Necessary Thing

[Ignorant]

I've been thinking about this more, and I might now understand why I am confused. I think that this "depends upon" or "contingent" language is being used in such a way that A is contingent on B if A makes up a part of B. So that B as a whole will not "exist", if one of its parts ceases to exist. I find this rather strange, if this is the case. It's a complete tautology. If something is made up of parts, then if any of the parts are missing, then not all the parts are there. What are we even investigating?

After reading your post, I think we are certainly approaching a common understanding of the terms, but I'm not sure we are there yet. Above, the contingency of A and B is worded a bit backwards (which could be just simple error, you tell me after I explain), and that makes a big difference. Also, The bit about the sum of its parts is getting closer, but with an important thing missing. Let me explain:

A is contingent on B if B makes up a part of A (not the other way around as you have written). So that A as a whole will not exist if one of its conditional parts ceases to exist. 

This is not a complete tautology. If something is made up of parts, and if any of the parts are missing, then the "something" is not there (as opposed to the parts not being there, as you wrote). In fact, the "something" could not exist without its parts, and so it is contingent upon them. Its own existence as that thing depends on the sum of the parts. <= An in that proposition, is contained a very important aspect of all of this. I return to the Helium atom:

A helium atom exists on the condition that two protons exist. <= That is true, but it is not the entire story. If you had a hypothetical container, and all you knew of its contents was that "two protons are in the container", without more info you can't know if you have two hydrogen atoms or a single helium atom or some other thing(s). What is that missing information? It must be an additional condition of helium's existence.

Because of previous scientific investigation, we have learned that, in order for helium to be present, the two protons must be existing in a certain way. If the protons are existing in that way, then the two protons are existing as helium. If they are not existing in that way, then helium is not existing in the container.

This directs us to perhaps an aspect I have not been clear about, or else haven't spent as much time on. Some things are made up of parts, and depend on most if not all of the parts for existence. However, the mere existence of all of the parts does not equal the existence of the thing. The sum of the parts must exist as the thing which depends on them. This principle is why it is not a tautology. Instead, A contingent on B is more of an existential definition derived, not from arbitrary language, but from scientific observation and investigation. This definition is ether more or less adequate depending on the number of true conditions (i.e. contingencies) it contains as elucidated through the scientific method. For example: 

Helium exist on the condition that two protons exist synchronously. <= That is a true definition, but an even more adequate one is: 

Helium exists on the condition that two protons exist synchronously, bound together in a nucleus. <= An even more adequate definition would be:

Helium exists on the condition that two protons exist synchronously (which exist on the condition that X exists synchronously, which exists on the condition that Y...), bound together in a nucleus (a bond which exists on the condtion that Z exists synchronously, which exists on the condition that W...), etc. 

Each condition is simultaneously a description of the what (i.e. definition) of the immediately greater whole.

I was approaching the problem with less assumptions. I was taking it to mean that the existence of entity A is contingent upon the existence of entity B if the sudden non-existence of B would cause the non-existence of A. I wasn't making any further implications as to how this is actually caused; just that it is cause and effect.

The bold part is certainly true, and it is a part of the concept for sure. If a fundamentally conditional part of the whole suddenly stopped existing, then the whole also stops existing. And if a fundamentally conditional part(1) (which is a condition of part(X) which is a condition of the whole(A)) suddenly stopped existing, then part(X) synchronously stops existing, and of course, the whole(A) synchronously stops existing. Part(1) is a part of a part of the whole, and yet the whole immediately and synchronously depends on its continued existence. Each fundamentally conditional part of the whole must exist synchronously together as  the whole(A), if the whole(A) is to exist at all.

How does part(1) cause part(X) and whole(A)? That's not relevant to this particular sort of analysis. In fact, all that this analysis requires is that part(1) really does contribute to the synchronous causing of part(X) and that part(X) really does contribute to the synchronous causing of whole(A). The "how" is an interesting question, but not for our question here. Instead, we merely rely on the findings of the scientific method which informs us that a causal relationship actually exists (e.g. like how science informed us about the part(two protons) fundamentally contributing to the causing of the whole(helium)).

If the problem is in fact only referring to the tautological version of "contingent", then the question simply becomes whether there's some sort of infinite regression of things piled on top of other things. So the bits of the helium atom or whatever are piled onto the rest of the atom, then the atom is piled onto the fabric of reality say; so that if reality ceased to exist there would be no place for the atom to exist in. (Or we could say "reality and everything in it" is contingent upon any of the things in the reality... you see what I mean about a tautology. You could of course use a bunch of other groupings first, such as the object containing the helium atom; and then the solar system containing the object... and so on. However you want to do it. Identifying groups of entities is entirely arbitrary.)

Thinking about it as piled "up" might be unhelpful. Rather, think of it as piled "in" within other things. So, the "bits of the proton" are piled "in" the protons and as the protons, which are piled "in" the helium atom and as the helium atom. What are the things piled "in" the "bits of proton" as the bits of proton? I don't know. Science may know (quarks or something, someone more knowledgeable can tell us) This thread is not looking for the answer to that question. 

Instead, this thread is asking: can this sort of questioning, in principle, go on infinitely? <OR> Does deductive logic tell us that we will necessarily arrive at some fundamental thing(s) which are not piles of anything, but which just exist without condition? It/they just exist(s). If it/they didn't exist, then nothing else could exist. If it/they stopped existing, so would everything else at the same time. Why? Because they lie at the fundamental center of every pile of parts of whole things.