Let's say that we grant that item "X" is eternal. By "eternal" we mean that it has always existed and that it always will exist.
Because "X" is eternal, does it follow that it MUST be uncaused?
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Causality and time are so intertwined that they’re nearly synonymous.
Time is a frame which we construct in order to capture causality. If you remove causality, you remove time, and if you remove time, you remove causality.
A cause comes before its effect. That is in fact how we understand “before”, the meaning we assign to it. A clock measures time by counting up how many pendulum swings or crystal vibrations or atom transitions have occurred before you looked at it. It is measuring change, counting effects.
If the effect is eternal, atemporal, then the concept of “before”, and therefore “cause”, is empty, meaningless, nonsense. It unasks the question by a priori embedding its answer. By saying the words “it has always existed”, you are saying the words “it is uncaused”.
Yes. Because "X" is an eternal, its cause must also be the continuity of that eternal. Otherwise you will get a discontinuity or you will have to agree that its cause existed before that eternal. This implies that the eternal you grated the item "X" is not eternal. And it becomes a folly. This necessitates or asserts that the thing you believed as the cause of the eternal must be that eternal itself. So the eternal object must be uncaused. Indian philosophers have already named it 'Brahman'. It is the causeless cause or the Uncaused. I believe, in some religions the word 'God' is also used synonymously to represent the Uncaused.
This link might also be useful: Kāraṇa, the Causeless Cause