The Way of Ways

There is something extremely puzzling
about there being more than one thing.

Consider, for example, these names:

Descartes             Newton             Cantor

Because there are those three names, there are, of course, these two:

Descartes             Newton             Cantor

And there are two other ways of having two of those names:

Descartes             Newton             Cantor

Descartes             Newton             Cantor

And there are three ways of having two of those three ways:

There is having the blue and green ways.

There is having the green and brown ways.

And there is having the blue and brown ways.

And because there are those three ways (ways of having two of the ways of having two of those names), there are three ways of having two of them. And because there are, there are three ways of having two of those ways. And so on:

Whenever there are three things, there are three ways of having two of those things.

There is no end to this, no final three ways of this kind (because for any three things, there are three ways of having two of them), so there are infinitely many ways of this kind (the word infinite comes from the ancient Greek for unending). Of course, infinitely many things is an awful lot of things to have, given only three names; are there really all of these ways? Well, those names clearly exist, and because they do, there are clearly three ways of having two of them. And because there are those three ways, there are, similarly, three ways of having two of them. And so on endlessly:

Each and every way of this kind exists because of the existence of the three things that it is a way of having two of.

Could these ways of having some of some things (ways that exist because of the existence of those things, starting with those three names and continuing in the endless sequence described above) be coming into existence endlessly? Could there be more and more of them forever, without there ever being all of them? Well, although it takes time for us to read descriptions of these ways, there does not seem to be anything like a temporal process involved in there being these ways of having some of some things. Whenever there are three things, there will of course be each and every one of them, so the existence of each and every way of having just one of those things is immediate and automatic, and there being each and every way of having two of those three names certainly seemed, at the beginning of this post, to be similarly immediate and automatic; and if, whenever there are three things, the existence of each and every way of having two of those things is immediate and automatic, then there will be all of those ways of having some of some things. So, presumably there are all of them, and so there will presumably be each and every way of having some (more than one, less than all) of them:

Each way of having some of them is a way of having some things all of which we are assuming there are.

And presumably there will, for the same reason, be even more ways of having some of those ways. And even more ways of having some of them. And so on endlessly. And given that there are all of those ways, there will presumably be even more ways of having some of them, and even more ways of having some of those ways, and so on endlessly. And so forth, endlessly. And given that there are all of those ways of having some of some things (starting with the blue, green and brown ways of having some of those three names), there will presumably be even more ways of having some of them. And even more ways of having some of those ways. And so on endlessly. And given that there are all of those ways, there will presumably be even more ways of having some of them, and so on endlessly. And so forth, endlessly. And so on and so forth:

For each and every one of these ways of having some of some things, that way exists because of the existence of all of the things that it is a way of having some of.

And of course, if each and every one of them exists, then they all exist. However, if there were all of them, then there would also, for the same reason, be all of the ways of having some of those ways: given that there are all of those ways, there is each and every one of those ways, of course, and each and every pair of those ways, similarly, and each and every way of having three of them, and so on endlessly, and also each and every way of having infinitely many of them, similarly. Those ways of having some of the ways of that kind would exist in addition to the ways of that kind, so presumably they would not be ways of that kind (and a precise mathematical reason why they could not all be ways of that kind is described in the Google document linked to below).

But those ways of having some of the ways of that kind would all exist because of the existence of all of the things that they would be ways of having some of, and those things would all be ways of that kind, so 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," if they existed, and would therefore be ways of that kind, if they existed (and while the phrase "and so on and so forth" is rather vague, the terminology in that Google document is much more precise).

And they would exist if there were all of the ways of that kind; so, as well as the rather logical reason why the ways of that kind would all exist, there is an equally logical reason why they would not all exist: if they did, there would be things that would be what they could not be.

A solution to that logical puzzle is described in my booklet Freedom (that link opens a 26-page Google document in a new window). In that booklet I describe how such logical versions of Cantor's mathematical paradox show that there is a God because only a God would be able to create such things as those ways in a never-ending (but not necessarily temporal) process of creation.