The obvious problem with that premise is that once you reach the conclusion, since everything that exists must have a cause, you have to ask what caused the intial cause, leading to infinite regress.
Agreed. Hence the modification of the premise.
By stating in P1 that everything that BEGAN to exist must have a cause, it assumes that there is an object, or class of objects really, that didn't begin to exist.
Rather, it assumes the possibility of a class of objects that didn't begin to exist. However, to argue that this makes a logical fallacy of a solid premise is just plain foolishness.
The premise that "what goes up must come down" used to be considered a simple truth. Then we discovered that if an object moved away from the earth quickly enough, it wouldn't come down. Thus we would have to modify the premise to, "What goes up below a set escape velocity must come down." Yet doesn't this assume a class of objects that acheive escape velocity? Yes, but so what? This in no way disproves the modified premise.
Neither does the assumption of a class of object that is eternal--that is, outside of the constraints of the physical dimension of time and hence without a beginning--create a logical fallacy in P1. And indeed, the assumption of such a class of object is the result of a simple use of Occam's Razor to break the otherwise infinite regress of causes.
Unfortunately that is what the conclusion of the argument is trying to demonstrate and, of course, you can make *any* argument work by stating or assuming the conclusion to be true in one of the premises.
You mistate the point. P1 is that "Everything that begins to exist has a cause." It is an unarguable point that stands independant of either P2 or the conclusion. Let me give you another example along the same vein:
P1: Anyone who is alive has to breathe.
P2: You are alive (I assume).
Conclusion: You have to breathe.
Now, the second premise is in no way predicated on the first. You could just as easily be dead. Likewise, the universe could just as easily be eternal, without beginning or end. If it didn't have a beginning, the conclusion of the argument would not follow.
But the universe did indeed have a beginning. Even if you dispute Big Bang cosmology, the Second Law of Thermodynamics tells us that in an infinitely old universe, there would be infinite entropy. For that and other reasons, we know for a fact that we live in a universe that has a beginning. Therefore, P2 is both independant of P1 and a solid position.
The problem is not with the logic of the argument. The problem is that you do not like where it leads.
Yours in Truth,