These are in progress and subject to revision. Feedback welcomed.
The subpoints provide further clarifying thoughts or definitions.
Presuppositions
Self-contradictions cannot take place or be true.
Premises
Assume all things are caused, including the whole of existence.
The “whole of existence” refers to everything, collectively considered, that exists, has existed or will ever exist.
If true, then a cause exists of the whole of existence.
A cause exists distinct or apart of its effects.
Causes are not identical with their effects.
Therefore, assuming all things are caused, then a cause exists distinct or apart of the whole of existence. (Definitional Substitution on #1-3)
A thing or quantifier distinct or apart of the whole of existence doesn't exist.
Therefore, assuming all things are caused, then a cause exists and doesn't exist of the whole of existence, which is a self-contradiction. (Definitional Substitution on #4-5)
Therefore, the assumption that all things are caused is false. (Reductio ad Absurdum on #2 & #6)
Therefore, not all things are caused. (Double negation elimination on #7)