Has anyone proven the Principle of Sufficient Reason?

Question

The Principle of Sufficient Reason is simply stated: “For every fact F, there must be an explanation why F is the case” (Melamed and Lin 2016, §1). The principle is most closely associated with Gottfried Wilhelm Leibniz (Melamed and Lin 2016, §3), although forms of the principle first appeared in antiquity (Melamed and Lin 2016, §4).

Leibniz joined the principles of noncontradiction and sufficient reason:

31. Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false;
32. And that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us. (Leibniz, cites omitted; Melamed and Lin 2016, §3.)

Did Leibniz offer any underlying proof for the Principle of Sufficient Reason? Whether or not he did, did anyone else do so?

Source:

Melamed, Yitzhak and Lin, Martin, "Principle of Sufficient Reason", The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), ed. Edward N. Zalta. URL accessed 15 June 2016, 5 December 2019. .

Answer 1

Émilie Du Châtelet (1706-1749) was a French philosopher who wrote a book of physics for her son that is famous for providing a strong argument for the Principle of Sufficient Reason:

If we tried to deny this great principle, we would fall into strange contradictions. For as soon as one accepts that something may happen without sufficient reason, one cannot be sure of anything, for example, that a thing is the same as it was the moment before, since this thing could change at any moment into another of a different kind; thus truths, for us, would exist only for an instant.

For example, I declare that all is still in my room in the state in which I left it, because I am certain that no one has entered since I left; but if the principle of sufficient reason does not apply, my certainty becomes a chimera since everything could have been thrown into confusion in my room, without anyone having entered who was able to turn it upside down.

In a weak sense this can be taken as an argument that everyone believes in the PSR rather than an argument for the PSR itself. If you didn't believe in the PSR, then it would be unremarkable for anything to happen. For example, if a bear were to suddenly appear in your living room and you didn’t believe in the PSR, you wouldn’t be surprised about it because there doesn’t have to be a reason for the bear to suddenly appear. Similarly, if your house were to suddenly disappear from around you, you wouldn’t be surprised because there doesn’t have to be a reason; things can just happen.

But the argument is about more than just what people believe; it's also about being justified in believing what you do. You would be justified in being surprised to find a bear in your living room but not justified in being surprised to see the couch that was there the last time you were in the room five minutes ago. Since you would be surprised at the bear, and since you would be justified in being surprised, it must be because things can’t just happen for no reason. In other words, everything that happens has a reason. Now, you could subsequently demand a proof that our surprise at the bear in the living room is justified, but we have to settle on premises at some point, and it's hard to imagine that anyone would seriously doubt that being surprised at the bear is justified.

This argument does have a weakness, and that weakness is that there are some events that don’t surprise us no matter what they are. For example, suppose you throw a die and it comes up six. There was only a one in six change for that to happen, but you aren’t surprised. Why? Well, it had to be some number and there was no reason it couldn’t be six, just as there was no reason it had to be six. It just rolled a six for no reason. If it had rolled a five, you would have been no more nor less surprised. So this argument for the PSR cannot (I claim) support the PSR for all events, only for events that have some order to them.

Answer 2

It's not clear what would be used as an actual proof of PSR - as Jo pointed out, it's taken to be self-evidently true or (per David's quote in his post) "true via argument from consequences" (a fallacy BTW).

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A broader problem with PSR is whether it is itself a fact or somehow a true non-fact.

If it is a fact then we need to explain why the PSR is True or else we just assert it as a brute fact, which invalidates the "Universal" version of the PSR that many people (especially Christian apologists) like to use.

If it is not a fact then why do we think it always holds? If we are honest, we'd have to admit it holds conditionally in circumstances where we would expect explanations to hold (as opposed to explaining the outcomes of a lottery, for example). Randomness is a strong counterexample to the PSR, especially because we have so many prosaic examples of this -- we don't need to appeal to exotic circumstances.

A related problem is that every explanation is also, by supposedly being a true statement, a fact...oops, infinite regress! It only ends at a brute necessity - that is the only logical place it can ever end (sufficiently or not).

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A good example where I think PSR goes too far is the Fine Tuning Argument for God. Here, we are supposed to think that there should be some intelligible reason for the entire universe to exist that itself doesn't require an explanation (contra PSR). Where you fall on this debate is largely determined by whether you think positing an extra-universal necessary being is more "sufficient" than simply asserting that the state of the universe at T=0 was simply necessary.

Apart from appealing to our evolved bias for agent-causation, it doesn't really get around brute necessities. If the being actually "fine tuned" the standard model parameters just so (a fact) then we need an explanation for that. "Because he wanted to XYZ" is the typical reason given (which is also a fact ;-); however, we then need to explain why he wanted XYZ and so on.

I've seen some heroic efforts to go from an abstract notion of a necessary being to a being with all the desired qualities of the Christian God but they all involve dubious (and perhaps false) dichotomies to get there.

As an example: Evil is the absence of God. This assumes we can only know X is evil if we can know God is not present in X. But, per "greater goods" theodicies, humans are not in a position to ever know this, which oddly leads to a form of "epistemic moral relativism".

Answer 3

Here are some explanations how Leibniz argues in favour of the principle of sufficient reason (PSR) in his Monadology, Section 31-38:

Leibniz applies PSR to propositions. He asks for a sufficient reason that a given proposition is true, equivalently for the PSR that the negation of the proposition is false.

Leibniz makes the following distinction of cases:

• The proposition is necessarily true. Here the PSR is the principle of non-contradiction: One shows that the negation of the proposition implies a contradiction.
• The proposition is contingently true. Here arises an infinite chain of sucessive reasons. This infinite chain cannot be the sufficient reason. The latter must be outside the chain, namely a necessary substance. “It is this that we call God”.

Summing up: For proposition which are necessary true Leibniz' PSR rests on a logical principle, and for propositions which are contingently true on an ontological principle.

Leibniz does not prove any of the two principles. He takes both as basic axioms or basic presuppositions of his philosophy.

Answer 4

Kant did style himself as having verified the principle of sufficient causal reasoning for events in time, and a principle of sufficient moral reasoning for choices outside time. An all-encompassing axiom of explanation he did not so much advance, though (he discusses the problem of trying to formulate unrestricted sequences of explanations on the side of the regress of reason, at the outset of the Transcendental Dialectic).

The more unified or generic approach would be in the context of modern formal explications of metaphysical grounding. In terms of zero-grounding, for example, we start out with the PSR in the form of a problem to solve, the problem of needing things that are ungrounded in one sense but not in another, to set up the scaffolding of existence-theoretic geology. By working out a good theory of zero-grounding, we achieve our essential desideratum, a proof-of-concept that there is a way to apply the PSR to itself that isn't "question-begging." Or so it might seem; others will point out other deficiencies in various technical metaphysics programs, with the monstrous shadow of "all possible worlds" looming over everything to this day, and all the trouble those otherwise very helpful things bring. (For an application of zero-grounding theory to metaphysics, see Muñoz[forthcoming?]. For other PSR-friendly grounding theories, see e.g. Swiderski[21] or Dillon[forthcoming?].)

Answer 5

IF reality is made of subcomponents that always existed...

THEN searching for "why" or "how" or "what caused them" would be questions that were null and void, since they always always existed.

ELSE and only else, can the "Principle of Sufficient Reason" be a provable notion.

Answer 6

principles cannot be proven (by definition). If you prove a principle, then you rely on other one(s), so the "proven" one is not a principle.

Answer 7

Heidegger addresses the groundlessness of The Principle of Reason, here:

What do we learn from these words of Leibniz? Two things are needed simultaneously for the path to reason and for residing in the province of fundamental principles and Principles: cleverness of thinking and reticence—but both always at the right place.

Therefore, in the fourth chapter of the fourth book of the Metaphysics, where he deals with what later is called the fundamental principle of contradiction and its foundation, Aristotle made the following remark: ἔστι γὰρ ἀπαιδευσία τὸ μὴ γιγνώσκειν τίνων δεῖ ζητεῖν ἀπόδειξιν καὶ τίνων οὐ δεῖ: "There is present a lack, namely of παιδεία, when one does not know for what one is to seek proof and for what not."⁵

5. Aristotle, Metaphysics, Γ (Book IV) 1006^[a] 6–8.

The Greek word παιδεία—still half alive in our word "pedagogy," which is not of German origin—cannot be translated. What it means here is the circumspect and vigilant sense for what at any time is appropriate and inappropriate.

What do we learn from the words of Aristotle? Whoever sets out into the province of fundamental principles needs παιδεία in order not to overestimate or undervalue them; we could also say, what is needed is the gift of distinguishing between what is pertinent and impertinent when it comes to simple states of affairs.

. . .

Everywhere we use the principle of reason and adhere to it as a prop for support. But it also immediately propels us into groundlessness without our hardly thinking about it in its genuine meaning.

In The Principle of Reason Heidegger goes on to draw together reason with being and ground, along the lines that no biological or whatever type of living existence can get anywhere without logical operations, cellular, biological, cognitive. Even backing it up with ancient ideas.

"Only when we contemplated what λόγος meant for Heraclitus in early Greek thinking did it become clear that this word simultaneously names being and ground/reason, naming both in terms of their belonging-together." GA10 112

Also from Being & Time p.215, footnote 3 Parmenides is quoted:

τὸ γὰρ αὐτὸ νοεῖν ἐστίν τε καὶ εἶναι, "For thinking and being are the same."

And of course, Being is necessarily groundless. Because if Being is what makes things be, as their ground, then like a sculptor makes a sculpture, the sculptor cannot be a sculpture, being cannot be a being. The foundation/ground of beings cannot be a being.

it has been maintained that 'Being' is the 'most universal' concept: τὸ ὄν ἐστι καθόλου μάλιστα πάντων.ⁱ Illud quod primo cadit sub apprehensione est ens, cuius intellectus includitur in omnibus, quaecumque quis apprehendit. 'An understanding of Being is already included in conceiving anything which one apprehends as an entity.'^1,ii But the 'universality' of 'Being' is not that of a class or genus. The term 'Being' does not define that realm of entities which is uppermost when these are Articulated conceptually according to genus and species: οὔτε τὸ ὄν γένος.ⁱⁱⁱ The 'universality' of Being 'transcends' any universality of genus. In medieval ontology 'Being' is designated as a 'transcendens'. GA2 p.22

i. Aristotle, Metaphysica B 4, 1001 a 21.

ii. Thomas Aquinas, Summa Theologica 11¹ Q.94 art. 2.

iii. Aristotle, Metaphysica B 3, 998 b 22.

So we have the ground of beings as being, and reason tightly instrinsic. So if this is suitably grokked it can be straightforward that reason is groundless and proofless.

we constantly spoke of "being" and "ground/reason" . . . What these words say can never be drawn together and packaged in a definition. To intend to do such a thing would be to pretend to be able to smoothly and nonchalantly grasp all the essential determinations of "being" and "ground/reason," and of being able to do this in a representation that would hover above time. But so conceived, the temporal would be the particular, limited actualization of the supratemporal contents of the definition. [GA10 p.95]