There's Heidegger's The Principle of Reason. He writes about Leibniz's formulation, Nothing is without a reason, nihil est sine ratione. So far so good, but fasten your seat belt.

Assuming I understand Heidegger - a very large assumption - I read him as focusing finally on the word "is." To be a something (not a nothing) is to be a being. The beingness of a being - the in-order-for-a-being-to-be - is grounded in the cognition of a being. That is, no thing is absent being the cognition of a being, the cognition being the ground/cause of the being.

I'd like to think that's worth a C from my Heidegger prof. If you get the book (a library is best, unless you want to own it, and why would anyone want to invest in and own an obscure book by Heidegger? Anyway, in it are thirteen lectures and an address at the end. The address, thirteen pages, is a summary of the lectures. You could even read it at a bookstore! It's far from Heidegger's worst; it's readable, but ir reads as if he were being paid by the word.

Assuming I understand Heidegger - a very large assumption - I read him as focusing finally on the word "is." — tim wood

That sentiment that I've heard so many times is one of the primary reasons for my aversion of reading him. Besides, I have piss poor concentration, so I doubt I'll ever get past the first page of his The Principle of Reason.

Heidegger's Introduction to Metaphysics discusses it as well, and he rightly emphasises that the second clause of the PoSR is often and mistakenly left out. It's not just 'everything has a reason' but that there must be a reason for this rather than that: hence the full formulation: why is there something rather than nothing? The qualifier is what makes it sufficient; it's not just a matter of 'looking for reasons', but reasons why this and not something else. The 'sufficiency' part is often forgotten when discussing the PoSR, which is understandable because it's actually an incredibly stringent condition on inquiry. Leibniz has to theorize an infinity of different possible worlds just to deal with it.

This, in turn, is important because it means that the PoSR is indissociably linked with the question of individuation; on the fact that reasons bear on this individuated thing, and not something else.

And let's not forget Schopenhauer's doctoral thesis "On the Four-Fold Root of the Principle of Sufficient Reason", which distinguishes four versions of the principle. I think it is in that work that the we get the first distinction made between the use of the principle in regard to causes for events and its use in regard to rational reasons for belief. As far as I recall Schopenhauer's critique of those who came before him, and especially Spinoza (who arguably pushed the principle to its limits in regards to the sufficiency angle StreetlightX mentions) was that they failed to distinguish the two.

Michael Della Rocca (a contemporary Spinoza expert) seems to think that the principle should be a central issue in philosophy, since for him - if it is true under some interpretation or other - then Spinoza's metaphysics follows (after some lengthy argument of course). The problem (and Della Rocca acknowledges this) is that we need an argument to show that the principle of reason is in fact true, and that is what appears to be lacking in most of the literature (he has a stab at it himself, but I'm not sure it is that convincing).

I think I hit the jackpot (thanks Google!) in regards to contemporary views of the PoSR and possible criticism it faces in view of Quantum Mechanics, Godel's Incompleteness Theorems, and foundational mathematics.

Here it is.

Please build on this or reference other papers if possible. It's been a great interest of mine to understand the PoSR, which seems so central to philosophical analysis.

Assuming I understand Heidegger - a very large assumption - I read him as focusing finally on the word "is." To be a something (not a nothing) is to be a being. The beingness of a being - the in-order-for-a-being-to-be - is grounded in the cognition of a being. That is, no thing is absent being the cognition of a being, the cognition being the ground/cause of the being. — tim wood

I think using the term "cognition" here may be misleading, since it implies the very sort of Cartesianism which Heidegger so strongly rejected. In Heidegger's analysis, the cognition of a being is grounded in, and derivative of, a pre-theoretical disclosure of the world (of beings in Being) and not the other way around. To break out of the deeply entrenched subject-object dichotomy, in favor of a radically new and non-dualistic conception of human existence, was the sine qua non of Heidegger's thinking from beginning to end.

Apologies if I misunderstood your position, tim. You're far more knowledgeable about these philosophical matters than I. It also seems like it's been about 20 since I read that particular work of Heidegger's, but the one thing I do recall of it, however vaguely, is something that @Posty McPostface may find congenial to his own Wittgensteinian background and influence: rational explanations eventually come to an end and we have to learn to appreciate the simple but extraordinary fact (in Heidegger's estimation) that beings are, and that we are in their midst. I think both Witty and Heiddy share that sense of finding the extraordinary in the seemingly ordinary, and by focusing on mundane everyday objects and practices in ways that challenge dominant guiding pressuppostions, they invite us to share in that experience.

I believe he concludes the work by quoting Novalis or some other poet - "the rose is without why, it blooms because it blooms," or something like that. So the principle of sufficient reason has its obvious uses and justification, but, if taken to an extreme, it ultimately cuts us off from the source of wonder and the ground of our own existence that is Being - which, once again, is without "why?".

I believe he concludes the work by quoting Novalis or some other poet - "the rose is without why, it blooms because it blooms," or something like that. So the principle of sufficient reason has its obvious uses and justification, but, taken to an extreme, it ultimately cuts us off from the source of wonder that is Being - which, once again, is without "why?". — Erik

There is a hidden paradox here, which I'm reading about in the previous link I posted, if you're interested. Let me quote (I hope at leisure) from what I have read there, that I have in mind.

Let me know if you find it of any use:

But what sort of principle is this? Is the PSR itself susceptible to proof? Must we take it as an axiom of sorts? Or is it just a general working assumption we make in order to proceed with proving other facts or theorems of interest? Schopenhauer argued that the PSR required no proof, in the sense that one “finds himself in that circle of demanding a proof for the right to demand a proof.” (Jacquette, pg. 280) Schopenhauer’s argument against proof is paradoxical: “This principle of truth requires no proof.” This is reminiscent of Gödel’s incompleteness theorem which utilized a form of the liar paradox: “This sentence is false”. According to incompleteness theorem a formal system is incomplete if a statement or its negation cannot be derived (i.e., proved) in the system. Is the PSR a provable truth? On its face this appears to be a valid question. If we use PSR as a sort of axiom, there is no further proof required, lest we fall into paradox, as Schopenhauer rightly claimed, in my view. — Unnamed

Thanks Posty, I'll take a look...

If I give a reason for something, I'm not necessarily proving it. If I have a black eye and you ask why and I say I annoyed someone so much that they hit me, I've given a reason why I have a black eye, but it would be a very strange notion of proof to say that I've thereby proved to you that I have a black eye.
In order to get a real paradox of the kind Schopenhauer hinted at, I think you'd first have to argue that all proofs are reasons and vice-versa. That might be the case in mathematics (i.e. that all proofs are reasons, and all reasons are proofs) but outside of mathematics there are distinctions to be made that might scupper the charge of paradox.

I think we might be using "proof" and "true" interchangeably here.

Hence,

Schopenhauer’s argument against proof is paradoxical: “This principle of truth requires no proof.”

How do we know it's true if no proof is required? If it is an axiom, then seemingly the issue resolves itself. However, even assuming that introduces metaphysical baggage, I think.

The Principle of Sufficient Reason has been falsified by the Free Will and Strong Free Will Theorems of Kochen and Conway.

Admittedly I've only just started reading the article, but they appear to be helping themselves to the notion of free will, which is precisely one of the notions that the PSR bears upon, and if so, they are not so much falsifying the PSR but begging the question against it. I'll continue reading their paper, but the philosophical roughshod-riding they engage in at the begining gives me initial reason to doubt that they have anything philosophically cogent to contribute to the debate about the PSR.

In case anyone is wondering, here is the article that @tom is referring to.

With the caveat that I have only skim read the article, the authors do nothing to recuperate their philosophical credentials by the end of the paper. Essentially the point seems to be that given certain assumptions about transmission of information, and possibilities for experimental outcomes, those outcomes are determined by choices made concerning measurements to make. The theorem then states that if those choices are the spontaneous acts of the free will of the measurement takers, then the outcome of the experiments is not determined by anything leading up to the measurements' being taken. Well, it would be a more interesting theorem if it were a biconditional rather than a mere conditional, since the conditional is (under classical rules of deduction) true, trivially, in those cases where the antecedent is false. The authors do absolutely nothing to establish that the antecedent is true, and do not even put any flesh on the bones of what they take to be "free will".
I await refutation from anyone who has read the paper more closely than I have - as I say, I have only skim read it - but as it stands my feeling is just to lump the authors into the category of competentent physicists but bumbling philosophers, and since the status of the PSR is a philosophical issue, they don't really have a great deal to contribute.

Admittedly I've only just started reading the article, but they appear to be helping themselves to the notion of free will, which is precisely one of the notions that the PSR bears upon, and if so, they are not so much falsifying the PSR but begging the question against it. I'll continue reading their paper, but the philosophical roughshod-riding they engage in at the begining gives me initial reason to doubt that they have anything philosophically cogent to contribute to the debate about the PSR. — MetaphysicsNow

I think you can go a little bit further: While the PSR is falsified if we have free will by the Free Will Theorem, if we do not have free will, then I'm not sure anything meaningful can be recovered.

If the universe is deterministic, then the FWT informs us that we inhabit a super-deterministic hell. There can be no "reason" that the distant entangled particle behaves the way it does, beyond "it was thus determined".

The authors do absolutely nothing to establish that the antecedent is true, and do not even put any flesh on the bones of what they take to be "free will". — MetaphysicsNow

If all they need to assume is "that the experimenter can freely choose to make any one of a small number of observations", what would be the point of complicating matters by adding unnecessary assumptions?

I have only skim read it - but as it stands my feeling is just to lump the authors into the category of competentent physicists but bumbling philosophers, and since the status of the PSR is a philosophical issue, they don't really have a great deal to contribute. — MetaphysicsNow

As if ad-hominem was relevant, neither Kochen nor Conway is a physicist. One is a pre-eminent mathematical logician with several important theorems in his name, the other, one of the most famous mathematicians alive.

And, If I remember correctly, the Principle of Sufficient Reason is not mentioned in either of the FWT papers

And, If I remember correctly, the Principle of Sufficient Reason is not mentioned in either of the FWT papers

That is true, but I thought your position was that the FWT refutes the PSR. It doesn't, and precisely because of the fact that the theorem is a conditional whose antecedent bears on the PSR, and they don't establish that the antecedent of their theorem is true.

How do we know it's true if no proof is required? If it is an axiom, then seemingly the issue resolves itself. However, even assuming that introduces metaphysical baggage, I think. — Posty McPostface

The reason no proof is required is that you employ the principle in trying to refute it. It is thus axiomatic.

Interesting, how so? Naively, the way to refute the PSR would be to establish that there are somethings that occur for no reason at all. Is the point that we would then need to answer the question "Why should the mere fact that something occurs for no reason at all refute the PSR" by relying on the PSR?

There's also this:

The PSR precludes “brute or unexplainable facts” as well as effects without causes. It would preclude mere factual coincidence, one thing following another without reason. (SEP on PSR, pg. 3)

The PSR is not equivalent to the assumption that the world is a rational place open to our questioning. The principle has radical implications:
“Among the alleged consequences of the Principle are: the Identity of Indiscernibles, necessitarianism, the existence of a self-necessitated Being (i.e., God), the Principle of Plentitude, and strict naturalism.” (SEP, PSR at pg. 4)

The PSR assumes that the world is constructed with internal logic (reasons and explanations) completely accessible to humans. As we’ve learned in the last century this may be an unjustified assumption. Incompleteness, QM uncertainty, and objective randomness produce brute facts (concrete and abstract) that are just so without reason. If there are exceptions to the PSR then it becomes merely an interesting heuristic device –not a universal law of truth. But frankly, I think the jury is still out on what sort of truth we are dealing with here. — Unknown

Would the PoSR not be itself a brute fact? One of many I assume.

Would the PoSR not be itself a brute fact?

Sly move - turning the PSR against itself. Indeed if it is to be treated as an axiom, it's truth might have to be taken to be a brute fact, and that would seem to indicate that the PSR is false. I suppose it is here that the exact formulation of the PSR becomes important. Loosely speaking its the claim that everything has an explanation. We could try restricting the domain of quantification to just events, say, in which case the PSR is not something that needs to be explained, since it is not an event. That seems like cheating, though. So let's assume we have to give an explanation even for the PSR, which would mean that there were principles upon which even the PSR would be based, but then those principles themselves would, by the PSR, have to have their explanations....and here we get to Schopenhauer's point. There might be an infinite regress here, on the other hand, perhaps we can construct a virutous explanatory circle where the PSR gets justified by some principles which in turn get their justification from the PSR.

Interesting, how so? — MetaphysicsNow

One reason would be that the principle is a priori.

Naively, the way to refute the PSR would be to establish that there are somethings that occur for no reason at all — MetaphysicsNow

If you can establish that something has occurred for no reason at all, then be my guest. I don't think such a thing is possible, for ex nihilo nihil fit.

Is the point that we would then need to answer the question "Why should the mere fact that something occurs for no reason at all refute the PSR" by relying on the PSR? — MetaphysicsNow

Sort of. The idea is that to give an explanation of anything just is to supply a reason why something is or is not the case. Thus, in explaining how the PSR is false, you presuppose it, because you are supplying a reason for why there are no reasons for anything.

ex nihilo nihil fit.

Well, and I'm not saying I agree with this, but I've heard some people claim that the virtual particles of QM are precisely things for which ex nihilo nihil fit (and with it the PSR) is false.

I find that when pressed on the alleged "nothing" out of which these particle originate, it is not nothing after all.

That is true, but I thought your position was that the FWT refutes the PSR. It doesn't, and precisely because of the fact that the theorem is a conditional whose antecedent bears on the PSR, and they don't establish that the antecedent of their theorem is true. — MetaphysicsNow

The PSR is refuted because the laws of physics disagree with it. The assumption being that an experimenter possesses sufficient freedom to press one of a number of buttons.

If the assumption of the ability to choose a button is false, then the laws of physics tell us that we inhabit a superdeterministic conspiracy. I'm not convinced that PSR has any meaning in that scenario.

The PSR is refuted because the laws of physics disagree with it. The assumption being that an experimenter possesses sufficient freedom to press one of a number of buttons.

You cannot refute a principle on the basis of an assumption which the principle (arguably) entails is false: that's called question begging.

If the assumption of the ability to choose a button is false, then the laws of physics tell us that we inhabit a superdeterministic conspiracy. I'm not convinced that PSR has any meaning in that scenario.

That's a different argument entirely, and quite an interesting one - along the lines of the PSR being self-stultifying.

In all cases, the FWT paper is irrelevant anyway.

We could try restricting the domain of quantification to just events, say, in which case the PSR is not something that needs to be explained, since it is not an event. That seems like cheating, though. — MetaphysicsNow

That's curious because my instinct here was to say that the PSR, whatever its status, is not just a fact. Maybe as a first approximation you could say it's a sort of second-order fact, a fact about facts. It's natural to see an infinite regress looming here, but to do that we'd have to recast the PSR as inherently recursive and thus implicitly leave it outside the hierarchy we're constructing. Which is odd. However that works out, I'd at least start by not assuming that the sort of explanation appropriate to garden-variety first-order facts is appropriate to higher-order facts.

I agree to some extent, the PSR, whatever it is, is not a fact of the garden variety scientific or non-scientific kind. However, if the following two statements are true
1) Any true proposition could constitute an explanandum.
2) All explananda have explanans
and if 2) is an acceptable formulation of the PSR, we either invite an infinite explanatory regress, invite a regress that can be terminated only by fiat and thus in violation of the PSR, or we need to come up with some explanatory circle that leads us satisfactorily back to the PSR. Since (2) is pretty much a matter of definition, it means we need to reject (1) to escape the regress/circularity and insist that somehow or other the PSR is not the kind of true proposition that could constitute an explanandum. This is presumably the approach of those who would look on it as an axiom.

Quick thoughts (since I should really be working):

This sort of "linguistic accent" flattens any hierarchy we might opt for, and blocks outright the kind of distinctions I was contemplating. I get the impulse, but it feels like a rush job, and I'd like to hold off a bit to explore.

I'm tempted to say that the PSR isn't exactly a proposition anyway, and thus isn't exactly true or false. It's almost like an inference rule. (And now I'm reminded that Ramsey wanted to treat conditionals this way in general.) Maybe rather than being a conditional itself ("If x is <whatever> then x has an explanation") it's a generator of conditionals, on the fly, as needed. So an "introduction rule".

So I guess I'm in the neighborhood of, as you suggest, treating it as axiomatic -- or, rather, it looks to me like this is how you could coherently use it. (I've actually never given the PSR any thought at all.)

I take the PSR to be an epistemological, not an ontological, principle. So @Thorongil is right to say that it cannot be refuted, epistemologically and logically speaking at least, because to do so would be to find reason that the principle does not obtain: a performative contradiction.

If there are natural events which are absolutely random, those events could never be anything for us, and so could have no bearing on the indispensability of the PSR for human experience and understanding.