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Cosmological Argument The First Mover

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Cosmological Argument: The First Mover
I think that the argument contains a major fallacy. Although I agree by the argument’s conclusion that there is a timeless, eternal, God, I would not use it to argue and prove God’s existence because it contains a non sequitur fallacy. I think premise 2 as presented in Aquinas’ second way (Miller and Jensen 224) contradicts the conclusion.
All this boils down to really is the claim that the argument is making that:
Everything that exists has a cause (first way – something can’t come from nothing). The universe exists. Therefore, there must be a cause for its existence (second way – could not be the cause of itself). Thus, if the universe has a cause for its existence, then that cause must be caused by

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