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 cannot exist.
 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
 addition.
 2.23 Therefore, the temporal series of
 past events cannot be actually
 infinite.
3. Therefore, the universe has a cause of its
 existence.