The Kalam Cosmological Argument, the argument most commonly used by Christian apologists today goes as follows:
1. Everything that begins to exist has a cause.
2. The Universe began to exist.
3. Therefore the Universe must have a cause.
This is a logically airtight argument. The first and second premises cannot be refuted, as they are logically correct. We can observe, in our own Universe, that if something begins to exist, there is a cause for its existence. For instance, a star begins to exist when cosmic gas and dust coalesces into a massive proto-stellar ball, which, once nuclear fusion begins, it begins to exist as a star. We also obviously know that the Universe began to exist. The third premise, however, has attempted to be vitiated, but every argument against it has been refuted time and time again.
The argument that the Universe has, in any way, shape, or form, existed eternally is logically impossible. If the Universe existed eternally into the past, that would mean that there are an infinite number of events leading up the the present, thusly, you would never reach the present!
The Penrose-Hawking Theorem states that the mass and spacetime of the Universe must have an initial singularity. Also, the Borde-Vilenkin-Guth Theorem states that any universe in a state of cosmic expansion cannot exist eternally into the past and must have a beginning. All this tells us that the Universe did, indeed, have a cause.
This cause of the Universe must itself transcend the Universe and space and time itself, and is not contingent upon these. If it were, it could not create the Universe, as it could not exist wholly apart from it. If it transcends space and time then this cause must be spaceless, and timeless. If this cause is spaceless then it must be immaterial and not physically bound. If it is timeless, then this cause must also be, itself and by its very nature, unaused, beginningless, and unchanging. If this cause exists timelessly that means that it transcends temporality, and therefore can undergo no changes. If it can undergo no changes, then it must be immaterial as material objects are undergoing constant change, especially at the subatomic level. So far we have established that this cause of our Universe must be uncaused, changleless, beginningless, spaceless, timeless, and immaterial.
Secondly, this cause of the Universe cannot be impersonal, as impersonal causes cannot exist eternally without their effects, which would assume the Universe existed eternally, and I've already shown why it can't.
For instance, water freezes at zero degrees centigrade. If the temperature had been zero degrees centigrade from eternity, then any water that was found to exist would have been frozen from eternity. There can exist no point at which the water began to freeze because the temperature has been zero degrees centigrade from eternity therefore any effects must also exist from eternity, such as water being frozen. Therefore, the cause of the Universe must be personal. Since the cause is an eternal cause, it must have the ability to freely choose when to bring about this change or this cause, it must have the freedom of will and, therefore, must be personal.
So, we've established that the Universe cannot be infinite into the past, and must have a cause. We've also established that this cause is by its very nature uncaused, changeless, beginningless, spaceless, timeless, immaterial, unimaginably powerful, and personal. In conclusion, we are brought not only to the inevitable beginning of our Universe, but to its personal creator as well.
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