Conjunction of Contingent Facts

One variety of the Leibnizian cosmological argument (LCA) is one in which the principle of sufficient reason (PSR) is “every fact has an explanation for why it is true.” A fact being contingent means it could have been false. An example of a contingent fact is “Abraham Lincoln was the President of the United States.” An example of a non-contingent fact is “two plus two equal four.” Behold the following argument for theism:

1. There is an sufficient reason (and thus an explanation) for every contingent fact (PSR).
2. The conjunction of all contingent facts (fact #1 is true and fact #2 is true and...) is itself a fact; call this CCF.
3. CCF is a contingent fact (surely a different conjunction is possible, since each fact is contingent).
4. CCF has an explanation (follows from 1 and 3).
5. If CCF has an explanation, that explanation is a necessary entity (it cannot be another contingent thing since that would be part of CCF, the very thing we are trying to explain, and contingent facts cannot themselves contain the reason for why they are true).
6. Therefore, there exists a necessary entity that is the explanation for CCF (follows from 4 and 5).

One of God’s classical attributes is necessary existence, i.e. that he is a being that exists in all possible worlds. And so, the final line, if true, would constitute at least some evidence for theism. Some versions of the LCA have a less modest conclusion, saying something like “Therefore, God exists” but here I’ll address the harder-to-attack version since if line (6) is true and justified by this argument, it would indeed constitute some evidence for theism and atheism is better off showing that line (6) is not justified here.

There is a reason to believe that premise (1) is false, but first, let me praise it a little bit. It is admirable to search for explanations for why some contingent fact is true; science looks for such explanations all the time. The trouble is when we take an idea that’s good in general but then take it to an extreme. The PSR in premise (1) is just such an example.

Suppose it’s true that the CCF has a sufficient reason for why it is that way and not otherwise. If so, that reason would itself have to be some sort of necessary fact; if it were a contingent fact it would be part of CCF, which is what is to be explained, and contingent facts cannot themselves contain the reason for why they are true (note the similar reasoning for this and line 5). But whatever is entailed by a necessary truth is itself necessary, which would make CCF a necessary truth, which of course conflicts with premise (3). So this version of the LCA is not a sound argument. If I had to pick a false premise, I’d say (1) is very likely false.