Peter van Inwagen famously rejected the PSR due to his argument that it implied necessitarianism: Take the conjunct C of all contingent facts. Being contingent itself, the PSR demands an explanation F. F must be necessary. But if F is necessary and sufficiently explains C, then C is itself necessary, and hence no contingent facts exist. Because contingent facts do exist, the PSR is false.

But what if we maintain that an explanation for a fact F need only necessitate F's possibility, and consider the (alleged) true indeterminacy we find in quantum mechanics. For example, suppose the contingent fact that needs explained is C : "the electron was found in position x.", and our explanation of C is F: "A quantum experiment was conducted which entailed a probability of the electron being found in position x."

This would be an explanation which does not entail or necessitate C. Does this pose a legitimate challenge to van Inwagen's argument?

  • If an explanation necessitates only F's possibility then it is only a partial explanation and not a sufficient one. In other words, PSR is false.
    – Conifold
    Feb 23, 2022 at 21:30
  • Why must a "sufficient explanation" require this strongest form of explanation, which is metaphysical necessitation?
    – Mark
    Feb 23, 2022 at 21:57
  • Because that is the meaning of "sufficient", and it is not the "strongest form", being sufficient to determine what happens still may not provide a satisfactory explanation. When some diluted "explanations" are enough we can call that PDR, not PSR.
    – Conifold
    Feb 23, 2022 at 22:30
  • Ok let me rephrase then. Let's call it the principle of elaboration: For every contingent fact C, there is a fact F other than C which explains why C is possible. Given my thoughts above, do you think this reasonably goes through?
    – Mark
    Feb 23, 2022 at 22:37
  • That is not a challenge to van Inwagen's argument, and considering the vagueness of "possible" and "explanation" I suspect that it is close to vacuous without much elaboration. Pointing to an example of quantum mechanics is not enough for a cogent general notion of "explaining possibility", or a justification of why we should believe it after PSR tanked.
    – Conifold
    Feb 23, 2022 at 22:52

3 Answers 3


For that to be true, it would require proof that a quantitative mathematical relationship in quantum mechanics furnishes a valid explanation for a certain qualitative philosophical relationship.

These two fields have nothing to do with one another. You cannot establish a valid proposition in philosophy by invoking the mathematics of quantum mechanics.


The PSR fails for multiple reasons. The indeterminacy of physics is only one. A further problem is the Munchausen Trilemma: Is the Münchhausen trilemma really a trilemma? Trying to recast it, to accommodate indeterminacy, is no longer the PSR.

Pragmatists accept that the universe is open, but also highly constrained, and often highly predictable. Absolute predictability is not necessary for pragmatically accepting the PSR as a useful but flawed and sometime falsified guideline.


Quite a tough nut ta crack for the likes of me. However, ta offer me two cents, it looks like Peter van Inwagen's definition of contingent involves the clause has no explanation and how else might we discover that but by assuming the PSR and then hitting upon an unexplainable.

We must, it appears, always assume the PSR, even to disprove it unless ... a pattern is discernible for stuff that have no explanation, a pattern that obviates the need to check for an explanation before we come to the conclusion that there is no explanation. Mayhaps this is why, the PSR is a principle and not, how would you describe it?, a law.

Second, another one of my pet peeves, when "proving" this class of negatives, it is hard to tell the difference between there are no fairies and I don't have evidence ... YET ... of fairies in a manner of speaking. That is to say, as I mentioned in another post a few moons ago ... knowledge of (metaphysical) negative claims is entwined with ignorance of evidence for the corresponding positive claims (does God not exist or is it that I haven't found evidence that God exists??!!)

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