Necessary Thing

[Ignorant]

Well, we can either use the scientific method to investigate observable (testable) reality, or we can speculate further than that. If we do the first, we create models that make predictions, and we test those predictions. We eventually improve the models until they are as close to reality as possible.

I'll start here before addressing the rest.

The "speculations" which extend beyond scientific investigations must be guided either by logical deduction when forming certain conclusions, and logical induction when "creating models that make predictions". A lot of scientific research proceeds by way of inductive reasoning toward the forming and testing of predictive models. In both deductive and inductive investigation, when the logic is poorly applied, you are bound to get poor conclusions and poor models.

If we are speculating about qualities of reality we can't observe, or indeed outside of our own reality, we can't know what is possible and what is impossible...

That is true if the investigation is "speculating" by means of inductive prediction. This is NOT true is the "speculation" proceeds by means of deductive logic. Here is an example illustrating both:

INDUCTIVE (The Prediction of Neptune - [edit] forming a conditional conclusion):

The orbit of Uranus was scientifically observed to have an irregular orbit. Based upon the data of the observed orbit, Anders Johan Lexell suggested that, if another, currently non-observable planet existed, it would explain the irregular orbit of Uranus. Then, based on observed data, other men predicted the position, mass, and orbit of that hypothetical planet. Absent the observation of the planet itself, all of these "speculations" were logically guided, and awaited the validation by scientific observation. That scientific observation eventually happened, and Neptune was discovered (as predicted).

1) Uranus has an irregular orbit

What causes Uranus have an irregular orbit? We have no direct evidence yet.

I) IF another planet existed near Uranus, it would cause Uranus to have its irregular orbit.

1) is true. I) is logically "induced" using a conditional/hypothetical clause and the laws of physics. I) is a CONDITIONAL and logical conclusion from 1) and the laws of physics. Searching for the truth of that conditional led us to the discovery of Neptune. 

DEDUCTIVE ([edit] Non-conditional conclusions)

1) If another planet exists near Uranus, it would cause Uranus to have an irregular orbit.
2) Another planet exists near Uranus.
C) Therefore, Uranus has an irregular orbit.

If 1) and 2) are both true, then C) MUST be true. If 1) and 2) are both true, then it is impossible that C) is false. In other words, if 1) and 2) are both actually true, our observations of Uranus's orbit is irrelevant to the truth of the conclusion that it is irregular.

If C) is false, then it must mean that either 1) or 2) or both are also false or that C) does not logically follow from 1) and 2).

Now, regarding our own discussion, here are my two premises:
1) Some things exist on the condition that another thing also exists.
2) A synchronous and infinite regress of conditions for existence is not possible.

C) Some things exist without the condition that another thing also exists

We agree on 1). If you think 2) is false, the burden of proof seems to be on you to demonstrate its possibility/coherence whatever you want to call it. I'm open to it being false, but for the logical reasons I have provided already a few times in this thread, I can't conclude that it is possible. Can you provide an argument that leads to the deductive conclusion that a synchronous and infinite regress of conditions IS possible?

[edit] If 2) is IN FACT false, then we don't have enough information to conclude whether or not "ALL things exist on the condition that another thing exists", or rather "some things exist without the condition that another thing exists." leaving the argument unable to tell us anything we don't already know.