Simple Logic Showing How The Principle Of Sufficient Reason Is Self-Refuting

A few weeks ago I was debating the principle of sufficient reason (PSR) with a bunch of theists and a pantheist over in the combox of Strange Notions.

To me, the PSR is blatantly false, and relatively easy to prove so. The PSR's own assumptions can show how it's self refuting. In this blog post I want to compile some of the logic I use to show what entails from the PSR's stated premises that show it's flaws. Consider this:


1. The PSR demands that everything has an explanation.
2. Explanations can only be either necessary or contingent.
3. If an explanation is contingent, it will need a further explanation that is either necessary or contingent.
4. If a necessary explanation is not an eventual option, then the only possible explanations will have to be either an infinite regress of contingent explanations, or a brute fact.
5. A fourth option is impossible because the PSR demands only two possible kinds of explanations, which will ultimately terminate in 3 logical possibilities.

(Furthermore...)

6. Since brute facts are incompatible with the PSR, and an infinite regress of contingent explanations would require a necessary explanation for the chain's existence, the only real ultimate explanation for the PSR is a necessary one.
7. Since this universe is not logically necessary (necessitarianism is false - per argument below), the last remaining option per the PSR — the necessary option — also fails.
8. Even positing a god who creates/explains the universe doesn't resolve the problem because it is not logically necessary that god create our particular universe.
9. Since the PSR negates all 3 options, the PSR's logic is inherently false.
10. This means one will eventually have to come to the conclusion that brute facts are a necessity. (Even an infinite chain of contingent explanations will itself be a brute fact).


Now some of these steps need further justification.

The first three points state the fundamental principles that underwrite the PSR and my logic is derived from them:

1. The PSR demands that everything have an explanation. 

2. Explanations can only be either necessary or contingent. 

3. If an explanation is contingent, it will need a further explanation that is either necessary or contingent. 

Every believer in the PSR will agree with 1-3 above because they form the grounding of what the PSR is. Once you have them, there are only 3 possible kinds of explanations. My argument is like the logic in math: you start from some axioms and you derive a necessary conclusion.

When it comes to number 4, this is logically impossible to avoid given 1-3 above. For any explanation it will either:

(a) have a necessary explanation 

(b) have a contingent explanation 

(c) have no explanation

Those are your only possible options. For any explanation you give for X, I can always ask "Is the explanation for X logically necessary or not?" There are only two possible answers to this: yes or no. You will fall into either (a) or (b). The only other possible option is it has no explanation, which gives you (c), a brute fact. These options are your only possible choices given the PSR's logic: axioms to necessary conclusions.

Now technically speaking, the PSR gives you 2 options: (a) logically necessary, or (b) contingent. That's it. A (b) can be explained by an (a) or another (b). But since a (b) explanation requires something else, it will always require an (a) or a (b) to explain it. If we remove the (a) as a possible eventual option, the only possible option is an infinite regress of (b) explanations — or terminating in a brute fact (c).

I'm including a brute fact as the only other possibility here just to offer all possible options. On the PSR there are no (c) options available.

For 7, necessitarianism states that what exists must necessarily exist and no other possibilities are available. It means our universe is logically necessary. But here's the thing, if our universe is logically necessary, there is no need for a god to create it; our universe must exist. So the PSR entails necessitarianism, which entails that our universe exists necessarily, no god needed. The PSR therefore cannot be used to conclude a god's existence. But necessitarianism itself is a deeply problematic idea. To say our universe exists necessarily is to say that a different universe would entail a contradiction. Since this is blatantly false, necessitarianism is false.

For 8, not even positing god can fix this problem of how do you get a necessary universe because you will still be left with contingent facts that cannot be justified logically: there is no logically necessary reason why god had to create our universe and not another one.

So to sum up, the PSR's own logic shows how explanatory chains cannot be justified on the PSR. One can only attempt to justify (a) explanations by making a case for necessitarianism, which no one has, or can ever do, since it is obvious that our universe is not logically necessary.