Source: https://plato.stanford.edu/entries/cosmological-argument/

1. A contingent being (a being such that if it exists, it could have not-existed or could cease to exist) exists.

2. This contingent being has a cause of or explanation[1] for its existence.

3. The cause of or explanation for its existence is something other than the contingent being itself.

4. What causes or explains the existence of this contingent being must either be solely other contingent beings or include a non-contingent (necessary) being.

5. Contingent beings alone cannot provide a completely adequate causal account or explanation for the existence of a contingent being.

6. Therefore, what causes or explains the existence of this contingent being must include a non-contingent (necessary) being.

7. Therefore, a necessary being (a being such that if it exists, it cannot not-exist) exists.

8. The universe is contingent.

9. Therefore, the necessary being is something other than the universe.

To avoid any hint of the Fallacy of Composition and to avoid its complications, Koons (1997: 198–99) formulates the argument for the contingency of the universe as a mereological argument. If something is contingent, it contains a contingent part. The whole and part overlap and, by virtue of overlapping, have a common part. Since the part in virtue of which they overlap is wholly contingent, the whole likewise must be contingent.

Kalam

1. Everything that begins to exist has a cause of its existence.

2. The universe began to exist.

3. Therefore, the universe has a cause of its existence.

4. Since no scientific explanation (in terms of physical laws) can provide a causal account of the origin (very beginning) of the universe, the cause must be personal (explanation is given in terms of a personal agent).

Finally, something needs to be said about statement 4, which asserts that the cause of the universe is personal. Defenders of the cosmological argument suggest two possible kinds of explanation.[4] Natural explanation is provided in terms of precedent events, causal laws, or necessary conditions that invoke natural existents. Personal explanation is given “in terms of the intentional action of a rational agent” (Swinburne 2004: 21; also Gale and Pruss 1999). We have seen that one cannot provide a natural causal explanation for the initial event, for there are no precedent natural events or natural existents to which the laws of physics apply. The line of scientific explanation runs out at the initial singularity, and perhaps even before we arrive at the initial singularity (at 10−3510−35 seconds). If no scientific explanation (in terms of physical laws) can provide a causal account of the origin of the universe, the explanation must be personal, that is, in terms of the intentional action of an intelligent, supernatural agent.

Craig's Additions to Kalam

5. An actual infinite cannot exist.

6. A beginningless temporal series of events is an actual infinite.

7. Therefore, a beginningless temporal series of events cannot exist.

Craig's Argument Against Temporal Actual Infinites

8. The temporal series of events is a collection formed by successive addition.

9. A collection formed by successive synthesis is not an actual infinite.

10. Therefore, the temporal series of events cannot be an actual infinite (Craig 1979: 103).