The Argument from the Impossibility of an Actual Infinite
- An actually infinite number of things cannot exist.
- A beginningless series of past events would be an actually infinite number of things.
- ∴ The universe began to exist. from 1, 2
Defended with thought experiments like Hilbert's Hotel, which are said to show that an actual (as opposed to potential) infinite leads to absurdities. Critics respond that Cantorian set theory renders the actual infinite coherent.
William Lane Craig & James D. Sinclair, “The Kalam Cosmological Argument”, The Blackwell Companion to Natural Theology, ed. W. L. Craig & J. P. Moreland, Wiley-Blackwell, 2009. doi.org/10.1002/9781444308334
The Argument from Cosmic Expansion
- A universe that has, on average, been expanding throughout its history cannot be past-eternal (the Borde–Guth–Vilenkin theorem).
- Our universe has, on average, been expanding throughout its history.
- ∴ The universe began to exist. from 1, 2
The BGV theorem shows that any universe with a positive average expansion rate is geodesically incomplete to the past. Whether past-incompleteness amounts to an absolute beginning — and whether exotic models escape the theorem's assumptions — is disputed.
Arvind Borde, Alan H. Guth & Alexander Vilenkin, “Inflationary Spacetimes Are Incomplete in Past Directions”, Physical Review Letters 90: 151301, 2003. doi.org/10.1103/PhysRevLett.90.151301