You are beginning to worry me. Your agreement is too easy; I get the feeling that you are just trying to draw me out so you can flush the whole thing at one fell swoop. Of course, that could be no more than paranoia so I will ignore it; you leave me no choice but to proceed with my argument. Considering your agreement to this point, I will try very hard to make myself as clear as possible. I will probably fail but hope dies hard in the soul of a true believer! (I believe that things should make sense!)
The next step I propose is to label these "things". Now I know the compulsion would ordinarily be to provide English words for these labels; but I am of the opinion that English words (no matter what words you were to choose) carry with them implications which may or may not be true (define true any way you wish; after all, this discussion is still in the realm of vague poorly defined terms).
My proposition is to label these "things" with numbers. Numbering a "thing" says nothing about what that "thing" is. The fundamental purpose of these numbers is solely to catalog these "things" in order that we can specify what "thing" we are referring to without making any attempt to define that "thing" or specify exactly what label will be used.
Since the number of numbers is infinite (here I rely on the field of mathematics which I take to be well thought out; at least well beyond my abilities to criticize), if follows that it is possible to label any quantity of "things" with numbers, totally independent of what those things are. The only difficulty which arises here is the abstract conceptual possibility of infinities; there are mathematicians who would balk at such a mapping if the quantities are infinite. It is my contention that the infinite issues are moot as we cannot consider an infinite number of "things"; that is, any achievable conception of the universe must be based on a finite quantity of different things for, if the quantity is infinite we cannot achieve the stage of considering them all (there will always be some which have not yet been considered). Now the quantity being considered (at this point, being considered means nothing more than having a number attached for the purpose of reference) can always be larger than any given number so there is in fact no constraint on the actual quantity which can be considered.
Please note that I am not specifying any procedure at all as to how this numbering is to be accomplished; I hold only the fact that a numbering procedure is possible (any procedure at all will do). It follows that, no matter what these "things" are, if we knew what they were, we could attach a number to each and so use these numbers to refer to them. That being the case, I will refer to the number attached to the "thing" which exists or attached to the "thing" which is imagined to exist (see point #5) instead of the actual thing itself. It should be clear that this is no more than a cataloging procedure and is, at this moment entirely open as it constrains what can be represented in no way at all.
In an attempt to be consistent with the format of my presentation to date, I will assert this conclusion as point #6:
***6. It is possible to label all of these "things" with numbers.
Have fun -- Dick