"The Existence of God and the Beginning of the Universe" -William Craig
1. Whatever begins to exist has a cause of its existence.
2. The Universe began to exist.
2.1. Argument based on the impossibility of an actual infinite.
2.11. An actual infinite cannot exist.
2.12. An infinite temporal regress
of events is an actual infinite.
2.13. Therefore an infinite
temporal regress of events is not
possible.
Hilbert's Hotel - Hotel with
infinite number of rooms, and all
rooms are full. Add a guest, shift
everyone up one room, still
infinite number of guests, i.e.
the number of guests hasn't
changed. BUT what if an infinte
amount of guests check out? The
absurdity illustrates the
impossiblity of an actual infinite.
3.Therefore the Universe has a cause of its existence.
2.2. Argument based on the impossibility of the
formation of an actual infinite by successive
addition.
2.21. A collection formed by successive addition
cannot be actually infinite.
2.22. The temporal series of past events is a
collection formed by successive addtion.
2.23. Therefore the temporal series of past events
cannot be actually infinite.