The following is from Heidegger's The Principle of Reason. For my part, it's just FYI. I'd say for fun, but the topic of the OP is a real bear, imo!

P. 9:
"But remarkably enough, the principle of reason doesn't deal at all with reason as such. Rather, the principle of reason says: every being necessarily has a reason. For its part the principle of reason already presupposes that what a reason is has already been determined, that it is clear wherein the essence of reason lies. The principle of reason is grounded on this presupposition. But is a principle that presupposes something so essential to be taken seriously as a fundamental principle, much less as the supreme one? The principle of reason does not help us much when we try to clarify what the essence of reason is. Yet it is necessary to know this if, when discussing fundamental principles, we do not want to have a blurred notion of what a principle-reason is."

P. 78-80:
"According to Kant a cognition is "transcendent" that pretends to know objects inaccessible to experience. In contradistinction to this, the transcendental method has a view to the sufficient ground of the objects of experience and thereby of experience itself. The transcendental method moves within the compass of grounds that found the objects of experience in their possibility. The transcendental method circumscribes the compass of founding grounds that come into play. The transcendental method holds itself to this compass and within that which it delimits. Because it remains in the circle of sufficient reasons for the possibility of experience, that is, within the essence of experience and is therefore in-herent, the transcendental method is immanent. But nevertheless the method is called transcendental because it pertains to the transcendent, for it critically sets the bounds of the authority of the transcendent. The transcendental method traverses the immanence of subjectivity, that is, it traverses that cognition wherein objects as the objects of representation reside as in their sufficient reason. That is their objectness, the being of beings....
"What is distinctive about the transcendental method is the fact that, as the determination of the objectness of objects, this method itself belongs to objectness. Cognition renders sufficient reasons for objects when, above all, it brings forward and securely establishes the objectness of objects and thereby itself belong to objectness, that is, to the being of experienceable things....
"The new manner in which being proffers itself consists not only in the fact that being now comes to light as objectness. Rather, what is new is that this coming-to-light manifests a decisiveness with which being is determined within the realm of the subjectivity of Reason, and only there.

I take the PSR to be an epistemological, not an ontological, principle.

I think this is probably how those who wish to treat it axiomaticallly in some sense need to take it - something like a rule for thought, which is what @Srap Tasmaner seems to be getting at. But, certainly one way of looking at it is that the PSR pushes at that very supposed boundary between the epistemological and metaphysical. After all, your second paragraph seems to be making some Kantian-style metaphysical point about what couldbe for us on the basis that this is restricted by the PSR. Also, considering the use to which it has been put to in the past by Leibniz, Spinoza and Schopenhauer amongst others, it is pretty clear that some significant thinkers have regarded it as having metaphysical import (which does not, of course mean that it does just that there is some reason for thinking that it might). As @tim wood says, it's a bear of a topic.

My limited understanding of the PSR

1. Every proposition must have a reason
2. Every event has a cause
3. Every entity has a reason/cause for its existence

1 has to do with logic and leads to the Munchhausen trilemma.

2 and 3 seem to be saying the same thing. They too lead, inevitably, to a causal formulation of the Munchhausen trilemma.

As for asking a question on the PSR is to run around in circles. We need/want a reason to believe/disbelieve the PSR. That amounts to assuming it is true from the get go.

The PSR is the first step in every inquiry. Even if it were to be proved false we still have to use it because to find an instance that violates the PSR we need to begin by assuming the PSR.

So, disproving or denying the PSR becomes a mere academic exercise having little effect on how we actually deal with knowledge seeking.

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. — Janus

How so?

First, as has been discussed here, the scope of the PSR may be limited to events or entities and not include "things" such as rules, principles, laws, etc.

But even if it did, the denial of the PSR would state that there is at least one thing that does not have a sufficient reason. That in no way contradicts the statement that there is one thing (the denial of the PSR) that does have a sufficient reason.

If there are natural events which are absolutely random, those events could never be anything for us — Janus

What do you mean?

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

It seems odd that someone would give up the ability to chose which button to press, rather than question a cherished principle.

The FWT would still hold if the choice was made by a pseudo-random number generator.

2. Every event has a cause — TheMadFool

This is proved false by quantum mechanics.

2 and 3 seem to be saying the same thing. They too lead, inevitably, to a causal formulation of the Munchhausen trilemma. — TheMadFool

I thought we had given up trying to prove theories true since at least the advent of the scientific method. Instead, we try to find problems with theories and find solutions.

So, disproving or denying the PSR becomes a mere academic exercise having little effect on how we actually deal with knowledge seeking. — TheMadFool

We have a deep theory of reality that says PSR is false. But yes, PSR has nothing to do with knowledge seeking.

It seems odd that someone would give up the ability to chose which button to press, rather than question a cherished principle.

Odd, perhaps, but if that's where a true principle or an apriori principle of thought or whatever it is taken to be leads, so be it: a principle that drives human discovery in one way or another is not to be discarded simply because it leads to apparently unpalatable results. Anyway, the whole freedom to choose/freedom of will/compatibilism/determinism debate has its own thread (several of them in fact), so that part of our discussion is better taken into one of those unless you think that there is an real argument that the PSR is undermined because it leads to determinism which in turn leads to the meaninglessness of the PSR (which is what I thought you were hinting at earlier, and which as I say is an interesting line of thought, but one which is entirely independent of the FWT).
And no, FWT has a very specific but undeclared notion of freedom of will in its antecedent, and it is that notion of freedom of will that is (arguably) undermined by the PSR. Pseudo-random number generators are not truly random - their outputs are in principle predictable and explicable and at base a matter of cause and effect, and that feeds through into any measurements finally made on their basis that the measurements to take are "chosen" by such a machine.
The FWT really is irrelevant to deciding whether the PSR is true or false or something else entirely.

2. Every event has a causeThe MadFool


This is proved false by quantum mechanics.

Not really - there are probabilistic conceptions of causality that are perfectly compatible with QM.
What some people claim is that QM refutes the "ex nihilo nihil fit" principle (that some people see embedded in the PSR) because of the fluctuation of virtual particles. But as @Thorongil points out, when QMers are pushed on the point of what these virtual particles are, it actually turns out that you are not really getting something from nothing at all.

Pseudo-random number generators are not truly random - their outputs are in principle predictable and explicable and at base a matter of cause and effect, and that feeds through into any measurements finally made on their basis that the measurements to take are "chosen" by such a machine. — MetaphysicsNow

Which pseudo-random number generator do you propose to use? How will you map the output of the number generator to the buttons?

The FWT also holds if the decision is made by a random number generator, which exist BTW.

Odd, perhaps, but if that's where a true principle or an apriori principle of thought or whatever it is taken to be leads, so be it: a principle that drives human discovery in one way or another is not to be discarded simply because it leads to apparently unpalatable results. — MetaphysicsNow

The PSR has never driven human discovery. It can't do that.

The FWT also holds if the decision is made by a random number generator, which exist BTW.

Well, quantum random number generators exist if that's what you mean, but if you are going to use that as a definition of free will used in the FWT then the FWT becomes an empty tautology saying that quantum systems have the freedom that quantum systems have.

The PSR has never driven human discovery. It can't do that.

Well perhaps I chose an inappropriate metaphor - but the idea that everything is explicable is a motivation for pursuing explanations, and science is - amongst many other things - the pursuit of explanations.

Which pseudo-random number generator do you propose to use? How will you map the output of the number generator to the buttons?

Why are you asking me for specifics like that - I'm not proposing that they should be used at all. All I'm saying is that the very notion of a pseudo-random number generator is that there is a causal determination of the numbers that they churn out.

Not really - there are probabilistic conceptions of causality that are perfectly compatible with QM. — MetaphysicsNow

Really?

The proof given in the FWT for uncaused events, has absolutely nothing to do with virtual particles.

Really?

Yes: take a look here for instance probabilistic causation

The FWT does not prove that there are uncaused events, it proves only that if there are uncaused events (the free will choices of experimenters) then there are other uncaused events.

Yes: take a look here for instance — MetaphysicsNow

Your claim that probabilistic causality is compatible with quantum mechanics, how?

Well, don't get me wrong, I'm not a proponent of probabilistic causation, but the basic idea would seem to be that the challenge QM poses for the traditional account of causation is that the traditional account entails a certain conception of determinsim which can be captured in the following idea: all the events leading up to the state of a system at time t allow for only one possible next state of that system. QM, well some interpretations of QM anyway, entail that all the events leading up to the state of a system at time t allow for many different possible next states of that system, each state being more or less likely, but no state being impossible. So, if that is right, QM undermines that specific notion of determinism. Probabilistic conceptions of causality attempt to keep some aspects of causality, but drop that specific conception of determinism, allowing that future states of systems have a probabilistic distribution, but are nevertheless in some significant sense caused by the existing state of the system, thus rendering causation compatible with (some interpretations of) QM.
That seems to be the gist of it, as I say, I am not a proponent so cannot really provide you any more details - there are plenty of references in the link I provided if you are interested. A probabilistic account of causation may be right, it may be wrong, it may in the end not even make sense, and may not in the end be compatible with all interpretations of QM. One thing is for certain, though, the FWT is irrelevant to deciding on those issues, just as it is irrelevant to the status of the PSR.

Probabilistic conceptions of causality attempt to keep some aspects of causality, but drop that specific conception of determinism, allowing that future states of systems have a probabilistic distribution, but are nevertheless in some significant sense caused by the existing state of the system, thus rendering causation compatible with (some interpretations of) QM. — MetaphysicsNow

This is refuted by FWT, and therefore by quantum mechanics, which is a theory that adheres to the axioms of FWT. Probabilistic causality is ruled out, as are hidden variables.

Even if you insist that your decision of pseudo-random number generator, and its output, and your mapping, is determined by the big-bang, probabilistic causality is refuted.

There appears to be some fundamental difference of understanding about what the FWT is, so in an effort to get at precisely what that difference of understanding might be, let me be clear on what my understanding of the FWT is and how that understanding entails its total irrelevance for PSR. After this, I think I'm going to have to move on to something else as, for one thing, its becoming a little boring saying the same thing over and over again in different ways.

The FWT is a conditional theorem to the effect thatif there are uncaused events of one specific kind, then there are other uncaused events. In the original paper the uncaused events of the antecedent are initially taken to be free will choices of experimenters about what measurements to take, and the uncaused events of the consequent are the outcomes of the measurements.

That is my understanding of the content of the FWT as expounded by the authors of the original paper, if you disagree with that understanding, please be precise as to what it is about my interpretation of the FWT you object to, and propose an alternative. Note that I am not addressing the authors' method of proving that the FWT is true - given the axioms they work with, and the rules of inference they rely on, their reasoning seems faultless to me. You tell me that they are mathematicians by training, so I'd expect nothing less in any case. What follows from this point on is based on my understanding of the content of the FWT being the correct understanding.

If there is no such thing as free will in the sense of it entailing the existence of uncaused human actions, then the antecedent of the FWT (framed in terms of free will) is false. Of course, the FWT itself remains true in such conditions, but trivially true by the classical laws of logical implication (which are the laws of inference being used by the authors to prove the FWT). Specifically, if the antecedent of a conditional is false, the conditional itself is true, but we cannot infer anything at all concerning the truth or falsity of its consequent. Now, the PSR - under many interpretations at least - entails precisely that there is no such thing as free will in the sense of allowing for uncaused human actions. So, under those interpretations of PSR, the antecedent of the FWT conditional is false. So, even if the PSR is true, FWT remains nevertheless true. If the PSR is false and there are uncaused human actions, FWT is also true, and we have the bonus of being able to use modus ponens to conclude that its consequent is true as well. Therefore, even if FWT is true, PSR could be either true or false. This is as much to say that the truth of the FWT is irrelevant to the truth or falsity of PSR.

The FWT is a conditional theorem to the effect thatif there are uncaused events of one specific kind, then there are other uncaused events. — MetaphysicsNow

Choices are not uncaused. All that is required is that choices exist and that in this particular case, choosing which button to press is possible.

As I have already pointed out, the choice could be relegated to a computer program, or any number of computer programs in series.

Another way of expressing the ability to choose, would be something like the assertion, "Science is possible." For surely, if an experimenter is not free to choose which experiments to perform, then science is impossible.

Read the paper - the authors are quite clear that the FWT states precisely and only that the measurement outcomes are free in the sense that the measurement choices are free. They even talk about measurement outcomes inheriting freedom from the freedom of choice. If that sense of freedom allows that choices can be caused, then the measurement outcomes are free in the sense that they can be caused also, and once again we are back to FWT being irrelevant to the PSR.

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

This is misleading. It's not that the free will theorem falsifies the principle of sufficient reason, but that one of its premises denies the principle of sufficient reason.

Taken from The Strong Free Will Theorem:

... if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic—the universe’s response near the particle) is not determined by the entire previous history of the universe.

Notice the antecedent. The rest of the argument is irrelevant (on this issue) as the principle of sufficient reason has already been rejected from the start.

So I don't know why you brought up the theorem at all (you do seem to have a strong love for it in general; you're always bringing it up). You can just say that free will falsifies the principle.

:up: Thank you for summing up concisely exactly what I've been trying to express in my admittedly rather long winded fashion. Let's hope that tom now drops this whole FWT refutes PSR gambit and picks up on the more interesting elements of some of his posts.

The FWT would still hold if the choice was made by a pseudo-random number generator. — tom

A true random number generator, yes, but not a pseudo-random number generator. Pseudo-random number generators are deterministic.

But if the principle of sufficient reason is true then true random number generators are impossible, so again this seems to beg the question.

Notice the antecedent. The rest of the argument is irrelevant (on this issue) as the principle of sufficient reason has already been rejected from the start. — Michael

As I mentioned earlier, I find it strange that people are willing to abandon science to protect a treasured principle.

I also mentioned earlier, that if it is not possible to choose which button to press, then the type of determinism that exists must be acausal.

I also mentioned that the PSR does not seem to survive either way.

As I mentioned earlier, I find it strange that people are willing to abandon science to protect a treasured principle.

I also mentioned earlier, that if it is not possible to choose which button to press, then the type of determinism that exists must be acausal.

I also mentioned that the PSR does not seem to survive either way. — tom

This doesn't address my issue with your claim, which is that it is misleading to say that the free will theorem falsifies the principle of sufficient reason.

Just say that humans having free will falsifies the principle.

Just say that humans having free will falsifies the principle.

But please don't just leave it at that. It would take a very specific understanding of what free will amounts to for its existence to refute the PSR. Once that specific conception is explicitly stated, the issue then is what happens if we deny that free will in that sense exists?

Tom seems to believe that denying the existence of free will in this sense entails that science is not possible. I'd like to see the argument for that, since - after all - science is possible, and so the possibility of science would prove the existence of free will (in that sense). But as indicated, there's some argumentative work to do to reach that point.

<SophistiCat already asked my question>

But please don't just leave it at that. It would take a very specific understanding of what free will amounts to for its existence to refute the PSR. Once that specific conception is explicitly stated, the issue then is what happens if we deny that free will in that sense exists? — MetaphysicsNow

If he's going by the free will theorem then "the choice ... is not a function of the information accessible to the experimenters".