The Principle of Sufficient Reason
Leibniz, Classical Theism, and the Problem of Evil - Chapter 1 (part 2)
Greeting subscribers. As those who follow Theological Letters know, I have a forthcoming book on Leibniz and the problem of evil with Routledge, and I’m working feverishly to hit my mid-Augst deadline.
On March 30, I posted the updated Introduction, which lays bare the purpose and outline of the book. Last Sunday, I posted the opening of chapter 1, which is devoted to explaining why Leibniz believes our world is the best of all possible worlds. Today, I offer part 2 on the Principle of Sufficient Reason — a principle that is indispensible to Leibniz’s theory.
If you have yet to read the Introduction, I recommend you do so. Truth be told, I expanded the Introduction considerably this week (and updated my Substack according), so you may want to read that even if you read the original post. In addition, I recommend reading over the opening of chpater 1 before delving into today’s post. If you read that opener, no need to revisit it, although the final paragraph did not post last week for some reason. You may want to at least read that for full effect.
I’ve linked to both of these prior posts below. Now, back to work. Enjoy!
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The Principle of Sufficient Reason
Fluorescent lights flicker overhead as students settle in for their first day of Introduction to Philosophy. The only sounds, aside from the luminescent hum overhead, are anxious clearing of throats and shifting in seats. Suddenly, the door flies open and in steps Professor Reinhold, a man of advancing years whose forehead bears the marks of one who has too often raised a skeptical eyebrow. He places his vintage briefcase atop the desk at the front of the class and swivels on his heels to look at the students, adjusting his tweed blazer and smoothing his unkempt white hair. His slitted eyes survey the room, assessing his latest victims.
He locks eyes on Kyle, a lanky young man who shifts in his seat, looking like a gazelle who has been spotted by a lion. The professor asks him pointedly, “Did you bring a copy of Aristotle’s Metaphysics?” Kyle goes whiter than usual, looking as though he might vomit. He swallows hard and mutters, “No.” The professor scowls and asks, “Then how do you plan to read it?” Whipping out the syllabus, Reinhold taps the paper, crinkled tightly in his clenched fist, noting that it says in black and white that they will be reading Aristotle in class today. Panic sets in and Kyle frantically points to the girl next to him, blurting out, “Jane! I’ll borrow Jane’s copy!” Kyle breathes relief. Crisis averted — for him. But Jane stares bullets at Kyle, looking as though he spat on her. She breathes deep, composing herself, and then sheepishly confesses to the steely eyed professor, “I don’t have a copy either.” But before the professor’s wrath is fully kindled, she quickly redirects to William, insisting that she’ll borrow his. William’s eyes bulge. He clears his throat, fessing up that he doesn’t have the book either, but he assures the increasingly agitated professor that he’ll borrow it from Tim. The professor watches the parade of ineptitude with mounting impatience until the excuses cycle through every student in the class and arrive back at Kyle.
All air is sucked from the room as the students realize that none of them brought the book. Reinhold’s brow has grown so furrow it threatens to swallow his face. They collectively brace themselves for the fallout of their carelessness. Through clenched teeth, the professor asks a simple question, “If none of you have the book to loan, how can any of you hope to borrow it?” The students shrink with embarrassment. They know the answer. Unless one of them has the book to loan, their chain of deference is impotent.
As the students brace themselves for their lashes, a smile forms on Reinhold’s face. Confusion washes over the class. With great delight, the old professor announces that they have perfectly demonstrated, as well as any could, the argument from contingency.
Reinhold snaps into lecture mode. Every being in our cosmos is contingent, depending on others for his existence. “Not only do you and I depend upon oxygen, food, and water, but my initial existence depends upon my parents coming together in the time, place, and manner they did to bring me into being. But,” he continues, “both these life-sustaining substances and my parents are themselves contingent, depending, in their turn, on other beings and events for their existence.” Wandering to the large glass windows overlooking the campus, Reinhold continues that if you ask the astrophysicists about the necessary conditions for life, you’ll hear about the extraordinary fine tuning required to make our planet suitable for life, conditions without which the air we breathe, the water we drink, and the atmosphere in which we move would not be possible. With wonder, the aging scholar explains that our entire world is an aggregate of contingent beings, each one borrowing his existence from next.
“Yet,” he declares, turning his gaze once again upon the students, “like your book borrowing, existence borrowing can only yield existence if something in the chain has existence to give.” With this, Reinhold pulls from his briefcase a weathered copy of Aristotle’s Metaphysics, bearing the marks of having been read time without number. He extends his copy to Kyle, who sheepishly takes it, and then hands it to Jane, who hands it to William, who hands it to Tim.
The professor watches as his books passes from one student to the next. With a smile, he asks, “So what is it that has existence in itself, without borrowing, and can give it to others?” The students expect they know the answer, but Reinhold does not wait for a reply, “In the words of Thomas Aquinas, this all men call God.”1
Our hypothetical classroom illustrates the argument from contingency, which makes the case that the existence of contingent creatures requires the existence of something else, something with self-existence or necessary being. In a word, the existence of creatures requires the existence of God. The case is an exceedingly ancient one with advocates amongst pagans, Jews, Christians, and Muslims.2 The argument takes several forms. In the kalām (or ilm al-kalam) cosmological argument, for example, the case builds to a First Cause of existence in the temporal sense — an eternal Being who pushes the first domino, as it were.3 So the case goes, any being whose existence begins must be caused by some prior being, and if that prior being also began to exist, then he too must have a prior cause. Granting that an infinite regress of causes is impossible, much like the infinite book borrowing in our hypothetical class, we must arrive at a Being whose existence has no beginning, who eternally has been.4
Aristotle’s cosmological argument,5 by contrast, does not require a beginning to time — nor could it, since Aristotle believed the world is eternal.6 Yet, even without a start to the world’s existence, Aristotle saw a fundamental contingency in the cosmos. We might think of it this way. The kalām case from contingency is horizontal, stretching backwards in time to a starting point in the chain of causes. Aristotle, by contrast, sees a vertical contingency.7 At every moment, every inch of the cosmos is undergoing some type of change or mutation, where some potential to be otherwise becomes a concrete reality. Such change requires a cause. But as Aristotle points out, potential things cannot serve as causes, only actual things can. Hence, every mutation represents a contingency — an unrealized possibility that moves into reality. And like all contingencies, such change is dependent upon something else, upon something real, upon something that exists and can serve as a cause.
To illustrate, if I clench my fist, there is a movement from potential to actual, where the potential for the skin enveloping my hand to be otherwise becomes real. So what sits beneath this change, moving that potential into reality? We can point to the movement of bone beneath the surface, but this too is a shift in potential. On what, then, does this shift stand? Of course, we will point to the tug of tendons and the contraction of muscles, but once again, these represent their own potential-to-actual shift. In short, what we discover is a new regress, not temporal but ontological — changes in skin upon bone, upon muscle, upon neurons, and on down to the subatomic level. Aristotle recognizes that this vertical stack of contingencies cannot recede in infinite regress.8 Much like the proverbial tale of one who claims the world rests on the back of a turtle, when asked what the turtle stands upon, we cannot reply that he stands upon another turtle, who stands upon another, who stands upon another in infinite regress. Beneath all these changes, there must be a ground at which the regress terminates, a First Cause upon which they all stand. Such is Aristotle’s “Unmoved (or Immutable) Mover,” One who is not contingent, One who moves these potentialities into reality without Himself undergoing such change because his Being is necessary.9
Such arguments were common in the medieval period. These and other versions would continue to be ushered out by the scholastics as proof of God’s existence. In addition to the kalām cosmological argument, we find in the pages of Muslim philosopher, Avicenna, an argument from contingency closer in kind to Aristotle’s case, though not identical. Avicenna argues that the cosmos is an aggregate of contingencies, and the entire set must have a cause that is not contingent, lest the identified cause be a contingent being who is part of the aggregate in search of a cause. Hence, this cause is God, the Self-Existent One.10 In Thomas Aquinas’ “five ways,” we find echoes of every version of the argument, from the kalām argument from temporal regress to Aristotle’s argument from mutation (or motion) to Avicenna’s argument from contingency.11 And such claims would not disappear with the dawn of the Enlightenment, but continue to echo in figures like René Descartes.12
In Modernity, however, the argument becomes closely tied to what is called the Principle of Sufficient Reason (or PSR). PSR is most often associated with Leibniz, who says of the principle, “[it] must be considered one of the greatest and most fruitful of all human knowledge, for upon it is built a great part of metaphysics, physics, and moral science” (G 7.301). As we will see, Leibniz’s entire philosophy depends upon there being a sufficient reason for our world. But PSR is not Leibniz’s invention, arguably appearing in some form or other in the writings of Anaximander, Parmenides, Archimedes, Plato, Aquinas, and Avicenna.13 Even within Modernity, Leibniz is not the first to invoke the principle.
In Baruch de Spinoza (1632-1677), the formulation of PSR is causal in nature, mirroring the aforementioned arguments from contingency. He writes, “Nothing exists of which it cannot be asked, what is the cause (or reason), why it exists.”14 The point echoes Descartes, who declares that “nothing can come from nothing,”15 which is an echo of one of the oldest metaphysical axioms, dating back to the pre-Socratic philosophy of the Eleatics.16 When asking why a thing exists, Spinoza explains, one has two options. Either the explanation for existence is found in the thing or in something external to it. This dichotomy becomes the basis for Spinoza’s distinction between that which exists and that which subsists in something else, a distinction that wades into the waters of “substance.” Descartes had (somewhat classically) defined substance as that in which properties subsist, which is to say that substance exists while properties subsist within substances.17 Likewise, Locke defines substance “in plain English, [as] standing under or upholding.”18 What Spinoza notices about this rather common definition is that it seems to require that substance is self-existent, lest it subsist in something else.19 In other words, the properties (or what Spinoza would label “affections of substance”) display dependence upon substance, but substance is not dependent upon something else. Hence, he defines substance as one “whose concept does not require the concept of another” or exists “in itself.”20 And from this he concludes that God alone is rightly called Substance.21 Creatures, by contrast, are falsely called substances since we are contingent or dependent, subsisting in God.22 Needless to say, Spinoza’s pantheism naturally follows from such conclusions, which is why he is often read as deriving his entire system from PSR.23
Although entirely unlike Spinoza in his opinions, we find equal enthusiasm for PSR in Samuel Clarke (1675-1729), one of Leibniz’s many dialogue partners. Clarke praises the principle as “the most incontestable” doctrine, and his definition, like Spinoza’s, is causal in focus:
Whatever Exists, has a Cause, a Reason, a Ground of its Existence; (a Foundation, on which its Existence relies; a Ground or Reason why it doth exist, rather than not exist;) either in the Necessity of its own Nature, and then it must have been of itself Eternal: Or in the Will of some Other Being; and Then That Other Being must at least in the order of Nature and Causality, have Existed before it.24
The resonance between PSR and the arguments from contingency are again evident. Clarke identifies the need for sufficient reason with the need for a ground of existence in which the regress of causal dependence terminates. The conclusion is very much a merger of the various arguments, invoking need for something prior to the order of nature (as per the kalām argument) that serves as a ground to existence (akin to Aristotle’s Unmoved Mover) and whose existence is necessary (akin to Avicenna’s contingency argument).
In Leibniz, we find a more expansive use of PSR.25 This is not to say that Leibniz denies that contingent beings find their footing in a Necessary Being. Certainly not. He plainly insists that the possible and contingent must be grounded in the actual and necessary, and this is precisely why, as we will see, he grounds all contingents and possibilities (as well as necessary truths) in the necessary and eternal God.26 But how Leibniz frames and uses PSR goes beyond what we see in Spinoza or Clarke.
To see how, we must look at how Leibniz pairs PSR with two other principles. The first is perhaps the best known principle of logic, namely, the law of contradiction (or non-contradiction, if you prefer). To use Leibniz’s framing of the law, “a proposition cannot be true and false at the same time, and that therefore A is A and cannot be not A” (G 6.355). By pairing PSR with the principle of contradiction, Leibniz makes clear that PSR is more than a causal principle — contingent beings finding footing on necessary ground. Rather, PSR is about truth and falsehood generally. Notice how Leibniz summarizes PSR, “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” (E 707, emphasis added; see also E 716; C 25-6; G 6:127; 7:301). PSR, says Leibniz, means that every truth and every falsehood requires a sufficient reason why it is so and not otherwise. There are no brute facts.
Now, this addition would not, in itself, make Leibniz stand out. After all, Spinoza too rejects the idea of brute facts.27 But Leibniz pairs this with a second, more peculiar commitment. According to Leibniz, when we say something true about a subject — for example, “The shirt is red” — the statement is true because the predicate (red) is somehow in the subject (the shirt). To quote Leibniz’s letter to Antoine Arnauld, “in every true affirmative proposition, whether necessary or contingent, universal or particular, the notion of the predicate is in some way included in that of the subject. Praedicatum inest subjecto; otherwise I do not know what truth is” (G 2.56).28
As odd as this claim may sound, like PSR, the principle is not Leibniz’s invention. The concept is traceable to Aristotle and also appears in the Logic text of Arnauld and Pierre Nicole.29 Perhaps an example from geometry might make the suggestion more palatable. Let’s say we were looking at an instance of a square, and one of us said truly, “This square is foursided.” To suggest that what makes this statement true is that four sides are substantially part of the square is not a terribly odd suggestion. Even if we moved from the particular square to the abstract idea of squareness and suggested, as Leibniz does, that God has in his Mind the Idea of squareness — that is, the archetype that is the measure of all particular squares30 — we could reasonably say that foursided is substantially part of that Idea.
The challenge, of course, is that Leibniz does not stop at geometry. He applies the claim to all true propositions, contingent or necessary, universal or particular. Applied to certain non-geometric examples, the claim continues to sound reasonable. Our proposition “The shirt is red” is one such example. The idea that red is a property somehow in the shirt seems sober enough. But what about a proposition like “Julius Caesar crossed the Rubicon in 49 BC”? In what sense is “crossing the Rubicon in 49 BC” in “Julius Caesar”?
The answer requires a shift away from more empiricist ways of thinking. We may be tempted to think of states of affairs or relations to time or location or other beings as mere mental associations, the mind placing one object relative to another by observation, but this association is only a habit of the imagination, not a concrete feature of reality.31 But if we shift our thinking to be a bit more Aristotelian, as Leibniz’s mature thought was,32 then his claim becomes more palatable. Keep in mind that, for Aristotle, a contingent being is a composite of concrete properties and unrealized potentialities. In my person, I bear a certain amount of physical strength, but beneath this strength is the potential for increase or decrease, to grow stronger or weaker. Through physical exercise, I can move that potential for increase into reality, and through sickness or neglect, my present strength can retreat out of being. Whatever the change, it is a shift in the properties within me. The same is true for the potential movement of a limb, the potential to speak a word, the potential to change positions, situations, time, or relations.33 Every change, every act involves new realities moving into being and old realities retreating out of being. So, if we think about predicates as the identification of properties, whether those are material properties of shape or color, or properties of action, or properties of situation or relation, we can see why someone of a more Aristotelian mind might think of true propositions as identifying properties that are somehow in a subject. To be sure, Leibniz is not a pure Aristotelian, but his own peculiar ideas about substance lead him to the same conclusion, namely, that such properties are substantially part of the subject.
What this means, in technical jargon, is that Leibniz believes all true propositions are analytic. Much like the way in which foursided is within the concept of square or unmarried is within the concept of bachelor, so crossing the Rubicon is in the concept of Julius Caesar.34
Now, two problems arise from this conclusion. The first is the most obvious and concerns free choice. If crossing the Rubicon is part of the very concept of Caesar, doesn’t this mean he does so necessarily, just as a square necessarily has four sides? We’ll devote ample attention to this problem in later chapters, but for now, let it suffice that Leibniz is bent on avoiding this conclusion.35 His answer, in brief, is this. What distinguishes a necessary proposition, like “A square is foursided,” from a contingent proposition, like “Caesar crossed the Rubicon,” is not whether the predicate is in the subject but how the predicate is in the subject. In the case of a necessary proposition, the predicate cannot be negated without contradiction. But in the case of a contingent proposition, the predicate can be negated without contradiction. So the opposite is possible (C 18-9). The difference is similar to Aristotle’s distinction between essential and accidental properties, the former being indispensable to the nature of the thing while the latter is not — say, a particular triangle is three sided (essential) and blue (accidental).36 What makes our proposition about a square necessary is that foursided is essential to squareness. But crossing the Rubicon, though true of Caesar, is accidental to him, making its negation possible without contradiction.37
The second problem is less obvious but illuminates a fascinating feature of contingent truths. Leibniz points out that the analysis of necessary truths resolves into a type of identity. The examination of mathematical truths or geometric truths or definitional truths, like bachelors are unmarried, go from the subject to the things said about it (predicates), and the result is a resolution where the entailment is evident — the way the definition of square entails four sides, equal length, and four right angles, for example. This is why mathematical truths and geometric truths can offer demonstrations or proofs. As Leibniz points out, this is the mark of a necessary truth, namely, it “can be demonstrated by the resolution of terms; these are necessary, or virtually identical, and so their opposite is impossible, or virtually contradictory” (C 18). Such resolution satisfies the demand of PSR. The relationship between the subject and the predicate is true because the concept of the subject entails the predicate in such a way that its negation leads to contradiction.38 Hence, the concept itself demonstrates why it is so and not otherwise.39
Notice, however, that contingent truths offer no such resolution and thus no such demonstration. As pointed out in reference to the free choice problem, whatever predicates are in the subject are in it in such a way that they can be negated without contradiction. Yes, Caesar crossed the Rubicon. But he did so contingently, which is why not crossing the Rubicon could be predicated of Caesar without contradiction. For this reason, no identity nor demonstration can be offered for this proposition. The proposition is true and intelligible, but the subject-predicate relationship it represents fails to offer a sufficient reason for why it is so.