Is the existence of two infinite beings possible (logical)?
What are the arguments for / against the possibility of the existence of two infinitely powerful beings?
What do you mean by "infinitely powerful", and what does it mean to be infinitely powerful in an intelligible universe?
Suppose you mean an omnipotent being. Is it possible to have two omnipotent beings? As I've noted elsewhere (see my remarks on the notion of 'unmakability'), this depends on what you intend "omnipotent" to mean — what the range of possible powers there is in the world.
For instance, an omnipotent being could presumably destroy any object, including another omnipotent being. Is this a contradiction? Not really, though it depends on the details. If the omnipotent beings both have the power to make each other cease to exist instantaneously without reaction, then it would simply happen as soon as one (or both) of them willed it. But can't either of them make themselves impervious? That depends on whether there's any particular mechanism to destroying objects — resistance against destruction only means that it can prevent that which brings about destruction from succeeding. So how one of the beings could possibly resist destruction now requires us to consider that there be a mechanism for the destruction: that is, that the world is one of mechanical principles, and the omnipotence of these beings consists in unfettered access to the resources (such as energy) by which the mechanism operates. Pretty much any impasse that can arise from two omnipotent beings can be characterized in this way: if one wants to make X happen and the other wants to prevent X from happening, then we must consider the mechanism by which X is possible — or posit a world in which the notion of "something happening" is much more complicated and nebulous than it is in our world.
Let us continue to consider the possibility of being A destroying being B. With normal physical objects, to see if one would be able to destroy (for instance, penetrate into) another, we would have to consider a balancing of forces: to see which force is greater, and consider the net effect, which consists of the difference between one force and another. With this sort of situation, involving what amounts to an immovable object and an unstoppable object, the corresponding difference of forces would be of the form ∞ − ∞ , which is a classic indeterminate form. When this occurs in mathematics or in physics, the message that one obtains is either that not enough information has been provided to obtain an answer, or there is no well-defined answer.
In the above, I have made one key assumption: that whatever powers we assume that these omnipotent beings have, that these powers are somehow intelligible. In essence, that despite the existence of these beings, that the universe is a world of laws, and that the power of these beings to do what they please stems from complete mastery within those laws. I see no way to answer this question — or indeed any other question whatsoever — if we assume that the universe is unintelligible even in principle; so I think this assumption is quite reasonable if we're going to entertain the question at all. But an important consequence of this assumption is that the question attains a definiteness which is not typical when such problems have been considered historically, and how precisely we choose to make the question definite enough to be answerable — what specific conditions we suppose in terms of how A and B act — will change the nature of the answer.
Two Von-Neumann Agents in a box can be modeled as one Von-Neumann Agent, if all you can ever see is the outside of the box. If the agents are using an advanced form of decision theory, they can even make meaningful decisions inside this box (collaborating on prisoner's dilemma), despite differing utility functions.
Von-Neumann Agents by mathematical definition can carry out infinite amounts of perfect reasoning in finite time, so they are in a sense infinitely powerful.
ETA: Further information and loose sources:
If there is a pair of coexistent necessarily omniscient and necessarily morally perfect omnipotent agents, then there is a pair of incompatible contingent states of affairs each of which is morally optional for these agents, that is, neither morally prohibited nor morally required for them.
If a plurality of coexistent omnipotent agents were even possible, then possibly, at a time, t, some omnipotent agent, x, while retaining its omnipotence, endeavors to move a feather, and at t, another omnipotent agent, y, while retaining its omnipotence, endeavors to keep that feather motionless.
Intuitively, in this case, neither x nor y would affect the feather as to its motion or rest. Thus, in this case, at t, x would be powerless to move the feather, and at t, y would be powerless to keep the feather motionless!
But it is absurd to suppose that an omnipotent agent could lack the power to move a feather or the power to keep it motionless. Therefore, neither x nor y is omnipotent. This line of reasoning appears to reduce the notion of a plurality of coexistent omnipotent agents to absurdity.
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If two beings are infinite in sense of ℵ0 there's nothing to keep them from coexisting in an ℵ1 universe.
A human is infinite in that a body can be subdivided infinitely (only conceptually beyond Planck size but still.) Yet there are many humans.
Or do you mean something else by infinity? Omnipotence?
Omnipotence only implies a specific potential at any given point of time: an omnipotent being may choose for anything to happen at any given point of time [not necessarily current]. Still, while the moment of effect is arbitrary, the moment of choice is specific and a subject of normal laws of casualty.
One of two omnipotent beings coexisting in a single universe may wish the other removed from existence, back since their beginning, or limit their omnipotence, say, by making self immune to such effect. Still, the moment of such action is a specific point of time. If one has been deprived of means of harming the other, including going back in time to undo that wish, they are no longer infinitely omnipotent. In that case two such cannot coexist. But then, if neither makes that choice, they are still both omnipotent - conditionally; until one choose to deprive the other of it.
Yes, power on one axis/being would simply be distributed in time on the other. Given that they are eternal as well as infinite, the more likely scenario is that they're wise enough to negotiate the boundaries are. Since there is a documented story of one such infinite being gaving rise to another being, that is the likely trajectory of Man if and when He/She completes their journey of Knowledge.