Why must the universe have a beginning?
Actual infinites cannot exist in the world
A beginning-less, temporal series of events is an actual infinite.
To say that the universe has no beginning, is to say that there is an actual infinite number of past events in the history of the universe.
This cannot be the case.
Craig uses the example of a library. The first library has an infinite number of red books, and the second has an infinite number of black books and an infinite number of red books. The second library has twice as many books as the first, but it can't have. Also, if each book has infinite number of pages, to read one would be like reading every book. This also cannot be the case.
Therefore, actual infinites are incompatible with the real world.
The impossibility of traversing an actual infiniteEven if we do accept that actual infinites are possible in the real world, there is another problem with their existence;
The actual infinite must occur all at once because you cannot traverse (cross) an actual infinite by successive addition.
A temporal series of events is formed by successive addition.
Therefore, the history of the universe cannot be infinite.
If it isn't infinite, it must be finite. Finite things must have a first term or beginning.
Thus, the universe must have had a beginning.
There are two explanations for the impossibility of traversing an actual infinite, which are shown on the next slide.