Principles of Sufficient Reason

I am sure most readers are familiar with the fact that there is a category of arguments for the existence of God that all go roughly like this:

  1.  For every fact, there is an explanation of that fact.
  2.  The physical world does not explain itself.
  3. Therefore, there is an explanation for the facts of the physical world that can’t be found in the physical world.

From (3), the argument continues that said explanation can only be found in the god of classical theism. (2) is easily established, but the “how” is depending on the exact formulation of (1). The important premise here is (1) and any statement like it is called a principle of sufficient reason. There are actually several of them, but there is one that is usually called THE Principle of Sufficient Reason (PSR for short):

(PSR) Every contingently true proposition is explained.

There’s also what’s sometimes called the Strong Principle of Sufficient Reason (SPSR), which states that (PSR) is necessarily true – an unexplained contingent truth is impossible.

But you can find a weaker principle, like what Richard Gale and Alexander Pruss call the Restricted Principle of Sufficient Reason:

(RPSR) Every contingent truth can be explained.

But you can evenmake this statement weaker.

(WPSR) It is possible that every contingent truth can be explained.

It’s clear that a stronger principle implies a weaker one, but you can actually just appeal to the (WPSR) in our initial argument and it will do all we wanted from the SPSR.  Why? Suppose the WPSR holds. Then there is a possible world that the RPSR holds. Suppose that in that world, some contingently true proposition is unexplained. By the RPSR, the fact that it is unexplained is contingent, so we can apply the RPSR to “X is contingently true and X is unexplained” and find an explanation for it. But the explanation of the conjunction has to explain both propositions in the conjunction, which is a contradiction. So in that world, every contingent truth  does in fact have an explanatio, including the conjunction of all contingent truths.  I’ll leave it to another day to show how to get from this result to classical theism (or like you to papers that do just that), but I think that this conclusion alone is interesting enough. The next question should be: How much more plausible do we have to make our appeal to the need of explanations?

Note that the deductions in this argument use Axiom S5 of modal logic.

For more on this, read Pruss’ papers and/or blog for yourself:


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