1. PSR (Principle of Sufficient Reason) has two parts:

(1st part) There must be an explanation of the existence of any being.
(2nd part) There must be an explanation for any positive fact whatsoever.
2. A dependent being depends for its existence on something external to itself.
3. A self-existent being is self-sufficient. It nature is such that it cannot fail to exists.

PSR entails that nothing "just happens" to exist. Everything that exists is either a dependent or an self-existent being - either contains the reason of its own existence (self-existent) or does not contain the reason of its own existence because it depends on something external to itself.

If this is given, then we can show that there must be a self-existent being.

The Argument

1. Suppose that all beings are dependent.
2. The set of all dependent beings requires a sufficient reason as much as any of its members does. (Required by the second part of PSR.)
3. The being that contains the sufficient reason cannot be internal to the set of all dependent beings, for then one of the dependent beings would contain the reason of its own existence.
4. Therefore it must be external to the set of all dependent beings.
5. But whatever is external to the set of all dependent beings must be an self-existent being.
6. Therefore there is (at least one) self-existent being on which the set of all dependent beings depends for its existence.

Problems

1. Why think the world depends on just one self-existent being?
2. Is PSR true?
3. What about the behavior of subatomic particles? Is there a "sufficient reason" in their case? Is the 2nd part of PSR true?
4. Must the set of dependent beings as a whole have a cause? Is the 2nd part of PSR true?
5. How do we know that the world is not an "self-existent" being?

It's "logically possible" that it's not?
But it's "logically possible" that God does not exist.
6. Why did God create the world? Was it necessary? Then isn't the world necessary too? Personal explanation and PSR.