The Sufficient Reason for Contingent Truths
Leibniz, Classical Theism, and the Problem of Evil - Chapter 1 (part 3)
Happy Sunday, subscribers. As those who follow Theological Letters know, I have a forthcoming book on Leibniz and the problem of evil with Routledge, and I am working feverishly to hit my deadline — which has been (graciously) bumped to September 9. (No further bumps allowed, come Hell or high water.)
To date, I have posted the Introduction and parts 1 and 2 of Chapter 1. Today, I offer part 3, The Sufficient Reason for Contingent Truths. (Chapter 1 consists of four parts in total, so next week will mark the final installment on that chapter.)
If you have yet to read the Introduction, I recommend you do so. In addition, I recommend reading parts 1 and 2 of Chapter 1 before delving into today’s post, since these sections build on one another.
I’ve linked to all three below. Be watching for more next Sunday. Enjoy!
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The Sufficient Reason for Contingent Truths
As odd as this demand may seem, there is an argument that once claimed to offer an existential analytic truth, namely, the ontological argument. The truth it offered is “God exists.” The argument, in short, claims that if one understands what God is, then he also understands that God exists. The case, in other words, is that the pairing of “exists” and “God” is as analytic as the pairing of “foursided” and “square.” And so, the statement “God does not exist” is a formal contradiction on par with “the square is not-foursided.” And this is precisely what PSR requires, namely, an analytic existential truth to ground contingent truths.
The ontological argument first appears in the second and third chapters of Anselm of Canterbury Proslogion seu alloquium de Dei existentia (Discourse, or Address on the Existence of God). In chapter 2, Anselm defines God as “a being than which nothing greater can be conceived,”1 a premise he takes to be self-evident, since even “the fool,” who says there is no God (Ps 14:1), grants this definition in his denial of God.2 Anselm then suggests that the concept of God must exist either in the mind only or in the mind and reality.3 This premise may strike the modern reader as odd, but it’s firmly rooted in medieval modal logic.4 Within medieval modal thinking, the categories of “impossible,” “possible but not necessary,” and “possible and necessary” presume a form of realism that determines modes of existence based on the relationship between logical possibility (the thing in the mind) and existence (the thing in reality).
To illustrate, the modal assessment of a “thing” begins with an assessment of the terms posited. Specifically, do the predicates ascribed to the subject result in contradiction? “Human,” for example, places before the mind a “rational” (specific difference) “animal” (genus), to use Aristotle’s method of defining a term.5 No formal contradiction appears in this subject-predicate combination. Nor does any arise when adding “bipedal,” “two-armed,” “ten-fingered,” etc. We thus have before us a logical possibility, or one that exists within the mind. The next question is whether this possible thing exists in the mind only or in the mind and in reality. A look in the mirror demonstrates one instance of “human” conjoined with “exists.” Hence, this possible being exists in both mind and reality. As for whether “human” is contingent or necessary, the answer concerns yet another subject-predicate relationship: Does the negation of the predicate “exists” in reference to “human” yield a formal contradiction? Nothing in the definition of “human” seems to entail existence, and if we grant that there was a time when no human existed, then this confirms that “exists” can be negated of “human” without contradiction. At that time, “human” existed in the mind only as a logical possibility, nothing more. From all of this follows that “human” is possible but not necessary (i.e., contingent).6
Now, contrast this with the subject-predicate pairing “not-foursided square.” Such a term places before the mind a formal contradiction, since “foursided” is an essential property of “square.” The word combination “not-foursided square” thus fails to rise to the level of a logical possibility. As such, the “thing” posited is impossible, existing neither in the mind nor in reality. Or put otherwise, before we can assess whether something exists (and if so, whether it exists contingently or necessarily) we must first posit a thing. Incoherent word combinations fail this basic test. Such contradictions exist neither in mind nor in reality because “they” are meaningless utterances.
Unlike either modal contingency or modal impossibility, modal necessity applies to those things that are not only possible but entail existence. To predicate “does not exist” of the subject, then, yields a contradiction on par with predicating “not-foursided” of “square.”
Returning to Anselm, his first premise presumes that God is logically possible. Hence, the thing signified by the word exists either in the mind but not reality or in the mind and in reality. Building on the premise that God is the greatest conceivable being, he concludes that God must exist both in mind and in reality. For a being who exists in the mind only would be inferior to a being who exists in mind and reality. In other words, saying that God — the greatest conceivable being — exists in mind only yields a contradiction, namely, that we can conceive of a being greater than he.7
Now, this initial formulation of the argument is dubious, since existence appears irrelevant to the place of a possible being in the hierarchy of possible beings. Here, the so-called “Great Chain of Being” provides critical context for both the claim and its deficiencies. Chain of Being metaphysics holds that the cosmos is composed of a hierarchy of beings that display an “order of excellence” (ordo eminentiae).8 Morton Bloomfield summarizes the view of the day:
The qualitative distinction between each level [of the Chain of Being] is its degree of perfection. The whole universe may be looked upon as a machine or organism for the production of increasing degrees of perfection. The chain took its origin in perfection and is characterized by a straining back towards its source and original perfection [i.e., God]. Creation is a great flowing out from God and a movement back to Him in a series of ontic steps.9
The concept of “perfection” (perfectio) here at work is complex, given to several definitions in the period.10 In the context of the Chain of Being, it concerns a creature’s excellence relative to other creatures, which determines its place in the hierarchy of beings relative to God. Put simply, a plant is higher in the chain than a rock because it possesses life, a perfection that rocks lack. An irrational animal, such as a dog, is higher in the chain than a plant, because a dog possesses a form of sentients and locomotion, perfections that plants lack. A human is superior to a dog because a human possesses reason, a perfection that irrational animals lack. And if we believe the Psalmist (8:5), a human is a little lower than the angels, which means the angels possess perfections that a human lacks.
This metaphysic is relevant to both the failure of Anselm’s argument in chapter 2 and its success in chapter 3. The deficiency of chapter 2 becomes evident when we consider the irrelevance of existence to the created hierarchy. The relative excellence of human to dog, for example, is based on a comparison of the essential properties of the two: That “rational” is predicated of “human” but not “dog” is what places “human” above “dog” in the Chain. Were God to choose to create a dog but not a human, this would have no bearing on the relative excellence of these two natures. For the comparative attributes of “dog” and “human” would remain the same. Therefore, the premise in chapter 2 — that adding existence raises the status of a possible being in the hierarchy of beings — is evidently false.
However, Anselm makes a key revision in chapter 3. He argues that necessary existence is qualitatively superior to contingent existence: “To thee alone, therefore, it belongs to exist more truly than all other beings, and hence in a higher degree than all others. For, whatever else exists does not exist so truly, and hence in a lesser degree it belongs to it to exist.”11 The claim is different from chapter 2. Rather than saying a being is greater if it has existence than if it does not, the argument shifts, claiming that modal necessity is superior to modal contingency. The revision is significant. Anselm now claims that existence is a perfection relevant to a being’s excellence if existence is intrinsic to its essence, as opposed to being an extrinsic accident.
The nuance is important. Amongst contingent beings, the relationship to existence is uniform: Existence is an accident in which created beings can participate and of which they can be deprived. So existence adds nothing to the ontological ranking of contingent beings. But modal necessity contemplates a different mode of existence. Existence here becomes an essential property of the nature posited.12 In keeping with thinking about the Chain of Being generally, then, if modal necessity indicates a good internal to the nature posited, then essential existence denotes a perfection that modally contingent beings lack.
Bringing these points to bear on the premise that God is the greatest possible being, the necessity of divine existence becomes evident. If we present to the mind two beings, being Q and being R, and both Q and R possess every perfection, but Q has existence as an essential property while R has existence as an accident — if it has existence at all — then which is the greater being, Q or R? As per the claim that essential existence is a perfection, the answer becomes clear: Modal necessity is superior to modal contingency. Therefore, Q is greater than R. Because God is the greatest possible being, it follows that R would wrongly be called “God,” since Q is greater. The name is rightly ascribed to Q and Q alone. Or to take a simpler route to the same conclusion, if God is a being having all perfections, and essential existence is a perfection, then God must possess essential existence. Hence Anselm’s conclusion: God is modally necessary and cannot not exist.
Within the modal system Anselm presumes, few means of evading the argument present themselves. One could deny that modal necessity is superior to modal contingency, but this is not an easy case to make, given the argument from the order of excellence. The alternative reply is that God is modally impossible. In other words, there is something problematic in the very idea of such a being. So it is here that Anselm fortifies his case.
As mentioned above, modal impossibility requires a contradiction, such that the “thing” presented is no thing at all; “it” is just meaningless words. For this reason, Anselm suggests that “the fool” proves that God exists when he denies that he exists. In chapter 2, he writes, “Or is there no such nature, since the fool hath said in his heart, there is no God? But, at any rate, this very fool, when he hears of this being of which I speak — a being than which nothing greater can be conceived — understands what he hears.”13 The fact that the fool understands what the theist means by the word “God,” argues Anselm, demonstrates that the logical possibility we call “God” exists even in the fool’s mind. For the fool knows what he declares to not exist. In this admission, the argument is won. For the fool, admitting that he has God in mind, admits that God is possible. The only question is whether God is contingent (in mind only) or necessary (in mind and reality). But as per the case of chapter 3, God necessarily exists in both mind and in reality.
Not all were convinced by Anselm’s case, Christians included. Aquinas does not include the argument in his “five ways,” though his criticism is less a critique of the argument’s claims and more a critique of its ability to prove God’s existence to someone who is ignorant of the nature of God.14 John Duns Scotus also criticizes the argument but in a way that anticipates what we find in Leibniz. Scotus believes the proof is incomplete. Why? Because Anselm is too easily satisfied that the concept of God is possible. So, how would one demonstrate the possibility of “God”? Scotus’ answer reflects the use of contradiction as the litmus test for possibility: One must show that the predicates ascribed to the subject are free of contradiction. In the case of God, Scotus suggests that a being having all perfections indicates “infinite being.” So, we must show that “infinite” can be predicated of “being” without contradiction. Only after demonstrating this can one prove that “infinite being” necessarily exists.15
We find something similar in Leibniz. With regard to proofs for the existence of God generally, Leibniz makes his position clear in his Nouveaux essais sur l’entendement humain (New Essays on Human Understanding): “I believe … that nearly all the means which have been employed to prove the existence of God are good and might be of service, if we would perfect them” (NE 505 / E 375). As for the ontological argument, Leibniz is positively disposed to the proof, but he believes that neither the case of Anselm nor its echo in Descartes, who Leibniz credits for its Modern resuscitation, is complete (G 4.405-6). What he means is the argument presumes something it fails to demonstrate. What precisely does it presume? He writes, “it is tacitly assumed that the idea of the all-great or all-perfect being is possible, and implies no contradiction” (NE 504 / E 375). In short, we find the very complaint leveled by Scotus.
Leibniz frames the argument as positing a being who has all perfections, or is all-perfect being, or is supreme perfection, or includes all degrees of perfection. He writes,
God is the greatest, or (as Descartes says) the most perfect of beings, or rather a supreme grandeur and perfection, including all degrees thereof. That is the notion of God. See now how existence follows from this notion. To exist is something more than not to exist, or rather, existence adds a degree to grandeur and perfection, and as Descartes states it, existence is itself a perfection. Therefore this degree of grandeur and perfection, or rather than perfection which consists in existence, is in this supreme all-great, all-perfect being: for otherwise some degree would be wanting to it, contrary to its definition. Consequently this supreme being exists. (NE 503 / E 374)
What Leibniz believes the case clearly demonstrates is that if God is possible, then God exists.16 Such a demonstration is no small matter, for it establishes a hypothetical necessity. If one can show that God, as defined by the argument, is possible, then the case is won and the existence of God is proved.
Now, the question “Is God possible?” may sound odd to the average ear, especially when considering that the question is really asking, “Is the concept of God as nonsensical as the concept of a square circle?” In other words, is the very idea nonsense? That you and I have an idea of God seems relatively uncontroversial. And as we saw, Anselm takes this fact — that “the fool” has an idea of God — to demonstrate the possibility of God. Likewise, Descartes’ own ontological argument also begins with the fact that Descartes has an idea of God.17 No doubt Leibniz would grant the point. So why does this not suffice to prove the possibility of God? Leibniz’s answer is that we have all sorts of confused and ill-defined ideas floating about in our minds, ideas like “square circle” that some think God could create but which are full of contradictions. The question is whether this idea, “God,” is a real definition or one of these ill-defined fantasms (e.g., A 6.4.589; G 7.305).18
For his part, Leibniz believes that “God” indicates something real, and the philosopher of Leipzig believes he can demonstrate the point.19 He offers several demonstrations throughout his writings, some of which are more complex than others.20 For our purposes, a brief overview of his several approaches should suffice without carrying us too far afield.
Essential to the ontological argument are questions about the nature of existence. Leibniz’s thought on this topic evolves over time.21 His mature thinking on the subject moves away from the idea that existence is a predicate,22 and the result is a rather idiosyncratic demonstration of the possibility of God. Rather than treating existence as a property that one may have essentially or accidentally, Leibniz embraces the peculiar notion that every essence lays claim to existence and naturally strains toward being. But not all beings are compossible, so only the maximal combination of essences comes into being. Here, the sufficient reason for a thing existing is perfection — that is, the being is part of optimal reality. Though we have yet to reach Leibniz’s theory of the best, needless to say, his optimism lurks in the background of this claim.23 The relevance of this theory to God is that the sufficient reason why any possible being would not exist is that it conflicts (or is incompossible) with something more optimal, some greater perfection that lays claim to existence. I trust the implication for God is evident: The greatest possible being necessarily exists because nothing greater could lay claim to being, edging it out of existence.24 As I said, the claim is peculiar.25
A second demonstration Leibniz offers concerns the definition of “God” as one who has “all perfections.” This definition offers a seemingly straightforward road to a demonstration. For it provides a neatly framed question: Do any perfections contradict one another? If so, then a being who has all perfections is like a square with a flowing circumference — impossible. But if all perfections are compatible (or compossible), then such a being is possible.
While the framing of the question is straightforward, Leibniz’s proof is less so. Leibniz believes that perfect being expresses all purely positive (pure positivum) qualities without any limits (A 6.3:578). The premise is important because when considering “all perfections,” we can likely think of plenty of goods that are incompatible with one another. For example, certain goods of the single life are incompossibe with certain goods of the married life. But Leibniz can respond that these goods are complex and not what he means by purely positive qualities.26 So what does it mean to be a purely positive quality? Well, let’s take the property of “being square.” This property excludes the property of “being circle.” Hence if “being square” is A and “being circle” is B, then A = not-B. In other words, A is not a purely positive property because it includes a negation, and the same is true for the goods of “being married.” Purely positive qualities are without limits and thus without such negations (A VI iii 572, 575, 577-9).27
The importance of this point is twofold. First, the natural result is that “perfect being” is equivalent to “infinite being,” since it has no limits, which is where Scotus landed in his framing of whether God is possible. The second, more important result is this. To formulate a contradiction, one needs negative predicates: A = not-A. If purely positive qualities have no limits and thus no negations, then purely positive qualities cannot contradict one another.28 Hence, if perfect being is infinite being, having only positive qualities, then none of these qualities can contradict (cf. A 6.3:396).