pondering the omnipotence paradox

Consder the classic omnipotence paradox, expressed as a logical conundrum thus:

Posit an omnipotent God who created the Universe. Can God create a stone He cannot lift?

If the answer is yes, then there exists a stone that God cannot lift, hence God is not omnipotent. If the answer is no, then God cannot do something, and hence God is not omnipotent.

Now, this is a bit of a problem for some as far as God’s existence is concerned (of course you can have degrees of omnipotence, but as far as the major religions go omnipotence is part of the job description).

However, the question itself is logically flawed, akin to asking “What color are the eyes of the King of the United States?” The reason for the flaw is because we are trying to shoehorn certain biased meanings into the words “stone”, “lift” and “cannot”.

Consider first the stone. The paradox doesn’t invoke more thorny creations like an equal to God (now, that would be a philosophical head-scratcher). It’s just about a stone. So, what is a stone? It’s a physical object, comprised of N ordinary bosons, and of radius R. Nothing more complex than that (though presumably at some very large radius R it would collapse under it’s own weight and become a neutron star). But let’s be really generous and rephrase the question, “Can God create a black hole He cannot lift?”

No, let’s turn our attention to lifting. For us to lift a black hole is sort of meaningless, but if you consider that to lift something is merely to manipulate it, then we can generalize further to “Can God create a black hole he cannot manipulate?”

Now by this point the Dawkins acolyte will accuse me of having moved the goalposts. “Surely your omniscient God could create a big stone, immune to gravitational forces which would cause its collapse but not immune to an external gravitational field which exists solely to provide something against which to literally lift it?” I suppose if you insist that this is different from what I described in my reformulation above, we can agree to disagree, because frankly creating a supermassive black hole (and just how masive, I am about to explore further) in an instant and then shoving it around seems pretty much just as miraculous to me. Then again, as a believer in a religious faith, I’mnot exactly addressing the paradox with an open mind, now, am I?

So let us continue. The last hurdle is the word, “cannot”. For a black hole to be so massive as to essentially be impossible to manipulate, it must be so large as to not provide any room for it to be manipulated. The physical manipulation of an object in N-dimensional space involves rotation about and translation along the N physical axes. Since God created the Universe of radius U, and the black hole is radius R, then the only way the black ole cannot be manipulated is if R = U – in essence, if the universe itself contains only the black hole (or the stone, if you insist) and nothing else.

Now, the question has reduced down to, Can God create the Universe? To which we already know the answer is yes, by virtue of the Posit above.

Alternatively, we could just be talking about a normal piece of rock, say the size of a softball, weighing less than a pound, and unremarkable in every way except that it has also been assigned a property that nothing (including God himself) can move it. This too is a meaningless paradox, though for a different reason than the one above. In essence, what does it mean to say that god cannot move it? God can choose not to move it, but since God is omnipotent, the definition of that power is that God can do whatever God wants to do. Defining omnipotence as “the ability to not do something” is not omnipotence but limitation.

To put it plainly, anything God creates, God can uncreate. Perhaps God can relinquish that power if God so desired; the ability to relinquish it would fall within omnipotence, but once relinquished, God would no longer be omnipotent. That doesn’t mean God wasn’t omnipotent before choosing to do so, though. In a sense, thats what this Interpretation 2 is asking: Can God choose to abdicate being God? The answer is probably yes, but that’s an affirmation of God’s present omnipotence, not a denial of it. Creating a stone He could not lift? No, he “can’t” do that, anymore than he can’t not be omnipotent while He is omnipotent.

That said, if you think that faith can be discussed with logic, then you’re kind of missing the point. But Douglas Adams said it best, which is rather ironic given how fierce an atheist he was.

This is what I do sometimes when I am procrastinating on doing something else much more important.

15 thoughts on “pondering the omnipotence paradox”

  1. A religious person who uses logic.

    Amusing.

    One who selectively ignores logic then uses it for his advantage to preach about an illogical philosophy that makes unlikely and unprovable claims.

    Amusing.

  2. Sorry, fledgling otaku, but this is hooey. You have taken a simple proposition and made it needlessly complex to try and debunk it.
    It doesn’t matter whether such a stone actually does exist or not, the point is that the whole logic of omnipotence can be broken with this very simple posit. Turning the stone into a black hole wasn’t just a huge leap but also a red herring to the logic.

    These claims of a being of great omnipotence were made thousands of years previously during a time where non-religious and anti-religious thought involved getting burned at the stake. Frankly, these people didn’t expect the level of critical thought that would be applied to their assertions thousands of years after they shuffled off the mortal coil – they probably figured that burning and/or threats of eternal damnation for those daring to question what they say would be encouragement enough to put up and shut up.

    Quoting Adams’ comment whose origin was outside of religious subject matter was unhelpful to your persuasive goal, and I suspect if he were to read this post, would bring up many of the points he raised on the linked page.

    Also, getting into philosophical debate as to whether a debunking stone could possibly exist is a nice mirror to the thousands of people wasting so much time on establishing or defending the existence of a divine God in the first place.

  3. I don’t know, I’d say that a god which is beyond logic is the only entity worthy of worship. Not that I believe in such a being, but then, I lack faith.

    I rather like this answer to the “stone god can’t move” question: “Yes, but he wouldn’t, because the act would destroy Creation.”

  4. The simpler way to put that is “God ‘can’t’ do that because it’s logically impossible, and even God can’t do the logically impossible.”

    God also can’t make an object that’s all-white and all-black at the same time (and in the same perceptual context) – this is not a limit on God’s power, but on the nature of what is possible at all.

    (Or, back to the Rock example, a limit on the possibilities of what an omnipotent being can do. What you said, but more simply expressed.)

    (And to preempt cj and his ilk, I’m an atheist. I just think that that particular argument “against God” is pathetic, relying on category mistakes and bad thinking.

    But then again, to find the use of logic by religious people amusing suggests for instance complete ignorance of millennia of theological thought, which is keenly, sharply logical… but contains axioms that cj does not accept.

    The best argument against God is the complete lack of evidence, not insipid word-games. The “paradox” here is merely apparent, an illusion created by fuzzy interpretation of the language.)

    1. I KNEW youd written something about this earlier! at first pass though I think you are binding God’s set of actions to those that can exist within the universe. Since god is meta to the universe, his set of actions V is a superset of those actions v which can be performed within the universe. I need to make a more rigorous answer later.. in a nutshell, though, Godel comes to teh rescue.

  5. I think the question is akin to “how many angels can dance on the head of a pin” or perhaps, more tellingly, “if Galactus fought superman, who would win?”

  6. And yes, Den Beste is right, even a subset of the concept of omnipotence that can be mathematically defined leads to a contradiction.

    That would mean that even this subset of omnipotence is impossible.

    Frankly I find he fact that people claim to have the ability to define the DETAILS of the properties of an entity whose very existence is conjecture to be pure hubris and bunk.

    It reminds me of the numerous details about what makes a correct Buddha statue, details about the length of the finger etc etc. Does anyone in their right mind believe that any historical Siddhartha had those precise proportions?

  7. ” A religious person who uses logic. Amusing. One who selectively ignores logic then uses it for his advantage to preach about an illogical philosophy that makes unlikely and unprovable claims. Amusing.”

    Condescension: the first and best refuge of the atheistic Left.

    1. actually, realjg – its not an unreasonable comment, if you fail to understand the nature of belief (as “religious” atheists do). These types think they have a monopoly on reason, and that the devout are forced to reject reason completely. In fact, the actual “belief” required to be religious is a very small leap of faith indeed – but from that single leap, all other inferences flow, inexorably, from logic and reason.

      In fact, thats what atheists do too. They assert their belief, and then let reason follow. The initial leap of faith in their case is different from, say, mine, but it is a leap of faith all the same.

      Literally, for our friend, atheism is a religion; he has total faith in his powers of observation and deduction as sufficient to explain the universe. His reaction to competing belief systems is precisely that of any other religious faith; denial of its validity, labeling it as heresy.

      There are principled atheists I know – and several who are dear friends of mine – who are much more rigorous in their disbelief. None of them would ever make such a statement because they not only understand logic, they also understand belief – and choose not to believe. I respect that immensely.

  8. If one maintains the supposedly ‘initial’ position that the necessary conception of omnipotence includes the ‘power’ to compromise both itself and all other identity, and if one concludes from this position that omnipotence is epistemologically incoherent, then one implicitly is asserting that one’s own ‘initial’ position is incoherent. This position finds that the ‘ultimate identifiable power’ can be identified only by requiring that it be, at once, subordinate and superior to an ‘omnipotence of thought’.

    From a certain cognitively lax outlook, to imagine an omnipotent agent as having ‘power over’ ‘logic’ is assumed to describe a state of affairs in which ‘logic’ is subsumed to omnipotence. But, the accurate description of this imaginary, nominal ‘state of affairs’ is that the omnipotent agent is being subsumed to the ‘logic’―that is, to the accurate description, or identity―of non-omnipotent agents.

    The accurate description, the logic, the order, of this subsumation is like two arrows, each of a differing degree of ‘straightness’, simultaneously nocked to one bow string, so that when the string is released, only one arrow hits the Bulls Eye. And, by this analogy, the description of the bowman and his point of view is that the bowman is so insensible as not to know that he has released two arrows at once, and so he concludes that the target, not his bowmanship, is incoherent.

    There once was a faithful hunter out to prove that a certain large animal was both a carnivore and didn’t exist. He was very pragmatic and clever, this hunter was. So, just in case the animal really did exist, this hunter wore fake ‘large carnivore’ feet over his boots that made huge, clawed tracks like what he was convinced the animal must make. This would prevent the animal, in case it existed, from detecting him by his own boot tracks and, in its noticing his boot tracks, either catch and eat him, or try to thwart his attempts to track it.

    So, off this hunter went, with fake clawed feet over his boots, looking for signs of the animal. Soon, he saw his own fake ‘large carnivore’ tracks, but mistook them for those of the animal. But, he was not about to admit that they proved that the animal existed, because he was well aware that he had been walking in the same circle as the animal. So, in seeing that the tracks led to nowhere but round-and-round, he concluded that the animal did not exist. Yet, he was convinced by these very tracks that he was right all along in what sort of tracks the animal made, and that, by its huge claw marks, that it was a truly monstrous carnivore.

    This faithful hunter was so proud of his accomplishment that he brought other faithful hunters to see the tracks, telling them that these were the tracks to look for, since these tracks did, in fact, lead to nowhere. Some of these hunters believed him. The other hunters insisted that the animal was invisible, ‘so that, of course, it could not be identified’. But, all of these faithful hunters, including the one who had made the tracks, ‘knew’ that the animal was a carnivore.

  9. Given the complexity of the Cosmos, and of a world that includes logical duplicity and existential evils, it is axiomatic that the obverse of the law of identity includes a complex reverse: a thing not only is only what it is, it also is not all those things which it is not. But, within an epistemologically passive stance regarding a given topic, the two sides of this axiom are conflated, allowing this stance to seem to itself to have a virtually unlimited body of logic upon which to confirm to itself the sense of its own soundness regarding that topic.

    Now, given the two-sided axiom of identity described above, it is epistemologically axiomatic that the greatest meaningful scope and degree of power which may inhere as a single agent (omnipotence) is identified, like infinity, partly by contrasting reference to the complex and variable logics of all those things which this agent is not.

    So, first, our concept of omnipotence is a cognitive action on our part to define the greatest meaningful scope and degree of power which may inhere as a single agent. Second, this concept obtains to our minds initially as immediately coherent. Third, its immediate coherence produces in us a specifically subjective sense of its epistemological stability.

    But, most of us are not particularly aware that, in our feebleness of mind of progressive biological entropy, we so easily transform this sense of the epistemological stability of our immediate concept of omnipotence into a cognitively lazy re-conception of omnipotence as logically indifferent or explosive. Such a re-conception is cognitively stable for its utter ease of being retained on its own terms. But, to maintain that stability in face of a world of variant logics requires stressing the ‘importance’ of the epistemologically ‘humble’―or, for the skeptic, superior―sheer insular ignorance with which such a reconceptualization initially is made.
    Part of the problem is that the subtlety of this transformation of the concept of omnipotence into an incoherent re-conception is cognitively so deep that many persons take for granted that the incoherent re-conception is, in fact, their own initial conception of omnipotence. The other part of the problem is even deeper:

    In a world of disharmony on all levels, we humans have a problem with power: we tend to conceptualize power as essentially adversarial or otherwise ‘dominative’. In other words, in the context of a basic psychological, social, organic, and general material insecurity, the human mind/psyche easily falls to ‘intuiting’ power not only as most essentially an action, but as an action which is a self-preserving or antagonistic response to inhospitable, intrusive, manipulative, domineering, or otherwise adverse external agents.

    In fact, this adversarial-dominative sense of power is so pervasive in the fallen mind that some people, despite their more-or-less conscious recognition that the concept of omnipotence is immediately coherent, adopt the view that its very coherence constitutes an external limitation on, or ontological counter to, the power of an omnipotent agent, called ‘logic’. They then are forced to ‘recognize’ that omnipotence must be remedied as irrational in order for them easily to maintain a sense of its epistemological stability: paradoxically in adverse relation to the logic not only of its own identity, but to all identities whatever.

    So, the subjective sense of epistemological stability is centrally involved in the task of defining the greatest meaningful scope and degree of power which may inhere as a single agent. But, this task is complicated by the possibility of our adopting an epistemologically lax bias. This bias is easy to maintain on its own terms, and is comparable to cognitive ease which arises from cognitive proficiency in regard to any complex task. An example of this ease-by-proficiency is in having become so experienced in driving a car that you no longer have to attend, with any strain of effort, to the complex task of driving. Another example is having attained such proficiency in rock climbing that you no longer grip the rock so tightly as to become quickly exhausted just holding on. But, to adopt an epistemologically passive bias is like a novice climber, or novice driver, who lounges in safety while mistaking a daydream of ease-of-task with a personal ability easily to climb or drive. The expression of this bias in terms of the concept of omnipotence is to adopt, unwittingly, the cognitively least demanding conception of power.

    So, never mind omnipotence for a moment. Just ask yourself what you know of the concept, or definition, of ‘power’. What do you mean by ‘power’? And, how do you know that that meaning is the most basic, much less the most deeply informative and relevant, meaning of the term? Firstly, unless something exists which has a simple, direct, immediate, ‘mechanically inexplicable’ effect, then there is simply an infinite regress of explicable agents/causes for every effect. In other words, the idea of a uniquely primary category of agent/cause is assumed to be logically necessary given the concreteness with which the agents of the sensible physical world are self-evidentially invested. But, secondly, those sensible agents all are instantiations of a host of other agents, both smaller agents and more mysterious agents. In other words, as concrete as they sensibly are, we find that they are synthetically, reducibly so.

    So, these two concepts, primary agency and synthetic agency, stand at opposite ends of the epistemological spectrum. The primary, irreducible agent is an agent about which nothing variable can immediately be known. All that which can be known of all secondary, or synthetic, agents is immediately knowable to be variable. But, these two concepts also underline the fact that the ‘billiard ball’ model of physics fails to account for the fact not only that agents cohere to make up any synthetic agent, but that agents are attracted and repelled at a distance in terms of forces and particles which, though possessing astonishing potential, are beyond our own most familiar sensory abilities. Even space itself, whether occupied or not, seems inexplicably not to be made of anything, yet it very much seems to exist. So, it seems that there must be something which not only is irreducibly what that something is, but which is concretely indivisible in any case.

    Now, the cognitively least demanding conception of power is that according to which dictionaries may define power: the ability to bring about a particular state of affairs that does not obtain prior to the act of bringing it about. This conception of power is a fully generalized abstraction from actual kinds of powers. We abstract it similar to how we abstract generalizations in math. Whether we add two pair of shoes, or one pair of shoes and one of socks, there is a particular sense that stays the same: four objects. Similarly, whether we observe a hammer as it strikes a nail, or the nail as it goes into wood, the most singular sense is always the same: something brings something about: simple agency.

    But, simple agency is the fully ambiguated, or logically indifferent, sense of the idea of power. It doesn’t say anything that we don’t already know: It can’t tell us that tornados cannot blow 2+2 up into 5, nor that human wishful-ness cannot cause tornadoes to cease. In fact, simple agency says much less than we already know if we think that it is sufficient to understanding any act of power: It can’t tell us that the logical potential to accidentally trip and hit your head is not strictly an example of power, but of a lack of the cognitive power to coordinate a less-than-perfectly-coordinated body sufficient to prevent accidents. Moreover, simple agency cannot tell us that the ontology of power is concretely neither the idea of ‘potential’ or the concreteness of action, so it can’t tell us what we most implicitly know about power: that power is an agent, and that there is, in fact, nothing which is not an agent. So, simple agency cannot tell us that the kind of agent that a particular agent is is what determines what powers it has, or, rather, is.

    So, to use the idea of simple agency as the singular metric for identifying potentials and actions of power, while being consistent on its own terms, nevertheless is ‘epistemologically adverse’: it is logically indifferent to the nature of the relations between results and their causes. It then becomes nothing but the idea of ‘effect’. So, to say that ‘power is defined in terms of its effects’ is to define power essentially as an adversarial relationship to the constitution of entities, rather than as a kind of entity in itself. In fact, if the ontology of power were simple agency, then power would not be anything in itself, but would consist purely in the fact that something changes. This, in turn, would mean that nothing could be held a priori exempt from being changed, including mathematical sums and other kinds of logical entailment.

    Given the complexity of the creature, if the obverse of the law of identity includes a complex reverse, then this double-sided-ness of the logic of identity presents a potential difficulty to understanding omnipotence. Specifically, the task of correctly identifying a thing, or a thing’s concept, is complicated by the all-too-convenient states-of-mind of the creature which are more-or-less not coordinated to that thing or to that thing’s concept. In fact, this lack of coordination is born of a kind of expertise in analytic philosophy which, in its more arrogant forms, is legalism―an ‘expertise’ reflected in the ironic saying among law students that ‘Nothing is understood.’

Comments are closed.