How can one with limited, finite knowledge possibly know with absolute certainty that there is no eternally, immutably self-existent first cause?
One cannot. I do not claim absolute certainty about such matters. I am an agnostic adeist with respect to the question of whether within reality there is some fundamental ground of all being that is eternal, immutable, and self-existent and therefore worth calling a “first cause”. I neither affirm nor deny that proposition but explore its potential metaphysical implications and inferences. My refusal to either accept or rule out the existence of such a metaphysical principle and my belief that at present the evidence is too inconclusive for anyone to properly affirm or refute belief in it makes me an agnostic with respect to that conceivable entity (assuming it is in fact a coherently and meaningfully conceivable entity). Since those bare traits (eternality, immutability, self-existence, and function as a first cause) are all compatible with mere deistic conceptions of the ground of all being and not at all unique to theism, I see my non-affirmation but theoretical uncertainty and openness to the proposition that such a being exists as only an agnostic adeism, rather than an agnostic atheism.
That said, I am a gnostic atheist (rather than an agnostic simpliciter or an agnostic atheist) because I see no reason whatsoever to think such a being as Ku described, even if it did exist, would be a personal being. In fact, as a basic metaphysical principle it would in all likelihood be nothing at all like those anthropomorphic projections that religious believers worship–i.e., nothing at all like Zeus or Thor or Yahweh or Jesus or Spider-Man. Those are all equally clearly anthropomorphic fictions dreamed up by human imaginations.
If there is an immutable, eternal, self-existent first cause it is nearly certainly impersonal as numbers are, as abstract entities are, as the fundamental laws of the universe, and the fundamental particles are. Personhood is a complex phenomenon made up of trillions (or more?) molecules interacting. It is an evolved phenomenon, specific to very particular kinds of beings. To impute it to the most basic metaphysical principle is sheer unjustified anthropomorphism. There is no reason to think an eternal, immutable, self-existent first cause would have any personality. It is as laughable as saying that it carries honey from flower to flower (as a bee might fantasize in hubris) or that it looks for mates by singing (as a bird with delusions of specialness might infer). Also given that personal beings as we know them are temporal as a matter of fundamental constitution, the notion of an eternal and immutable personal being is incoherently contradictory and therefore a logical impossibility.
With no reason to think that the thus far unprovable and irrefutable notion of an immutable, eternal, self-existent first cause would have a personality and many reasons to think it would not, I feel comfortable saying there are no personal gods. That makes me an atheist who thinks we can know with a very high degree of confidence that there is no personal god. I call this “gnostic” (or knowing) atheism.
Also, I see no reason to infer that an immutable, eternal, self-existent first cause would be any more likely a being separate from either our universe or, say, a total multiverse rather than its most foundational feature. In fact, the principle of parsimony leads me to think that it is somewhat more likely that if there is such a being it is a feature of Nature (or is “Nature itself”) rather than anything mysteriouslyoutside the universe or multiverse. These considerations make me quite confident that preponderance of the evidence is that even if there is an eternal, immutable, self-existent first cause that is meaningfully and coherently capable of conceptualization and demonstration, it is not a being independent of the universe (or multiverse). It is more likely and more rational to infer that it either inextricably expresses itself as the universe or multiverse (as Spinoza argued) or it is just an integrally connected “piece” of the universe or multiverse.
These considerations also make me think that the metaphysical proposition of a theist god is most likely false. It is likely enough false that I feel confident in saying that I know that no theist god exists. Therefore, again, I am a gnostic atheist. I am not absolutely certain but I do not need to be to make knowledge claims. None of my knowledge claims are absolutely certain. I am open to considering new arguments and even though I think I know I could be wrong and even could be persuaded that I am wrong. But based on everything I know and have read at present, I feel confident enough to say that I know.
There is no God.
(By which I mean more specifically, “There is no personal/theistic/interventionist Yahweh, Allah, or any other personal god believed in and worshipped by the world religions.”
Below are links to just three key posts, one defining different kinds of atheism and two explaining more of my reasons for rejecting personal god theism: