I'm to present an imaginary world of vessels (containers) where each two vessels are separate from each other as it is the case in the ordinary world, a vessel is a hollow container. Now lets say in that world each container can only contain vessels inside it, and that each container possess a containment rule that dictates which vessels are allowed to be contained in it, and also lets stipulate that no two distinct vessels can have the same containment rule. Now we define an "actual containment instance" as the actual containment of a single vessel inside a vessel at some moment of time, lets denote it by C*, so a C* b means that there is some moment of time t at which the vessel a is contained inside the vessel b. Lets define "potential containment instance" as the allowance of a single vessel to be contained in a vessel, lets denote it by C, so a C b means that vessel a is allowed to be contained in vessel b. Of course this allowance is determined by the rule of containment of vessel b and it has nothing to do with time or the actual occurrence of such containment. Its important to be realized that this allowance might never be actuated, yet this won't affect the status of the "allowance" of containment, its like "invitation", if I invite somebody to the party and the invitee never showed up, still she\he is considered as an invitee. So a container might even possess an allowance rule that allows "itself" to be contained in it, yet there is no moment of time where this containment can happen.

In this game all containers where created at the same time, from the first moment. Its only actual containment of some in others that is time related.

Now to complete the game we add containment rules over the whole world of containers. Like the rules of ZFC for example, so we have for any two containers there is a container that solely allow only those two containers to be inside it, this is the pairing rule, the power container rule states that for every container A there is a container B that allows every container that can contain some of what container A contains, to be contained in it, and only those, etc...

We can stipulate that at each moment in time only finitely many containers can actually be contained inside a vessel. We can imagine a container that has a 'fulfilled' containment rule in which the empty container is contained inside it at some moment of time, and if any any container was contained inside it at some moment of time, then the container that only allow that to be contained in it, would also be contained inside it as some moment of time, and no other than those are permitted to be contained inside it. This container would stand the set of all iterated singleton sets of the empty set. This would be the axiom of infinity.

Now those containers can emulate sets and the actual containment instance can emulate set membership, while the potential containment instance can be useful in non-well founded set theories, or in accommodating large cardinals.

The real problem occurs if we think that time is just a series of successive moments, much as the naturals, so there would be only countably many moments, this would collide with power containment, since the power container would contain uncountably many containers, but there is no enough time for that since at each moment we can only have finitely many containers inside a container. This would call us to say that time itself is uncountable and it is like a real number line, i.e. a continuous line. But again the power container of that power container would also necessitate a bigger amount of time. So to make this world interpret all sets in ZFC we need to have inaccessibly many moments of time? The other way is to resort to "allowance" rather than actual containment, and keep time countable, which is in some sense weak!

There do not seem to be a problem with imagining such an imaginary game. It emulates set theory in a viso-spatial concrete imaginary manner. It can be viewed in some sense to be illustrative of it.

The problem is that even if we assume the existence of some Platonic realm where all of those vessels exist, still why should we consider such a realm as the basic structure in which mathematics is to be ingrained?

One would prefer his imaginary logical games to in some sense simulate the real world, so they can stand as logical simulation of the real world, some kind of an ideal logically driven virtual reality, or at least help in understanding some intuitive concepts like succession, identity, part-whole, or even some moral or aesthetic aspects like with ethic or music, etc.. this can help as regards applicability is concerned more than going into an imaginary huge flabbergasting mind-boggling world of objects. That is if we want our logical games to be of any significance to knowledge about our own world or in assisting us in our real daily life.