everything, nothing and something
If the universe develops over time in some specific, identifiable, one-way direction ... and ... that development appears to occur in all places in the observable universe ... then ... the only reasonable, intellectual position one may take is that the universe had a beginning. If the universe indeed had no beginning, the above argument is still the most reasonable track to follow because the "no beginning" track has no empirical evidence to back it up (at present). The "no beginning" idea is backed up only by intellectual conjecture (much of which is well-meaning but still only conjectural).
Hence, I work from the supposition of a "beginning" to everything we observe.
The Initial Set
Consider then the initial state of the universe. It must be a "null set", i.e. there are no members in it ... or ... we may say that it has an infinite number of members which are "self-cancelling" and so leave nothing but the aforementioned "null set".
Then from this null set we must show that we are in some way wrong about it's "nullness" in such a way that its opposite ("everythingness") is not the next alternative. That is, our initial condition is in need of "refinement". So, I propose that "everythingness" replaces "nullness" over what we call "time" - the succession of events that number (objectify or display) the integers. And ... further ... that after an infinite succession of events the state of "everythingness" is achieved which is then congruent with "nullness" (which was given before) and we are back to where we started from.
This does not require that we "do" the universe over and over to achieve the same result. One photograph of "existence" is sufficient, i.e. we needn't make an infinite movie of the same photo. Remember here that the universe as a whole does not exist in time or space ... rather, it is congruent with those concepts so that there is no time or space "before or after" or "outside of" the universe to compare to. So, we can conceive of the concepts of nullness, everythingness and somethingness as being logically congruent members of a set (from that unobtainable, imagined perspective) ...
From another perspective ...
To get from nullness and everythingness to finite things, we must only note that this beginning state is only one state. That is it's special quantity.
So, we now have that the initial set (from the standpoint of a finite observer) must be ...
And this introduces the the concept of "two" since the initial set now has two members.
And this in turn begets the integers.
Straightforward observation indicates that "to be" requires some sort of a show to embody whatever it is that the universe IS and DOES. Hence, we are here ... and do observe the growing and aging universe. This is what we see (at least by my lights).
Understand that "0" and "" are qualities and not quantities. There behavior is mathematically different. When you multiply any finite number by them, you get back the same "0" or "".
But the integers denote quantity and give back a finite number when used as multipliers. "1" differs from all other integers in that it gives back the same number that it was multiplied by, i.e. 1x5=5, 1x243=243, etc.
So that I have only one equation that puts all three "basic" numbers in a logical relationship. Namely,
Sets (which we typically make use of) do not have existential value in the physical world
In logic, a valid set consists of something like ...
Hence, the protons (or perhaps neutrons) are the geometric representatives of the integers. And, as I have pointed out elsewhere, the universe does not "save" information encoded on our brains nor will it save genetic information except by the accidental arrangement of DNA which continues on only because of its atomic properties.
Thus, a proper explanation of existence only requires a limited understanding of its simplest attributes, i.e. physics, elementary logic and geometry.
This leads to another way out of Russel's paradox
"A" is the set of all sets which are not members of themselves.
There are a few workarounds on the table such as dealing with "types" of classes and forming classes from the "bottom up" (empirically).
From the perspective of the physical universe, no such classes or sets exist. They are human concepts not recognized by phenomenal logic. Human concepts (like dreams) are not subject to physical restrictions nor is our logic then the "pure" logic that we suppose.
An uncontaminated, consistent logic is exemplified only by the physical world at the atomic level ... by definition. Ergo, we cannot suppose that "nature" is confused by logical conundrums. These are our inventions which we have ascribed to nature thinking that they are reasonable ones belonging to that purest state.