While there are a number of arguments for the existence of a divine being, none of them require that there be only one divine being.  Why should we think there is only one God, then?

The simplest reason to think there is only one God is the principle of parsimony: Do not multiply entities beyond what is needed to adequately explain the effect in question.  Since only one God is needed to explain the origin of the universe, there is no reason to believe there is more than one God.  The burden of proof would be on anyone wanting to postulate the existence of more than one God to explain why we should think there is more than one God.

While the principle of parsimony is instructive, it is not conclusive.  It is based on probability, not logical necessity.  It’s one thing to say no more than one God is necessary to explain reality, but that doesn’t necessarily mean there is only one God.  After all, only one human is needed to explain how a house got built, but the fact of the matter is that more than one human was involved.  So are there any logical arguments that would logically require the existence of only one God?

Some have argued for monotheism on the basis of divine omnipotence.  Theists ascribe omnipotence to God because God is the greatest being possible.  As the greatest being, He must possess the greatest amount of power possible.  How could the divine attribute of omnipotence argue for monotheism, then?  Some have argued that omnipotence cannot belong to more than one being because omnipotence entails having “all power.”  If there was more than one God – and thus more than one omnipotent being – no one God would have all power.  Power would have to be distributed among them.

The problem with this argument is that it falsely construes power as a substance.  Power is not a substance that can be divided up and distributed.  Power is simply the ability do some particular thing.  Indeed, if power is a substance, and God has all power, then no one else could have any power whatsoever, including human beings.  But clearly we have a limited amount of power.  To say a being is omnipotent is only to say that such a being possesses the ability to do anything that is logically possible to do.

It’s possible to construe an argument for monotheism based on omnipotence in another way, however, that does not involve construing power as a substance.  Any being who possesses the property of omnipotence must possess the ability to destroy other beings.  What would happen, then, if there were two omnipotent beings?  Let’s call them Omnipotent Being A (OBA) and Omnipotent Being B (OBB).  Could OBA destroy OBB (or vice-versa)?  No, because OBB has the power to sustain His own existence.  OBA, then, would lack the ability to destroy OBB.  Since omnipotence requires that one be able to do all things that are logically possible, and it’s logically possible to destroy OBB, OBA must not be omnipotent after all.  The same would be true of OBB, leaving us without a being that is truly omnipotent.  And yet, if God is a metaphysically necessary being and omnipotence is a divine property, then omnipotence is a metaphysically necessary property.  Since the property of omnipotence can only obtain in a world in which a single being possesses such a property, there can only be one divine being.

The problem with this argument is that it fails to take into consideration the metaphysical necessity of OBA and OBB.  A divine being is not only omnipotent, but metaphysically necessary, meaning he must exist.  He cannot not exist.  Since it is logically impossible for an eternal, metaphysically necessary being to cease to exist, then it would be logically impossible for OBA to destroy OBB.  Omnipotence entails the ability to do anything that is logically possible to do, and since it is not logically possible to destroy a metaphysically necessary being, the fact that OBA could not destroy OBB does not count against OBA’s omnipotence.  This argument fails as well.

But perhaps there is still an argument to be made for monotheism from omnipotence.  Rather than focusing specifically on the power to destroy other beings, this argument focuses on volition more generally.  An omnipotent being (OB) has power over everything.  For any X that comes into being, it is either caused to exist by OB or passively allowed to come into being by OB.  For example, OB may actively cause the creation of human beings, but passively allow human beings to create other things like cars and computers.  So let’s say there were two omnipotent beings: Omnipotent Being A (OBA) and Omnipotent Being B (OBB).  If OBA wanted to exercise his power to cause X, OBB would have to allow OBA to cause X for X to obtain in the actual world.  But what if OBB was not willing for OBA to cause X?  There are only two possibilities: (1) OBA would be unable to cause X, or (2) OBA would cause X.  Both scenarios are impossible, however, for a truly omnipotent being. If OBA was prohibited by OBB from causing X, then OBA is not truly omnipotent because he was unable to do something that was logically possible for Him to do.  If OBA was able to cause X despite the fact that OBB did not want Him to, then clearly OBB did not have the power to stop OBA, demonstrating that OBB is not omnipotent.  It seems, then, that it is not possible for more than one being to possess omnipotence, and thus there can only be one God.

The only way to escape the logic of this argument is to argue that there could never be a conflict of will between OBA and OBB or to argue that all conflicts of will would always be resolvable.  I have never encountered an argument for either of these propositions, however, and I find it difficult to conceive how such an argument could be made.  In the absence of any argument for either assertion, it stands to reason that the inevitable conflict of wills between two omnipotent beings makes it logically impossible for there to be more than one omnipotent being, and thus logically impossible for there to be more than one God.