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The Kalam Cosmological Argument:
1. Whatever begins to exist has a cause of its existence.
2. The Universe (physical world) began to exist.
Argument based on the impossibility of an actual infinite.
2.11. An actual infinite cannot exist.
2.12. An infinite temporal regress is an actual infinite.
2.13. An actually infinite temporal regress cannot be traversed to the present.
2.14 Therefore, an actually infinite temporal regress cannot exist.
AND
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. The Universe has a cause of its existence.
Why does the conclusion entail the necessity of God's existence?
The following is my own syllogistic summary of the conclusion regarding the only possible cause of the physical world:
3. The Universe has a cause of its existence.
3.1. If the cause of the universe's existence were impersonal, it would be operationally mechanical.
3.2. An operationally mechanical cause would be a material existent.
3.3. The causal conditions for the effect of an operationally mechanical cause would be given from eternity.
3.4. But a material existent is a contingent entity of continuous change and causality!
3.5. An infinite temporal series of past causal events cannot be traversed to the present.
3.6. Indeed, an actual infinite cannot exist.
3.7. Hence, a temporal existent cannot have a beginningless past.
3.8. Hence, time began to exist.
3.9. A material existent is a temporal existent.
3.10. Hence, materiality began to exist.
3.11. The universe is a material existent.
3.12. Hence, the universe began to exist.
3.13. Hence, the cause of the universe's existence cannot be material (per 3.10.).
3.14. Hence, the cause of the universe's existence cannot be operationally mechanical (per 3.2., 3.10.).
3.15. Hence, the eternally self-subsistent cause of the universe's existence is wholly transcendent: timeless, immaterial and immutable (3.13.).
3.16. The only kind of timeless entity that could cause the beginning of time sans any external, predetermining causal conditions would be a personal agent of free will (per 3.3., 3.14.).
3.17. Hence, the eternally self-subsistent cause of the universe's existence is a personal agent of free will.
Broadly summarized: the eternally self-subsistent cause cannot be natural (or material), as no continuously changing entity of causality can be beginningless. The latter would entail an infinite regress of causal events, which cannot go on in the past forever. There must be a first event, before which there is no change or event. In short, given that an infinite regress of causal events is impossible, the physical world cannot be the eternally self-subsistent ground of existence. The eternally self-subsistent cause cannot be abstract either. An abstract object has no causal force, and, in any event, abstractions contingently exist in minds. Hence, the uncaused cause is a wholly transcendent, unembodied mind.
