The Way of Ways

Here are three names:

Newton       Descartes       Cantor

Here are three ways of having some (more than one, less than all) of those names:

Newton       Descartes

                   Descartes       Cantor

Newton                              Cantor

Note that even if no one had ever thought of having some of those particular names, there would still have been those three names, and each of those pairs of names would still have been some of those three names, so there would still have been those three ways of having some of them.

And because there are those three ways, there are, similarly, three ways of having some of those three ways.

And there are, similarly, three ways of having some of those ways.

And so on endlessly.

There are, in short, infinitely many ways of that kind. And there are far more ways of having some of those ways. And far more ways of having some of those ways. And so on endlessly.

And because there are all of those ways, there are far more ways of having some of those ways. And far more ways of having some of them. And so on endlessly.

And so forth, endlessly.

And because there are all those ways of having some of some things (starting with those three names), there are also, for every way of having some of them, those ways. And so on endlessly. And so on and so forth:

For each of these ways of having some of some things (starting with those three ways of having some of those three names), there is that way because there are all of those things.

Does it follow that there are all the ways of that kind?

It does seem to; although if there were all of them, then there would also be every way of having some of them, because for each way of having some of them, the ways that that way would be a way of having would be some of the ways of that kind, and there would be all of them. Indeed, there would be more of those ways of having some of the ways of that kind than there would be ways of that kind.

Even though those ways of having some of the ways of that kind would all have fallen under the scope of that "and so on and so forth" and would therefore have been ways of that kind.

That contradiction means that it is logically impossible for there to be all of those ways.

It did seem to follow that there would be all of those ways, though. That is a logical (or ontological) problem, not a mathematical (or formal-ontological) problem, and because it has a theistic solution that is perfectly logical (see the Google document Freedom for that solution), it is a problem for rational atheism:

In the absence of an atheistic solution that is perfectly logical, not just formal-logical, that theistic solution amounts to a perfectly logical refutation of atheism.

It amounts to a proof (an ontological proof) that there is a creator of all things whose view of all things determines and defines them and whose opinion of them is therefore the only opinion that really matters, at the end of the day.