There is an argument that I’ve paraphrased below that the PSR implies determinism. This is sometimes taken as a reason to reject the PSR. I think however that it could be that the PSR holds and the world is in fact deterministic.

Necessary facts (eg 2+2=4) have as reasons other necessary facts. Contingent facts (eg it is raining) have as reasons other contingent facts. So is it impossible to mix necessary and contingent facts in the same causal chain. Seems to me either everything in existence is necessary or everything is contingent, not a mix?

Further its seems that all facts are necessary (IE determinism holds):

1. Non-determinism implies the existence of all objects in the universe are represented as contingent facts
2. Leibniz’s PSR: Every fact has a reason either within itself or in some other fact.
3. Contingent facts therefore have reasons.
4. The reasons for contingent facts must in themselves be contingent (else they would be necessary facts)
5. The existence of all objects in the universe are therefore represented by contingent facts
6. The conjunction of all these contingent facts is itself a contingent fact (often referred to as the Big Contingent Conjunctive Fact - BCCF)
7. The reason for the BCCF must be contingent and therefore must be contained in the BCCF
8. But no contingent fact can be contingent on itself
9. Therefore determinism must hold: all facts are necessary facts

To reenforce this argument the existence of a first cause must be a necessary and self-explaining fact (eg God is timeless and uncaused, always existed so no possibility of being contingent) so all facts that have the first cause directly or indirectly as reasons must be necessary facts too.

This line of reasoning obviously takes away both our and God’s free will.

I’m not quite sure how this fits in with the possibility of a ‘null world’. If a ‘null world’ is possible then could it not be said that God is contingent? IE worlds with and without God could exist? But God would seem to be a necessary fact in our world so would he not therefore be necessary in all worlds? (So that ‘null world’ is impossible?)