- Whatever has a beginning has a cause of its existence. (Premise)
- The physical cosmos (=the sum total of all physical reality) has a beginning. (Premise)
- So, the physical cosmos has a cause of its existence. (By 1 and 2)
- The cause of the physical cosmos is not physical (on pain of circularity). (Premise)
- So, the physical cosmos has a non-physical cause. (By 3 and 4)

- Necessarily, once enough time to complete a task has elapsed, the task is complete.
- If an infinite past is possible, then someone could have been counting down from infinity and finishing today.
- Necessarily, someone counting down from infinity would have had enough time to complete the task yesterday.
- Necessarily, someone counting down from infinity would have been finished yesterday. (By 1 and 3)
- So, an infinite past is impossible. (By 2 and 4)

1. If an infinite past is possible, then someone could have been counting down from infinity and finishing today.

- Necessarily, if someone were counting down from infinity and finishing today, there would be no explanation for why they finished today rather than yesterday.
- So, an infinite past is impossible.

- If the past is infinite, there is no explanation why all the events in history happened when they did rather than a day earlier.
- Everything has an explanation.
- So, the past is not infinite.

- If an infinite past is possible, one can finish counting down from infinity.
- A task every prerequisite of which has a prerequisite cannot be completed.
- Finishing counting down from infinity is a task every prerequisite of which has a prerequisite.
- So, one cannot finish counting down from infinity. (By 2 and 3)
- So, an infinite past is not possible. (By 1 and 4)

1. Given an infinite past, every possible combination of events would have happened.

2. If there is no necessary being, then one possible combination of events is there not being anything.

3. So, given an infinite past, either there is a necessary being or at least once there was nothing. (By 1 and 2)

4. If there was once nothing, there would still be nothing.

5. There is something.

6. So, it is false that at least once there was nothing. (By 4 and 5)

7. So, given an infinite past, there is a necessary being. (By 3 and 6)