It's a matter of your premises, not your conclusion.
The First Cause argument says, effectively:
- there has to be an uncaused "first cause"
And arguments are typically provided in support of such claim. If you disagree you are expected to deal with such arguments.
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Yes that is part of the definitionof God.
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The KCA doesn't commits you to that claim, there could be other uncaused stuff.
Some philosophers of math and scientists claim that numbers are abstract objects (and therefore uncaused)
You can in principle propose the existence of a timeless (and uncaused) string
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therefore, by process of elimination, the only thing available to be a "first cause" is God.
The KCA provides a detailed explanation for why the the first cause most be timeless spacless inmaterial personal etc. We simlly call it God (you can give it an other name)
To get to your conclusion, you need to establish your premises. That's what this is all about.
And arguments are typically provided in support of those premises. If you disagree you most deal with the arguments.
Imagine someone who was trying to diagnose a disease said "well, out of the 10 different viruses on our short list, we know enough about 9 of them to say that they don't cause the symptoms we're seeing. That means that the disease must be caused by the 10th virus on our list, a mystery virus that we know basically nothing about."
Do you think it would be off-base for one of the other researchers to say "hang on - let's figure out if that mystery virus can even cause the symptoms before concluding that it must be the culprit"?
And even that analogy is overly generous. What you're doing here is more like arguing "because 10 different viruses couldn't have caused the symptoms we're seeing, the disease must have been caused by a wizard's curse. And don't bother me with questions like 'are wizards even real?' and 'can they actually cast spells?' I've proven my case."
That is a strawman the KCA is not a process of elimination. (But as a sude noteI don't see anything wrong with process of elimination ) for example Dark Matter was proposed as a consequence of a process of elimination.
However the KCA is more like
P1 simthoms X and Y are caused by viruses
P2 John has simthoms X and Y
P3 John has a viral infection.