Strictly speaking, this isn’t the cosmological argument, because as it stands there is no inference to a creating Agent. But it does establish the groundwork for it. This is from William Lane Craig’s *Kalam Cosmological Argument, *pp. 23-27.

- There are six self-evident principles
- Two bodies of which one is not greater than the other are equal.
- Equal bodies are those where the dimensions between their limits are equal in actuality and potentiality.
- That which is finite is not infinite.
- When a body is added to one of two bodies, the one receiving the addition becomes greater.
- When two bodies of finite magnitude are joined, the resultant body will also be of finite magnitude.
- The smaller of two generically related things is inferior to the larger.

- No actual infinite can exist because:
- If one removes a body of finite magnitude from a body of infinite magnitude, the remainder will be a body of either finite or infinite magnitude.
- It cannot be finite.
- Because when the finite body that was removed is added back, the resultant would be finite (see 1.5).
- The body would then be both infinite and finite
- But this is self-contradictory (see 1.3).

- It cannot be infinite
- Because when the finite body that was removed is added back to the remainder, the resultant body would be either greater than or equal to what it was before the addition.
- It cannot be greater than it was before the addition.
- Because then we would have two infinite bodies, one of which is greater than the other.
- The smaller would be inferior to the greater (because of 1.1).
- And the smaller would be equal to a portion of the greater.
- Thus, the smaller body and the portion would be finite because they must have limits (1.2).
- The smaller body would then be both infinite and finite.
- But this is self contradictory (see 1.3).

- It cannot be equal to what it was before the addition.
- Because the whole body composed of the greater portion and the smaller portion would be equal to the greater portion alone.
- Thus a part would be equal to the whole.
- But this is self-contradictory.

- It cannot be greater than it was before the addition.

- Because when the finite body that was removed is added back to the remainder, the resultant body would be either greater than or equal to what it was before the addition.

- Therefore, the universe is spatially and temporally finite because:
- The universe is spatially finite
- Because an actual infinite cannot exist.

- The universe is temporally finite
- Because time is finite.
- Time is finite
- Because time is quantitative
- And an actually infinite quantity cannot exist.

- Time is the duration of the body of the universe.
- Therefore, the being of the body of the universe is finite.

- Time is finite
- Because motion is finite.
- Because motion is the change of some thing.

- Body cannot exist prior to motion.
- Because the universe is either generated from nothing or eternal.
- If it is generated from nothing, body would not precede motion.
- Because its very generation is a motion.

- If it is eternal, body would not precede motion.
- Because motion is change.
- And the eternal cannot change.
- Because it simply is in a fully actual state.

- If it is generated from nothing, body would not precede motion.
- Thus, body and motion can only exist in conjunction with each other.
- Motion implies time.
- Because time is a duration counted by motion.

- Time is finite.
- Therefore, motion is finite.
- Therefore, the being of the body of the universe is finite.

- Because the universe is either generated from nothing or eternal.
- Because the universe is composed.
- Composition involves change.
- Because it is a joining of things together.

- Bodies are composed
- Because they are made up of substance and three dimensions.
- Because they are made up of matter and form.

- Motion involves time.
- Because time is a duration counted by motion.

- Time is finite
- Therefore, motion is finite.
- Therefore, composition is finite.
- Therefore, the being of a body is finite.

- Composition involves change.
- Because time must have a beginning
- Otherwise, any given moment in time would never arrive.
- Because infinite time is self-contradictory.
- The duration from past infinity to any given moment is equal to the duration from the given moment regressing back into infinity.
- Knowledge of the former duration implies a knowledge of the latter duration.
- But this makes the infinite to be finite.
- But this is self-contradictory.

- Because infinite time cannot be traversed.
- Before any given moment to have been reached, an infinity of prior moments would have to have been reached.
- But one cannot traverse the infinite.
- So any given moment could never be reached.
- But moments are, in fact, reached.

- Because infinite time is self-contradictory.
- Moreover, future time cannot actually be infinite.
- The future consists of consecutive additions of finite times.
- Past time is finite
- Therefore, future time is finite.

- The future consists of consecutive additions of finite times.

- Otherwise, any given moment in time would never arrive.

- Because time is finite.

- The universe is spatially finite