Asked in Atheism, Creation

What is the evidence for the first premise of the cosmological argument?



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It is based upon logic only.

However, it is a fallacy to appeal to the Cosmological "everything must have a creator" argument in trying to explain the existence of God, since it leads to the "What created God" retort. Everything created needed a creator, but God is not in that category.
Rather, you can show God's existence by pointing to the bottomless, infinite wisdom which we see in the Creation.
True, some people are willingly blind to this wisdom and are not moved even when you point it out in detail, but all you can do is your best. Talk to your children and to anyone who doesn't have preconceived notions.See also:

Can you show that God exists

God's wisdom seen in His creations

More about God's wisdom

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If you mean the Kalam cosmological argument used by William Lane Craig in which the first premise is "Everything that has a beginning of its existence has a cause of its existence." The answer is that there is no evidence for this claim. In fact there is evidence to the contrary.

In quantum mechanics, things happen that are not caused. Such as radioactive decay or when an atom in an excited energy level it loses a photon. No cause is evident in the decay of a radioactive nucleus. Craig has said that quantum events are still "caused" just in a non-predetermined manner - what he calls "probabilistic causality." Craig is thereby admitting that the "cause" in his first premise could be an accidental one, something spontaneous and not predetermined. he therefore destroys his own case for a predetermined creation. Even if the KCA was sound, why would the cause itself not be natural?