The Omnipotence Paradox… IT’S NOT THAT DIFFICULT

During my time on YouTube, I’ve seen various different arguments between theists and non-theists. But perhaps the most infuriating to watch is the conflict between theists and non-theists over the omnipotence paradox. And I’ve been racking my brain trying to think of some way to articulate the problem, because it seems so often, theists and non-theists seem to be talking past each other whenever this topic is brought up. So in trying to come up with a way of tackling this issue, I was asking myself: how could I make a video which explains this as simply as possible?

On the one hand, I was thinking maybe I’ll take the approach of Anti Citizen X and do this as a thought experiment and try and point out the problem of trying to discover whether someone is omnipotence who turns up on your door

Or I could do a video response to some of the attempts to “solve” this paradox with weird and wonderful claims about language and planes of existence

But after weighing up all of the options, I thought it was best to just put it as simply as possible

So the bottom line is this, as far as I can tell, the problem is, there seem to be two completely different ways of looking at the omnipotence paradox

The line of reasoning which theists typically base their argument on, is something along these lines:

P1) God exists

P2) The proposition “God exists” means, that there exists some entity which has, as part of its a nature the traits of omniscience, omnipresence and – the most important feature for today’s video – omnipotence

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 able to do everything which is logically possible, then God cannot create a rock so heavy he cannot lift it

P6) God can do everything 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 logically impossible

And thus, because creating a rock so heavy God cannot lift it is impossible, the paradox does not actually address the concept of God which theists believe

Now, although you probably won’t find many theists presenting this argument, it certainly captures the sentiment of what many actually believe

The reason being, that most theists affirm that omnipotence means being able to do only things which are logically possible

Therefore, if creating such a rock is indeed impossible, then this does not detract from the concept of omnipotence because it does not include the ability to do anything logically impossible

So, based on 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

Therefore, this is what we can think of as a top down type of reasoning, in which the theist already affirms the existence of God as a given, and then tries to work backwards to come up with a definition of omnipotence which fits

Thus, the theist attempts 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

Now in my experience, this seems to be the most common response to the paradox, that God can do everything logically possible and so, the paradox of the stone is not something which even touches the concept of omnipotence because God cannot create a rock so heavy he cannot lift it because such a rock cannot possibly exist

So to the theist, it would be like saying to someone who claims to be unbeatable at arm wrestling and so any arm wrestling opponent put in front of my I can beat

Thus, the theist seems to suppose that the paradox is saying that because an individual can beat you at tennis, this does not detract from being unbeatable at arm wrestling because that is comparing apples with oranges and thus, the paradox of the stone has no relevance to the concept of omnipotence and thus, the God they believe in

However, the issue for me, is that we are not talking about a literal God which actually exists, attempting to actually create and/or lift a literal rock, but instead, the issue is whether the concept of omnipotence is coherent such that any entity may have the trait of omnipotence

And that means that we should not be thinking of the paradox as being based on whether a literal being is able to actually create and thus, physically lift up an actual stone, but whether the definition of omnipotence is coherent

Thus, before we can even get into the issue of whether God is omnipotent and especially before we consider whether God exists, we first need to establish whether the concept of omnipotence is coherent

Because 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 assuming that one does not want to accept that God cannot possibly exist, we need to ensure we have a definition of omnipotence which is coherent

And the best way to do that, is to strictly define omnipotence and see whether the definition is coherent or whether it contains any contradictions.

So as I mentioned earlier, most theologians adopt the definition made popular by St. Thomas Aquinas

He argues that omnipotence, properly understood means “the ability to do anything logically possible” which is pretty much the consensus view of modern theologians regarding what omnipotence is.

Taking just a cursory look, it seems reasonable enough.

I mean, what is wrong with saying that God can do everything that is logically possible?

Well in this video, I will be going through, even if we accept this definition of omnipotence, this is not without its problems

So basically the million dollar question is: is “the ability to do anything logically possible” itself, logically possible?

Or to put it another way, is it possible for any entity to perform all actions which are considered to be logically possible?

Well, 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 can not 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

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

Thus, the argument would continue as:

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

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

Or at least that is one interpretation of the argument