- I exist.
- If there is something that exists, then God exists.
- Therefore, God exists.
- Every object has a cause.
- Causal chains cannot be infinite.
- Therefore, if something exists, then it must be the result of a finite causal chain.
- The beginning of that chain is God.
- Every contingent object implies the existence of another object, namely, its cause.
- Causal chains cannot be infinite.
- Therefore, if a contingent object exists, then it must be the result of a finite causal chain, which can only begin with a non-contingent (or "necessary") object.
- That necessary object is God.
Now that we've gotten to a reasonably good formulation of the cosmological argument, we can question its premises.
The first premise assumes every contingent object has a cause. But is that really true? I'd question the very idea that causation is a truly fundamental concept. For example, it is possible to describe physical laws without the notions of cause and effect. Furthermore, you have to consider the full range of contingent objects. My keyboard is contingent, and has a cause, but what about more abstract things? Is time contingent, and does it have a cause? Is love contingent, and does it have a cause? Maybe you think so, maybe you don't.
The second premise assumes that causal chains cannot be infinite. But why can't they? Plenty of religions see the world as being in an infinite cycle, so what's logically impossible about that? If a particle is moving along in space, you can say that its arrival at any point B was caused by its previous position at point A. And then you could follow its path back indefinitely. Of course, in our universe, it is difficult to actually do this, because the path will eventually be traced back to the Big Bang. However, as a matter of science, I will say that the Big Bang is not certainly the beginning of the universe, and is almost guaranteed to be a mere wall past which our current understanding of physics is inconsistent. Near the singularity, Quantum Mechanics and General Relativity contradict each other, indicating that we need better theories before we can reliably determine that the Big Bang was truly a beginning.
But my above objections, while valid concerns, are not the real killers of the cosmological argument. The unsolvable problem in the cosmological argument is in step 4. This problem remains in every variation of the cosmological argument I've ever seen. Though we might prove the existence of a necessary being, why must it be God? Perhaps you'll say that the necessary being is God by definition. But if you've given God this new definition, there is no guarantee that it will have all the other traits normally attributed to God. Must the necessary object be conscious? Must it be good? Must it be omnipotent? Must it be singular rather than plural? Would it even make sense to worship, respect, or ponder this object? None of these are guaranteed, much less the idea that the necessary object listens to prayers, or sends prophets.
Personally, I think the necessary object is probably the world. Nothing unusual about that. The world is simply the ground of all possibilities. Without the world, things couldn't possibly exist within it. There you go.