getting distracted with the whole issue of the philosophy of mathematics) the view of Platonism holds that there exist abstract objects which are eternal and entirely causally inert, given that they are non-spatial, non-temporal and thus, entirely non-physical and non-mental. Therefore, they cannot be involved in cause-and-effect relationships with other objects, even though they are eternal. While this may seem as though this is a secondary issue, the point I’m making here, is that just because something is eternal, it does not follow that such entities are incapable of doing nothing. So I am honestly not sure why he thinks whether something is eternal necessarily entails it cannot do nothing.

But anyway, let’s see where he’s going with this:

1:42 – 2:04

Like I said earlier, a rock too heavy for an all-powerful being to move is logically incoherent. That makes it logically impossible, that’s not a thing. It’s a nothing. God cannot create a rock too heavy from him to move because such [a rock] cannot exist. Every thing is possible for God but no thing is impossible for God. God can do anything, but he can’t do nothing.

Before I get into the two problems with this, I just wanted to point something out. This is the problem with pseudo-philosophers or amateur apologists you see online. You can almost tell that he’s just regurgitating the same arguments he’s heard William Lane Craig et al., offer without really understanding it. This is because, this is just a paraphrase of what Craig and others have been arguing for years! While I might be being hyper-critical, it just seems as though he doesn’t know what he’s saying, but just repeating what he’s heard other apologists say. I might be wrong, but whether he knows what he’s saying, I’m almost certain he doesn’t understand how wrong he is. 

To explain, the first problem is that, he keep swapping back and forth between what he means by omnipotence, sometimes referring to an all-powerful being, while before he spoke about an infinite being and also suggested that it means able to do anything/everything. The problem with this, links to the the second issue, that he seems to be equivocating the definition of anything.

 

So the second and more devastating problem with Faded Pixels’ analysis here, is that he has argued both that anything is possible for God, that nothing is impossible for God and God can do anything, these each entail that God, by which we should interpret this as an omnipotent being can do literally anything. However, he has also argued that an infinite being cannot create a rock too heavy to lift, because (we are to assume) an infinite being cannot do anything which is logically incoherent and thus, the omnipotence paradox is an example of a logically possible task. So which is it: does omnipotence entail that literally nothing is impossible and thus, can do anything. Or are we to believe that God cannot do certain things because they are logically incoherent?

The way he tries to salvage this (we are to assume, although he does not spell out) is that a thing is something which is logically coherent. Thus, when he says that nothing is impossible for God and God can do anything, what this really means is that God can do any thing which is logically possible. However, this is merely the same problem I have already responded to (see this video and this video which explains this in more detail). The simple response to this, is that as far as I can tell, the problem is, there seem to be two completely different ways of looking at the omnipotence paradox. Thus, the line of reasoning which he is basing his argument on, is something along these lines:

P1) If an entity is omnipotent, then such a being can do every/any thing

P2) A thing is possible if it is not logically impossible

C1) Therefore, a thing is logically possible

P3) God is omnipotent

C1) Therefore, God can do every thing [which is logically possible]

P4) If God is able to do every thing [which is logically possible], then God cannot create a rock so heavy he cannot lift it

P6) God can do every thing [which is logically possible]

C2) Therefore, God cannot create a rock so heavy he cannot lift it

C) Therefore, creating a rock so heavy that God cannot lift it is not a thing [as it is not logically possible]

The consequence of this, is that because Faded Pixels is claiming that creating a rock so heavy God cannot lift is not a thing, the paradox does not actually address the concept of God which he is talking about. Thus, when he means God can do any thing this actually means that God can only do that which is logically possible. Now this is pretty much the stock response that Christians rely upon. The trouble is, this response is fundamentally flawed for one of two reasons. 

The first problem with this, is that he seems to think creating a rock so heavy God cannot lift is logically impossible. This relies upon the fact that God can lift all rocks he has created. However, while it is often assumed that part of the definition omnipotence means that such an entity can lift all rocks they have created, no argument is given for this assertion. Thus, the assumption here, is that omnipotence means (among other things) an entity which can lift all rocks they have created.

To explain the problem of such a notion, if we assume omnipotence means an entity which by hypothesis, can lift all rocks they have created, then such a being cannot create a rock so heavy they cannot lift. As saying that a being which can lift all rocks they have created can create a rock so heavy it cannot lift would be a contradiction in terms. This may sound like music to the ears of the apologist! However, while it would be logically impossible for a being which can lift all rocks they have created to create a rock so heavy it cannot lift, the million dollar question is; why is this part of the definition of omnipotence?

As I will explain in more detail below, this is not because it is only logically possible for an entity to lift all rocks they have created. In fact, we have sound reasons for saying that we any number of examples of entities which cannot lift all rocks they have created. While in contrast, we have no confirmed instances of beings which can lift all rocks they have created. This is not to say such a being is impossible, instead, the issue is merely that there is no argument as to why part of the definition of omnipotence is such an entity must only be able to lift all rocks they have created. So given the definition of omnipotence which is provided, simply talks about doing anything which is logically possible and given that one can conceive of an entity which can create a rock so heavy they cannot lift, while equally imagine a possible entity which can cannot create a rock so heavy they cannot lift, we therefore encounter a problem. Although both are logically possible, no entity could, as part of their nature, be able to both create a rock so heavy they cannot lift and lift all rocks they have created, as one precludes the other. Therefore, the paradox of the stone is highlighting that there are certain logically possible states of affairs which cannot both be actualised by a single entity as one precludes the other. Thus, an omnipotent being can have one or the other as part of their nature, but not both. Hence, this is why we have the paradox to begin with!

It is important to note, while it is true that a being which can lift all rocks they have created cannot create a rock so heavy they cannot lift it. However, it is equally true that there could exist a being which can create a rock so heavy they cannot lift and asking it to lift a rock they cannot lift is a contradiction in terms and thus, it would therefore not be possible for a being which can create a rock so heavy they cannot lift to lift a rock which they cannot lift. So, it would not be possible for a being which can create a rock so heavy they cannot lift it, to lift the rock they have just created. But the fundamental issue is, what reason do we have to assume that part of an omnipotent being’s nature is that such an entity can lift all rocks they have created?

To explain this in simple terms, we can imagine two identical beings in every way, apart from they differ in one feature. One being, we’ll call O1 is a being which, by hypothesis, has part of their nature, the ability create a series of increasingly large rocks such that one eventually become so heavy they cannot lift. This, of course, is easy to imagine given that humans are more than capable of creating something which they are incapable of lifting. Equally, we could equally imagine a being which is able to do everything which O1 can do, but could, by hypothesis, instead of being unable to create a rock so heavy they cannot lift, O2 can lift every rock they have created. That is, one can conceive of an entity which, as part of their nature, is able to lift every rock they have created, such that there could exist a being that for every rock they create, they can also lift it. Given we can imagine an entity which, as part of their nature, can create a rock so heavy they cannot lift it, while another which can lift all rocks they have created, no entity can have both as part of their nature. Thus, we can therefore think of the stone paradox as being an attempt to answer the question, should O1 or O2 be considered omnipotent? Given that both beings are identical in every way, other than whether they can lift all rocks they have created or be unable to lift certain rocks they have created, if we assume that an omnipotent can only have one of these as part of their nature, one must question which one would it be?

As both O1 and O2 are indistinguishable in every other way, and creating a rock so heavy they cannot lift it would be logically impossible for one, while lifting a rock they have created which is of sufficient mass which is too heavy for them to lift is logically impossible for them, each entity would be omnipotent by this metric because being unable to either lift or create such a rock does not detract away from the concept of omnipotence. Given that logic is silent on the issue as to which should be removed, but as no entity could have both as part of their nature, removing one of these cannot be achieved by claiming that one or the other of these would-be omnipotent being’s natures are impossible. Therefore, what apologists often claim is that an omnipotent being has a nature in which they are able to lift all rocks they have created. However, the problem is that there could equally be a being which is identical in every way, but can create a rock so heavy they cannot lift it. The consequence of this, is while the apologist may respond by saying, it is logically impossible for an omnipotent being to create a rock so heavy they cannot lift it, this is in no way implied by the definition provided. 

 

The only other option for the theist, is to claim it is just simply logically impossible to create a rock so heavy the maker cannot lift it. However, if we slightly modify the paradox of the stone, we could ask, is it possible to create a series of snowballs of increasing size until it reaches the point in which the final member has a mass so great that it has a property of being unable to be lifted by its maker? Well, given that it is possible to create a snowball which is unable to be lifted by its maker, given that you or I could personally go out and roll a snowball and lift it, roll another until it is a bit bigger and lift it again and keep doing this until there will eventually become a point in which you create one with a mass is so great that it has a property of being unable to be lifted by its maker. Therefore, if we hold this view, given that this is something that has performed and thus, must logically possible, here is my formulation of this argument:

P1) Let S be defined as the set of propositions which corresponds to the actualisation of all possible actions (P)
[Set of logically possibly actions]

P2) Let P be defined as any action which can be actualised in at least one possible world by at least one entity
[Definition of that which is logically possible]

P3) Let O be defined any entity which is able to perform all logically possible actions (P) within the set S
[Definition of omnipotence]

P4) Let Q be defined as the set of all logical impossibilities (Y)
[Set of logically impossibly actions]

P5) Let Y be defined as anything in the set Q which fulfils the criteria of being a string of words which purports to describe an action, but cannot be actualised in any possible world by any entity
[Definition of that which is logically impossible]

In other words, this is merely trying to say that there are two sets, we have what may (somewhat inaccurately) refer to as logically possible and logically impossible actions. So as I alluded to above, we need to establish some criteria as to when something goes into each of these sets, in which case we could say:

P6) Let A be the act of creating a series of snowballs of increasing mass until the point one becomes unliftable by its maker
[Performing the action of (eventually) creating a series of snowballs so heavy it cannot be lifted by its maker]

P7) If A is P then A is within the set S
[If it is possible to create a series of snowballs so heavy it cannot be lifted by its maker, then this action goes into the set of “logically possible actions”]

P8) If A is Y then it is within the set Q
[If it is impossible to create a series of snowballs so heavy it cannot be lifted by its maker, then this action goes into the set of “logically impossible actions”

While this may look complicated, all this amounts to, is that omnipotence is defined as the ability to actualise any possible state of affairs which is logically possible and that any action which can be actualised in at least one possible world by at least one entity must therefore be logically possible. After all, I hope we can all agree that no entity can do something which is impossible. In contrast, an action which cannot be actualised in any possible world by any entity is logically impossible and assuming one does not hold to absolute omnipotence, we can all grant there are certain thing which are logically impossible for any entity to do. The issue is then, some attempts to respond to this paradox try and argue that the act of creating a series of snowballs so heavy it cannot be lifted by its maker is logically impossible itself. However, the issue is if we continue the argument:

P9) Any action which has ever been performed in the actual world is P
[Modal Axiom B (A→□◊A)]

P10) Entity H has performed A
[A human has created a series of of snowballs of increasing mass until the point it becomes unliftable by its creator]

C1) Therefore A is within the set S
[Therefore creating a series of snowballs of increasing mass until the point it becomes unliftable by its creator is a logically possible action]

Now this is where we get into the issue of the paradox. So one cannot argue that this is logically impossible, because if a human has completed this action, then this means it must be logically possible. After all, humans cannot do anything which is logically impossible. Therefore, the response which theists often resort to, is that while this is something that we as human beings can do, that is we can build objects so heavy we cannot lift them, but an omnipotent being cannot create an object they cannot lift (which I will respond to below). Obviously, very few people would try and argue that the act of creating a series of snowballs so heavy it cannot be lifted by its maker is itself logically impossible, so most take the option that although humans can do this, this does not mean that an omnipotent being can do it. While I will respond to this below, if we continue the argument:

P11) Entity O cannot perform action A

This is where the rubber hits the road, because this is little more than the assertion that an omnipotent entity cannot create a series of snowballs so heavy it cannot be lifted by its maker. Now sometimes, you have more sophisticated theists who might try and defend this premise by saying that there exists no such rock that satisfies the description of being “unliftable by its maker”. That is, there could exist a being which is omnipotent such that all snowballs they create they can also lift, so if there is a one to one correspondence between the snowballs they create and the snowballs they can lift, there would be no final member which is of sufficient mass which they cannot lift. However, the issue is, while it is certainly true that there could be being a which is omnipotent, such that all snowballs they create they can also lift, the definition of omnipotence which is provided simply talks about doing anything which is logically possible. And if this has been actualised by at least one possible entity in at least one possible world, it cannot be argued that this is logically impossible to do. Therefore, although there may be an entity which can lift all rocks they have created, it is equally possible for an entity to create a rock so heavy they cannot lift it (as explained above).

Given that both are logically possible, to claim it is logically impossible for an omnipotent entity to create a snowball so heavy they cannot lift it, this does not follow from the definition of omnipotence as it currently stands. The reason is, because if the omnipotent being, as part of his nature, can lift all snowball they can create, then it would be impossible for them to create a snowball so heavy they cannot lift it. While equally, if an omnipotent being, as part of his nature, like humans, can create things they cannot lift, like a snowball, then it would be impossible for them to lift a snowball they cannot lift because it is too heavy. Either way, if we affirm premise 11 and continue the rest of the argument, it would mean:

C2) Therefore O is unable to perform all P within the set S
[Therefore, if an omnipotent entity cannot create a rock so heavy it cannot be lifted by its maker, then it can’t do everything logically possible]

C) Therefore the definition of O is incoherent
[As the ability to perform any logically possible actions (P) within the set S contains a contradiction]

The issue is, if human being can and indeed do perform the act of building objects so heavy we cannot lift them, this must therefore be logically possible, as humans cannot do anything logically impossible. Therefore, if an omnipotent being can do anything logically possible, then such an entity must by logical necessity complete the act creating a series of snowballs of increasing size, such that the final member is so heavy that it cannot be lifted by its creator. Thus, the fundamental issue, is that theists do not hold to a consistent definition of omnipotence because they claim on the one hand that omnipotence means such a being can do everything logically possible. But the paradox of the stone highlights that there are things which are logically possible to do, which an omnipotent being apparently can’t. And this is a contradiction in terms, because it would be saying that an omnipotent being can do everything logically possible, apart from some logically possible things.

So here for me is the bottom line. The paradox of the stone is based on whether you start with the assumption that God exists and therefore must be omnipotence and so, any form of omnipotence paradox must be rejected a priori. Or, if you do not start with this assumption, it seems difficult to see how anyone can come to the conclusion that omnipotence is coherent, as currently defined, when there are logically possible things which theists maintain are impossible for an omnipotent being to do. So either, omnipotence is not coherent and thus, we need a new definition which does not fall pray to any form of omnipotence paradox. Or that if theists insist this is the definition of omnipotence, they paint themselves into a corner and seem to render omnipotence as being a incoherent and thus, God cannot possible exist. It really is that simple!

2:05 – 2:29

But what about the second problem; can God perform evil? Well no, like the first question, it’s also a logically incoherent question. For a maximally great, eternal being to actively go against his own nature, is a logical contradiction, which is not realistically reconcilable and is not a thing, again it’s a nothing. So God cannot do evil because it is logically impossible for him to contradict himself. 

Obviously, when you see this, the first problem is that he does not actually justify why God, as a maximally great being cannot perform evil. Instead, all he offers is a word salad about God being eternal and cannot act against his own nature. So given he again he did not actually spell out his response, I’ll fill it in. This line of reasoning is that God is a maximally great being, which includes not only omnipotence but also moral perfection. Thus, if God’s nature is such that he is morally perfect, then it is logically impossible for God to actualise any evil acts, but this does not detract from God’s omnipotence… Or so the argument goes.

However, the problem with this, is that this again misses the point of the paradoxes associated with omnipotence. The issue is, God cannot be considered to be both morally perfect and omnipotent, given that the notion of moral perfection is incompatible with omnipotence. As Wes Morriston [4] notes: “[i]f God is omnipotent, He must be able to do evil (even if He never actually does any), whereas if God is necessarily morally perfect, it follows not only that He does not, but that He cannot, do evil.” The problem with holding to both of these, is that we encounter a paradox. Therefore, merely asserting that God can be both morally perfect and omnipotent is just that, an assertion. To explain why they are mutually incompatible. We can therefore put this formally, to say that:

P1) If God is necessarily morally perfect, then there is no possible world in which such an entity can actualise any state of affairs which is morally evil

P2) God is necessarily morally perfect

C1) Therefore, there is no possible world in which such an entity can actualise any state of affairs which is morally evil

P3) If God is omnipotent, such an entity has the power to actualise any possible state of affairs which is logically possible

P4) Let S be defined as the set of propositions which corresponds to the actualisation of all possible actions (P)

P5) Let P be defined as any action which can be actualised in at least one possible world by at least one entity

P6) Let O be defined any entity which is able to perform all logically possible actions (P) within the set S

P7) Let Q be defined as the set of all logical impossibilities (Y)

P8) Let Y be defined as anything in the set Q which fulfils the criteria of being a string of words which purports to describe an action, but cannot be actualised in any possible world by any entity

P9) Let A be the act committing an action which is morally evil

P10) If A is P then, A is within the set S

P11) If A is Y then it is within the set Q

P12) Any action which has ever been performed in the actual world is P

P13) Entity H has performed A

C2) Therefore A is within the set S

P14) If God is omnipotent, then such a being should be able to commit an action which is morally evil

P15) Entity O cannot perform action A

C3) Therefore, O is unable to perform all P within the set S

C4) Therefore, there exists some possible state of affairs which God cannot actualise

C) Therefore, the notion that God is both omnipotent as well as morally perfect is incoherent

The above argument therefore highlights, that omnipotence and necessary moral perfection seem to be incompatible, given that both cannot be simultaneously affirmed without invoking a contradiction. Thus, as we consider the argument above, it would be inconsistent to claim that they believe in a God which can perform all logically possible actions and at the same time claim that they believe in a God which cannot perform any morally evil actions.

The reason for this is clear, given that the above argument highlights, claiming that God is both omnipotent and necessarily morally perfect is problematic, as this would mean that such a being, by the fact they can do anything logically possible must therefore be able to both actualise a morally evil state of affairs due to the definition of omnipotence, while simultaneously maintaining that a morally perfect being could not actualise a morally evil state of affairs due to their necessary morally perfect nature. The consequence of this therefore, is that if one believes that each of the premises above are true, then it would follow that God cannot be both omnipotent and necessarily morally perfect. 

 

In response to the above, one may attempt to argue that omnipotence is a coherent concept iff one also affirms that a second component of the definition of omnipotence; namely that an omnipotent entity can only do everything logically possible but also consistent with their nature. Namely that one can be omnipotent while affirming that there are logically possible things which this entity cannot actualise. While this seems to resolve the above problem of actualising moral evil, then such an entity can still be considered omnipotent even if they cannot perform he logically possible task of actualising moral evil. Thus, that in every world in which such an entity exists, it would be logically impossible for such a being to actualise moral evil. However, the biggest issue with the defence of omnipotence must be based on the nature of the being in question, to say that while something may be possible for one entity or in one possible world, it does not mean it is logically possible in every context it appears. You then you run into the issue of merely defining omnipotence as being able to do everything an omnipotent being can do. Which, while true, does not tell us what omnipotence actually means or what an omnipotent being can or cannot do.

The bottom line, is that his line of reasoning is simply:

P1) God exists

P2) The proposition God exists means, that there exists some entity which exists and has a nature which includes (among other things) omnipotence and omni-benevolence

P3) If an entity is omnipotent, then such a being can do everything which is logically possible

P4) God is omnipotent

C1) Therefore, God can do everything which is logically possible

P5) If God is necessarily morally perfect, then there is no possible world in which such an entity can actualise any state of affairs which is morally evil

P6) God is necessarily morally perfect

C2) Therefore, there is no possible world in which such an entity can actualise any state of affairs which is morally evil

P6) If God is omnipotent and necessarily morally perfect, then God can do everything which is logically possible, excluding anything which is morally evil

P7) God is omnipotent and necessarily morally perfect

C2) Therefore, actualising an evil state of affairs is logically impossible

C) Therefore, the concept of a God is coherent

The implication of this therefore, is that when one begins with this starting point, one has to therefore reject a priori any form of omnipotence paradox as being malformed or in some way irrelevant to the Christian conception of God. The reason being, if there exists a being which is omnipotent and morally perfect, then the concept of omnipotence must therefore be coherently defined, as no entity can have a component of their nature which is contradictory. The trouble is, omnipotence, or if add into the issue of moral perfection does contain problems, but all he seems to be arguing is that God must be omnipotent and omni-benevolent, even though these are mutually exclusive.

The problem is, he knows perfectly well that entities with an incoherently defined nature cannot exist. As he points out:

2:36 – 2:47

A logical contradiction like creating a married-bachelor or a square-circle is impossible, because it cannot exist and is a nothing. God cannot do a nothing. 

However, he does not seem to allow for the fact that God has at least two traits which are incompatible. In other words, if we consider the following argument:

P1) Any proposed entity which has a component of their nature which is incoherent cannot possibly exist

P2) Omnipotence is incoherent

C1) Therefore, any entity which is by hypothesis omnipotent cannot possibly exist

P4) God is by hypothesis omnipotent

C) Therefore, God cannot possibly exist

 

While he would accept this, if we change P2) to “being a married-bachelor” or “being a square-circle” but does not accept this about omnipotence. And this is only on the basis of an a priori assumption that God exists and thus, must have a coherent nature (or else God could not exist to begin with!)

Anyway, let’s continue with what he has to say:

2:52 – 3:27

So in reality, God is only a square-circle, if he can do logically incoherent things. A God that is omnipotent and can do everything cannot do something which is logically impossible, because it is not a thing. So God cannot create too heavy for him to move and he cannot do evil because they are both logically impossible. God cannot create something that can’t exist, or do something that can’t happen. Again, God can do everything, but these aren’t things they’re impossible, they’re not things. So what we realise here, is God’s omnipotence and and omnibenevolence is still intact and logically sound. 

The bottom line is this: the only way you can argue that God can do everything thing while equally maintaining that God cannot create too heavy for him to move and cannot do evil because they are both logically impossible, it would only follow based on the fact that an omnipotent entity is one which can do everything logically possible for that entity to do. In other words, this only follows if you hold to the view that an omnipotent being can lift all rocks they have created and only act consistently with their morally perfect nature. However, as the above points out, theologians holding to such a view are therefore working on a top-down principle, that omnipotence must be coherently defined, rather than the bottom-up process of attempting to establish whether omnipotence is coherently defined before coming to the conclusion about whether God exists. The consequence of this therefore, is that the assumption of the argument is that because God exists, and that the concept of God must be omnipotent, as no entity can exist which has a self-contradictory nature, omnipotence must be a coherent or else God could not be omnipotent. Thus, when he attempts to respond to the paradox, this is not by really addressing the issue, but seem to be working backwards from the belief that God exists and is omnipotent, rather than actually understanding what the omnipotence paradox is really asking.

The obvious conclusion after considering the above, is that this does not in any way resolve the omnipotence paradox, but merely operates based on the assumption that God exists, is omnipotent and omni-benevolent. Therefore, given that no entity can exist which has a self-contradictory nature, omnipotence and omni-benevolence must be a coherent or else God could not exist and be omnipotent. But the theist, upon reading this might simply shrug, dust themselves off and continue to believe God is each of these things, even though the above arguments demonstrates both cannot exist in the same entity!

Sources:

  1. See: https://www.jstor.org/stable/2214105
  2. Philosophy of Religion: An Anthology (p. 109)
  3. Omnipotence Defined Philosophy and Phenomenological Research Vol. 43, No. 3 (Mar., 1983), (p. 363-375)
  4. See http://spot.colorado.edu/~morristo/wes2mawson.pdf

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