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First, a common misconception used to argue against the Cosmological Argument:
��it is sometimes argued (e.g., by Bertrand Russell) that there is a self-contradiction in the argument, for one of the premises is that everything needs a cause, but the conclusion is that there is something (God) which does not need a cause. The child who asks "Who made God?" is really thinking of this objection. The answer is very simple: the argument does not use the premise that everything needs a cause. Everything in motion needs a cause, everything dependent needs a cause, everything imperfect needs a cause.� --Peter Kreeft
Ultimately a denial of the "Cosmological Argument" entails either 1.) a denial of one or both undeniable premises by which we know anything at all and by which we actually live, or 2.) a denial of the conclusion(s), which simply combine(s) these premises.
1. A thing cannot both be and not be at the same time in the same way - a thing is or is not (principle of non-contradiction). Simplified: If a thing exists it doesn't not exist.
2. Existing things change - things have potential to be or not be.
3. A thing which has potential, which can be or not be at a particular moment, a.) cannot determine itself to be or not be at a particular moment (or it is violating premise 1, both being and not being at the same time in the same way); it cannot choose it's own path, therefore something must determine it to be or not be or it hasn't been determined-which we know it has; b.) cannot be determined by nothing, for if nothing determined it, then it's the nature of nothing to make determinations; if nothing has a nature, then it's something, and something has determined it--that something must have no potential, it cannot not be; and c.) cannot be determined by another thing with potential, for at the same moment that thing also needs determination.
Additional Conclusion from 3:
4. The universe (a collection of things with potential) can be or not be at a particular moment, therefore it is determined by something which cannot not be (God is the name we give to a being which cannot not be).
OR
1. A thing cannot both be and not be at the same time in the same way - a thing is or is not (principle of non-contradiction). Simplified: If a thing exists it doesn't not exist.
2. Existing things change - things have potential to be or not be.
3. A thing which has potential, which can be or not be at a particular moment, needs a cause to determine whether it will be or not be *.
4. The cause itself (from #3) must not have potential to be or not be, otherwise it�s in the same undetermined state needing to be caused and cannot cause anything.
5. Since every thing with potential existing at a given moment (the universe) can be or not be, then everything (the universe) with potential to be or not be needs a cause at every moment of it�s existence.
6. Something exists which cannot not be, as the cause of existing things which change -- the universe.
*Something is self-evident when it�s opposite cannot be conceived. �Something which changes needs a cause��this is self evident because it�s opposite -- nothing can cause something -- means the nature of nothing is to cause something, which is another way of saying nothing is something (we have to conceive of nothing as something (it�s nature is to cause)). Therefore we cannot conceive of nothing causing something without admitting it�s something. Thus it�s self evident that �things which change need a cause.�