1. The Leibnizian Cosmological Argument
The Rev. Sir Doctor Sen. Zachary Lawson, Heavyweight Champion of the World**, Ph.D

2. Formulations Why do contingent things exist?
Why does the physical universe exist?
Why is there something rather than nothing*
*beware of Platonists

3. Stated
Everything that exists has an explanation for its existence, either in the necessity of its own being or in its contingency on an external entity.
If the universe has an explanation for its existence, that explanation is God
The universe is an existing thing.
From 1 and 3 it follows: The universe has an explanation of its existence
From 2 and 4 it follows: The explanation for the existence of the universe is God

4. Premise I ‘The Principle of Sufficient Reason’
Undergirds all philosophical and scientific inquiry
Denial would be immensely anti-intellectual
Contingent
A thing is contingent if it could exist and it could have failed to exist.
A thing’s existence is contingent if there is some possible world where it exists and some possible world where it doesn’t exist.
Similarly, a contingent truth is something that is true in some possible world and false in some possible world.
Necessary
A being’s existence is metaphysically necessary if it cannot fail to exist; the being exists in all possible worlds.
A truth is metaphysically necessary if its truth can’t be and couldn’t have been otherwise; it is true in all possible worlds.

5. Premise I Objections usually fall into one of two categories
God is exempt from PSR (inconsistent)
Universe is exempt from PSR (G.O.G.)

6. Premise II Implicit affirmation Toned down
If atheism is true, the universe has no explanation
Toned down
God = ‘transcendent personal cause’
Conclusion is at least a bizarre form of atheism

7. Premise II
The logical possibility of alternative composition is evidence against the universe’s necessity
The finite past is evidence for the universe’s contingency

8. Premise III
The universe exists
duh

9. Alternative Formulation
There are contingent constituents to the universe
Given the contingent constituents of the universe, the existence of the universe is highly unlikely under the hypothesis that these constituents are themselves uncaused or self-caused.
Given the contingent constituents of the universe, the existence of the universe is not unlikely under the hypothesis of a first uncaused cause
Therefore, the existence of the universe strongly supports the existence of a first, uncaused cause over the existence of a non uncaused cause.
(Max Andrews, sententias.org)

10. Further Reading Alexander R. Pruss
The Leibnizian Cosmological Argument
Blackwell Companion to Natural Theology pp
Maverick Christian
Search: Leibnizian Cosmological Argument
JW Wartick
Leibnizian Argument
Max Andrews
Abductive Thomistic Cosmological Argument