Everything exists

[Tiberius]

So a proposition with no supporting propositions is able to operate as a stand alone statement that requires something to disprove it?

No. Nothing is allowed to stand alone, and this is why there are so many arguments for and against the existence of God. Each one has numerous flaws that have been pointed out over the years. If one logical step is shown to be illogical, the argument falls apart.

Take the Cosmological argument for the existence of God: ( simple version taken from http://www.philosophyofreligion.info/the...l-argument )

(1) Everything that exists has a cause of its existence.
(2) The universe exists.
Therefore:
(3) The universe has a cause of its existence.
(4) If the universe has a cause of its existence, then that cause is God.
Therefore:
(5) God exists.

Note that (1), (2), and (4) are the premises, and (3), (5) are the conclusions.

The first part of the argument is sound. Given (1) and (2), (3) logically follows. (1) is also verified by causality, and (2) by observation.

Where the argument fails is in step (4), where the assumption is made that God is the cause of the universe existing. This is, as you would put it, a standalone statement, which is as unverifiable and illogical as me saying:

4) If the universe has a cause of its existence, then that cause is Pizza.
Therefore:
(5) Pizza exists.

It is an invalid argument because whilst the conclusion (5) does follow logically from the premises, the premises themselves are unverifiable and illogical. Premise (4) commits a non sequitur by arguing that the cause of the universe existing must be God, when this does not necessarily follow.

Further, the argument can be questioned itself by relating the conclusion (5) back to the premise (1). Since God exists, and by (1), everything that exists must have a cause for existence, God must have been caused to exist.

This poses problems on two fronts. Firstly, if we accept that God has a cause to its existence, then positing God's existence in order to explain the existence of the universe only increases the complexity of the question. We find ourselves continually asking "Ok, X caused Y, but what caused X?".

Secondly, if we reject the notion that God has a cause, then the existence of God (of which the argument seeks to prove) is a counterexample to the first premise of the argument itself. If God exists but doesn't have a cause, then (1) is false, and the argument is unsound, since if (1) is false, one could argue that the universe itself could be uncaused, and the argument proves nothing.