Philosophical Multicore

Sometimes controversial, sometimes fallacious, sometimes thought-provoking, and always fun.

Omnipotence and Everything

Posted by Michael Dickens on August 1, 2009

This is an exploration into the world of omnipotence and everything, and an alternative proof that omnipotence is impossible. (The original proof is in the form of a question: “Can an omnipotent being create a rock so large that even the being cannot lift it?”)

Omnipotence can be defined like this:

An omnipotent being is one that can do everything.

The problem is, what is “everything”? Time for set theory.

Imagine a set S. If there is some item i not contained in set S, then S is not the set of everything. If no such item i exists, then S is the set of everything.

In this case, S contains all command. An omnipotent being should be able to perform every command in set S. Since S contains all commands, it contains some command which we will call P: “do not ever execute any command in set S.” It is impossible to comply with this. To not execute any command requires that the being not exist, since existence itself is a command. If you have trouble buying that, think of it like this: set S contains some command “continue to exist.” The being must be able to comply with this. But it is impossible to comply with this and with P. Therefore, it is impossible to do everything.

While we are in this set, let’s look at some other contradictions. There must be some command “stop existing”; this conflicts with “continue to exist.” Only one of them can be done. Additionally, since one has to either exist or not exist, one of these two commands has to be performed; no matter which one it is, it contradicts action P.

Assuming that there are infinitely many possible commands, there must also be infinitely many possible commands of the form “do not ever . . . .” These commands are extremely restricting, and more contradictions pop up. For every single “do not ever X”, there is an “always X”, and these are also contradictory. So not only is there one contradiction, but there are infinitely many contradictions.

Set theory can work wonders to destroy the concept of omnipotence.

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9 Responses to “Omnipotence and Everything”

  1. Joel said

    The argument fails when you attempt to define “omnipotence.” The vast majority of theologians since Aquinas have used “omnipotence” as the English equivalent of it’s Latin origin omnipotentia, which simply means, “all things possible.” Thus, if something is possible, then said omnipotent being can accomplish the possible task.

    For instance, omnipotent being B can create object S because object S can possibly exist. However, object Y (e.g. a round circle, or an object that both exists and doesn’t exist) cannot exist because it is self-contradictory. It is not possible for Y to exist because of its irrational nature. Thus, B cannot create Y, though if B so chose, B could create S.

    So the set theory is really irrelevant based upon a proper definition and understanding of omnipotence. Since is is not possible for certain contradictory commands to co-exist in actuality, the omnipotent being, once actualizing one set, will no longer actualize the other set without first removing the first set.

    • Its possible to execute the command “do not execute any command other than this one.” But if you execute it, it’s impossible to execute anything else. And if you want to be able to execute any other command, then it’s impossible to execute this one. Well, I suppose I see what you’re saying. What is possible changes with each command executed, but it is still possible to do all things possible. In fact, it’s tautological.

      So using a more practical definition of omnipotence, omnipotence is indeed possible, at least theoretically.

      • Joel said

        But certain possible things negate other possible things.

        If I create a world, but make the command that no unicorns will evolve on said world, then it is not possible in an ontological sense for unicorns to exist on said world. However, in a metaphysical sense, unicorns can still exist. As the creator, if I had so chosen, I could have created a world where unicorns are allowed to exist. Thus, ontologically it is not possible for unicorns to exist. Metaphysically, however, it is quite possible.

        Thus, if a being created our universe and set certain parameters that those within the system must follow, to us such instances seem impossible. Of course, the being certainly has the right to intervene against said parameters whenever he/she/it so pleases (unless the being has placed limits on him/her/itself).

        But there are certain things that simply cannot exist, no matter what. For instance, can an eternal being create another being like himself? Of course not, because the second being would be created, thus making him temporal. So there are some things that are logically impossible and, therefore, such a being cannot perform these actions.

        This is how omnipotence has been understood for 2,000 years. The few deviations come from Muslim theologians (who believe Allah can do anything he pleases) and deep Calvinists within Christianity. Modern deviations come from (and I don’t mean this to demean such people) people who have never opened a philosophical book or read a theological treatise on the nature of God.

        So the idea that omnipotence means, “can do anything” might carry some weight among the laypeople of society, but among those who actually deal with these theological terms and who understand philosophy, it’s a straw-man definition.

        This is also why the omnipotence paradox has been dropped in academic circles. Notice how among academic atheists you never hear the objection brought up. That’s because it has been answered. 🙂

      • Very true. I never said that this was a disproof of the existence of God. As long as we’re talking about the Deist God, I don’t think there is any such disproof. My intent was to create a mental exercise involving the concept of what I’ll call “strong omnipotence”, i.e. the ability to do anything at all. Though less practically important, it is a very interesting theoretical idea that leads to some fun paradoxes.

      • Joel said

        Well, the difference between a paradox and a contradiction is that a paradox seems like a contradiction prima facie, but ultimately is not.

        The “strong omnipotence” argument would actually lead to contradictions. For instance, could a being make a world in which he does and does not exist? Of course not, that’d be absurd. But under the strong omnipotence view, he’d have to. But this is a contradiction, thus rendering the belief false.

        Maybe it’s the debater in me, but I always choose to take the shortest road possible when defeating an argument. Your argument does work against strong omnipotence, but there are shorter routes there. 🙂

        And for the record, I’m a conservative evangelical Christian (not the type that blows up abortion clinics and thinks that Thomas Jefferson was Christ’s most beloved disciple – more of the “let’s reason our way through this” type). So though I made an argument for a Deistic version of God, given the proper medium I would expand that further to make God far more personal. For the sake of brevity, however, I simply assumed a deistic stance. Hope you don’t mind.

        As a side note, I noticed that you have some interesting critiques of the pro-life movement on your site. I’m curious if you’ve read books by Francis (Frank) Beckwith, Tristram Englehardt, Peter Kreeft, or other pro-life philosophers. You seem fair in your stance, I just hope that you’ve come across some of the more intellectual and scientific writings from the opposite side.

        • My argument may not be the shortest to prove that strong omnipotence is impossible, but it’s one of the shorter arguments to prove that there are infinitely many contradictions.

          Your defense of the deistic stance is fair; as I stated, I know of no sound argument against the existence of the deistic God. The Christian God is another matter (the problem of evil comes to mind, though I’ve never been a big fan of that argument), but that’s getting somewhat off topic.

          I have not read any literature relating to the morality of abortion; unfortunately, most of my experience on the subject comes from the internet. If I can find something written by one of those philosophers that I don’t have to pay for, I will definitely give it a look.

        • Joel said

          Not to distract from the topic anymore, I offer two links to you. One is to my series on abortion and the other is to my series on the problem of evil. Not that I’m some key philosopher or anything, but I’ve studied it enough to be able to butcher it, so I hope these series shed some new light on the issues for you:

          Abortion and Christianity Series: http://en.wordpress.com/tag/abortion-and-christians-series/ (start from the bottom up)

          Exploring the Problem of Evil Series: http://en.wordpress.com/tag/exploring-the-problem-of-evil-series/ (again, start from the bottom up)

          I haven’t really run into any good arguments against belief in the Christian God concerning philosophical quandaries or logical errors. Instead, most of the good arguments concern the issue of miracles, the test of revelation, the ability for God to directly reveal Himself, historical inaccuracies, and the ethical dealings of the Old Testament. There are a few others, but those seem to pose the biggest problems to Christianity.

  2. LRFLEW said

    Nice big, long entry, but there is one problem, “can be”, which says it is not definite. If you are looking to counter with a definition, use an actual dictionary like New Oxford American Dictionary.

  3. Joel said

    Ah, so the understanding of the term among those who use it as well as its Latin meaning (which is the same as the English) doesn’t count? Since when has this occurred? In fact, since when has the New Oxford American Dictionary been used to define philosophical and theological terms?

    For instance, the “New Advent” encyclopedia is respectable in terms of offering a philosophical definition. They define “omnipotence” the same way I do (http://www.newadvent.org/cathen/11251c.htm). Or what about the Oxford Dictionary of Philosophy, which puts forth the same answer I did?

    Or, an even better question, why should I have to supply a dictionary definition when the OP failed to do so? What about that I offered the Latin meaning of the text, which should be sufficient?

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