Leibniz’s Principle of Sufficient Reason

Author: Marc Bobro
Category: Historical Philosophy, Metaphysics, Philosophy of Religion
Word count: 999

Imagine that your bicycle keeps dropping its chain. Annoyed, you take it to a bike shop to determine the cause in order to fix the problem. The mechanic informs you that the problem cannot be fixed because there is no reason why your bike drops its chain: it just does. It’s not that the cause of the chain dropping has not been determined: it’s that there is no cause why this is happening.

Gottfried Leibniz’s Principle of Sufficient Reason (PSR) entails that the bike mechanic’s claim is patently false:

“No fact can hold or be real, and no proposition can be true, unless there is a sufficient reason why it is so and not otherwise.”[1]

According to the PSR, there are no brute, unexplained facts; no uncaused events or anything happening without a cause; and no claims or beliefs are true without there being a reason why they’re true. This essay will explain why Leibniz accepted the PSR, its various applications, and its place in contemporary philosophy.

1. Leibniz’s PSR

Leibniz (1646 – 1716) is the Principle of Sufficient Reason’s most famous proponent, but he’s not the first to adopt it. The earliest recorded application of the PSR seems to be Anaximander c. 547 BCE:

“The earth stays at rest because of equality, since it is no more fitting for what is situated at the center and is equally far from the extremes to move up rather than down or sideways.”[2]

Also prior to Leibniz, Parmenides, Archimedes, Abelard, Spinoza, and Anne Conway were all proponents of some form of the principle.

Leibniz never explicitly offers an argument for the PSR, but it’s suggested by his definition of truth in this passage:

“… it is evident that all truths … have an a priori [i.e., not sensory-based] proof, or some reason why they are truths rather than not. And this is just what is meant when it is commonly said that nothing happens without a cause, or, that there is nothing without a reason.”[3]

Other remarks suggest that he might accept some reasoning like this:

All statements involve a subject and a predicate, e.g., ‘Washington crossed the Delaware.’ ‘Washington’ is the subject. ‘Crossed the Delaware’ is the predicate. Leibniz claims that a true statement is one where the predicate “belongs” to the subject. Since Washington did cross the Delaware River, the statement ‘Washington crossed the Delaware’ is true.[4] Now, it isn’t a necessary truth that Washington crossed the Delaware: it could have been the case that Washington didn’t cross the Delaware; his crossing is a contingent truth: true, but could have been false. In the case of a necessary truth, e.g., ‘Mary the bachelorette is unmarried,’ it’s obvious why the predicate belongs to the subject: the predicate ‘is unmarried’ belongs to Mary because it would be a contradiction to assert otherwise. To be a bachelorette is to be unmarried. But how is it that ‘crossing the Delaware’ belongs to ‘Washington’? There must be a reason.

Voila! We have the PSR.[5]

2. Applications of the PSR

Leibniz draws some important consequences from the PSR. His ‘Principle of the Identity of Indiscernibles,’ that if what seem to be two distinct things share all of their properties, then they are actually one and the same thing, follows from the PSR. Suppose there seemed to be two indiscernible spheres, sharing all of their properties: “each made of chemically pure iron, had a diameter of one mile, had the same temperature, color, and so on….”[6] But then there would be no sufficient reason for either one of the indiscernible spheres to be in the place it currently occupies and not the other. Therefore, by the PSR, if what seem to be two things share all of their properties, then they are actually one and the same thing: there’s only one sphere.


Leibniz also uses the PSR to develop a cosmological argument for God’s existence. Returning to the bicycle example, say that you’re able to explain the dropping of its chain because of misaligned gears. But then a further question arises: Why were the gears misaligned? And so on and on. Explaining a contingent truth with another contingent truth faces an infinite chain of “why” questions. A chain of answers to “why” questions that fizzles out or continues indefinitely cannot constitute a sufficient reason. Such a reason must go outside the series of contingencies. Indeed, Leibniz claims that any successful pursuit for reasons must end with a “necessary substance”—a substance that exists necessarily, namely, God.

The PSR plays an important role in Leibniz’s account of God’s creation:

“Since there is an infinity of possible universes in God’s ideas, and since only one of them can exist, there must be a sufficient reason for God’s choice, a reason which determines him towards one thing rather than another.”[7]

In other words, there is no other possible universe on par with our own, because otherwise God would have created neither.[8]

Leibniz also employs the PSR to reject Newton’s absolutist conception of space and time:

“[Newton believed that] space is something absolutely uniform, and without the things placed in it, one point of space absolutely does not differ in any way from another point of space. Now, it follows … that it is impossible there should be a reason why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner and not otherwise …. The case is the same with respect to time.”[9]

Leibniz’s own view is that space is the order of co-existing things and their states, and nothing more. Time is simply the order of successive things and their states.

3. Conclusion

Wolff and Schopenhauer, among others, defended versions of the PSR after Leibniz, but the PSR has never been the consensus view of philosophers; Plato, Descartes, and Hume were all detractors, to name just three.[10] Leibniz’s concern to avoid brute facts, uncaused events, and truths without reasons, however, remains a living concern for contemporary philosophers, although the terminology often differs.[11]


[1] Leibniz (1), Monadology §32, 217. He also writes,

“The fundamental principle of reasoning is that there is nothing without a reason; or to explain the matter more distinctly that there is no truth for which a reason does not subsist” (Leibniz [2], “Metaphysical Consequences of the Principle of Reason,” 172).

See also Leibniz’s Discourse on Metaphysics §13 and his Fourth and Fifth letters to Samuel Clarke.

[2] Aristotle, On the Heavens 2.13 295b11-16.

[3] In a 1716 letter to Samuel Clarke §5.125. Leibniz may be writing this because he is frustrated with Clarke at this point in his correspondence and doesn’t want to engage in defending the principle itself.

[4] Strictly speaking, according to Leibniz, in every true statement, the concept of the predicate is contained in the concept of the subject. This is called Leibniz’s concept-containment theory of truth.

[5] For Leibniz, every truth has its determining reasons, even those that obtain in merely possible worlds, for possible worlds too have their own sets of truths. This way of thinking seems to point to the PSR as a necessary truth—true in every possible world. But there is controversy over its modal status, i.e., whether it is necessarily true or contingently true. Is Leibniz saying that there cannot be a universe that has two, or more, indiscernible spheres? Or is he saying merely that our universe cannot contain such things? The great majority of commentators favor the former, but Owen Pikkert and Julia Jorati, for example, argue for the latter. In a letter to Bernoulli, Leibniz seems to point to the latter:

“I don’t say that the vacuum, the atom, and other things of this sort are impossible, but only that they are not in agreement with divine wisdom. For even if God were to produce only that which is in accordance with the laws of wisdom, the objects of power and of wisdom are different, and should not be confused” (Leibniz [1], 170f.)

This passage seems to indicate that indiscernible entities, such as vacua and atoms, are possible—that God has the power to actualize them—and that therefore the PSR is contingent. But this is the only passage of its sort, so the jury is still out over the modal status of Leibniz’s PSR. Anthony Savile points to another way of reading Leibniz:

“To the best of my knowledge, Leibniz never explicitly chooses between these two alternatives—Sufficient Reason as a necessary truth or as a necessary methodological postulate—and commentary can do little more than point out the attractions of each…. [T]he methodological proposal is rooted in the thought that unless Sufficient Reason holds in full generality the world of fact will scarcely be comprehensible at all” (Savile, 37).

[6] Black, 156.

[7] Leibniz (1), Monadology §53, 220.

[8] This move is reminiscent of the famous example of “Buridan’s Ass,” where a donkey, trying to choose between two equally enticing piles of hay and therefore lacking sufficient reason to act, starves to death.

[9] Leibniz (1), Third Letter to Clarke, 325.

[10] Plato says in the Timaeus that it is impossible for anything to come to be without a cause. This sounds like the PSR, however he also believes that there are things that don’t “come to be,” and some of these things (e.g., the pre-existent disordered motion before mathematical order is imposed on it by the demiurge) have no cause or reason.

Regarding Descartes, even though he sometimes insists that “nothing comes from nothing,” he also claims that God “creates” metaphysical and mathematical truths. They aren’t independently true apart from God’s choosing. Descartes adds that God creates these truths by a genuinely free and indifferent act of will; there can be no reason for God’s will to create any of these truths. This is in violation of the PSR.

As for Hume, although it may be in fact true that all things that exist actually do have a cause, the claim that all things that exist must have a cause is problematic. Hume argues that since the ideas of cause and its effect are separable, we can clearly imagine an object without its cause. In other words, even though everything that exists may have a sufficient reason, it is careless to judge that they in fact do or must.

[11] Dasgupta, 12, for example, argues for a version of the PSR that is formulated in terms of “grounds.”


Black, Max. “The Identity of Indiscernibles,” Mind 61, 1952: 153-163.

Dasgupta, Shamik, “Metaphysical Rationalism,” Noûs 50/2, 2016: 379–418.

Jorati, Julia. “The Contingency of Leibniz’s Principle of the Identity of Indiscernibles” Ergo 4/31, 2017: 899-929.

Leibniz, Gottfried. (1) Roger Ariew and Daniel Garber (ed. and trans.). G. W. Leibniz: Philosophical Essays. Indianapolis & Cambridge: Hackett, 1989.

Leibniz, Gottfried. (2) G.H.R. Parkinson and Mary Morris (ed. and trans.). Gottfried Wilhelm Leibniz: Philosophical Writings. London: Everyman, 1995.

Melamed, Yitzhak and Martin Lin, “Principle of Sufficient Reason,” in The Stanford Encyclopedia of Philosophy (https://plato.stanford.edu/entries/sufficient-reason/), 2016.

Pikkert, Owen. “The Modal Status of Leibniz’s Principle of Sufficient Reason.” Unpublished.

Savile, Anthony. Leibniz and the Monadology. London: Routledge, 2000.

Schopenhauer, Arthur. On the Fourfold Root of the Principle of Sufficient Reason. La Salle, Ill.: Open Court, 1974.

Spinoza, Baruch. Ethics and Selected Letters. Indianapolis: Hackett, 1982.

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About the Author

Marc Bobro is Professor and Chair of Philosophy at Santa Barbara City College in California. He holds a PhD in philosophy from the University of Washington, Seattle, an MA in philosophy from King’s College London, and a BA in philosophy from the University of Arizona, Tucson. He specializes in the history of modern philosophy, especially Leibniz. Bobro is also the bassist and tubist for the mythopoetic punk band Crying 4 Kafka and collaborates on art with Elizabeth Folk. https://marcbobro.academia.edu

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