Can Leibniz satisfactorily account for contingency?

Throughout the Discourse on Metaphysics and the Letters to Arnauld , specifically, Leibniz embarks on an exploration of necessity and contingency in relation to the key metaphysical principles he postulates. Since the publication of the Discourse, Leibniz’s work has been subject to a barrage of philosophical criticism, the majority attempting to demonstrate the incompatibility of Leibniz’s metaphysical principles with the desirable ideas of divine and human freedom and the contingency of some propositions. In this essay, I will seek to sustain the line of argument that although Leibniz’s initial proposals within the Discourse are susceptible to stark criticism, he does seem to manage to justify his beliefs in the face of it and present a reasonable account of contingency.

Leibniz’s consideration of necessary and contingent truths follows directly from the postulation of his ‘Predicate in Notion Principle’ which states that ‘the notion of the predicate is contained in some way in that of the subject’ (Leibniz, ‘Extracts from the letters to Arnauld’ in G. W. Leibniz: Philosophical Essays ed. Ariew and Garber) ; all subjects contain within them all predicates relating to them. His exploration of necessity and contingency stems from what Leibniz calls ‘a great difficulty’ (Leibniz, ‘Discourse on Metaphysics’, 13), namely that the containment of all predicates that a subject has ever had, presently has, or will ever have, seems to suggest a world of necessity and determination. He expresses this clearly in the Discourse: ‘We have said that the notion of an individual substance includes once and for all everything that can ever happen to it and that, by considering this notion, one can see there everything that can truly be said of it, just as we can see in the nature of a circle all the properties that can be deduced from it. But it seems that this would eliminate the difference between contingent and necessary truths, that there would be no place for human freedom, and that an absolute fatalism would rule all our actions as well as all the other events in the world.'(Leibniz, ‘Discourse on Metaphysics’, 13) Essentially, Leibniz is generating an objection against himself here; he is raising the issue of the compatibility of the Predicate in Notion Principle, which he so firmly adheres to, and his idea of contingency and human freedom. A similar concern about the compatibility of the Predicate in Notion principle and the idea of contingency can be stated as follows. Let x represent a subject and y a predicate; if x=y , then the proposition ¬x=f is a contradiction. Contradictions are impossible. The opposite of impossible is necessary. Therefore, every true proposition we would have to claim to be necessary; no true proposition can be contingent posing a grave problem for the assertion that humans and God have freedom.

This invites him to delve further into the conception of necessity. A necessary proposition, for Leibniz, is true in any and every possible world, contingent propositions are true in this world but could easily have been false in another. It is through this idea of possible worlds that Leibniz is able to escape the aforementioned worry; thought it seems that a subject containing all its future predicates is necessarily going to perform certain actions or think certain things, in another possible world which God could have actualized, the same subject could easily have had different predicates. Therefore, it is not true that the actions or thoughts of that individual are necessary because they are not the same in every possible world. Leibniz suggests that ‘we must distinguish between what is certain and what is necessary’; future contingents are evidently certain because God, in his omniscience, knows all that will happen in his world, but this certainty does not entail necessity since God could have actualized a different possible world in which different things occurred. As Broad notes, ‘the behaviour of any actual body under given conditions is physically necessary, though metaphysically contingent.’ (Broad, C. D. Leibniz. An introduction,p.28)

Leibniz also draws the distinction between absolute and hypothetical necessity in order to address the issue. Absolute necessity is that ‘whose contrary implies a contradiction…this deduction occurs in the eternal truths, for example, the truths of geometry.’ (Leibniz, ‘Discourse on Metaphysics’, 13) The contrary of many propositions which we would want to call contingent, however, does not imply a contradiction; Caesar not crossing the Rubicon does not imply a contradiction. Instead, this type of proposition ‘is necessary only ex hypothesi and, so to speak, accidentally, but it is contingent in itself, since its contrary does not imply a contradiction. And this connection is based not purely on ideas and God’s simple understanding, but on his free decrees and on the sequence of the universe.’ (Leibniz, ‘Discourse on Metaphysics’, 13) Everything is determined by God; it is not metaphysically impossible for it to be the case that one performs a different action to that which is determined but it would be impossible for this to occur due to God’s pre-determination, his choice to actualize the best possible world. God’s choice to actualize the best possible world is also, according to Leibniz, a contingent action for ‘it is reasonable and certain…that God will always do the best, even though what is less perfect does not imply a contradiction.’ (Leibniz, ‘Discourse on Metaphysics’, 13)

As an aside, Broad also offers a method through which we can counter the claim that the Predicate in Notion Principle is incompatible with contingency. He claims that propositions are only necessary if the subscribe to two conditions: ‘the term must have a commonly accepted definition or description… [and].. the proposition in question must be entailed either by this definition or description alone, or by it in combination with premises all of which are necessary.'(Broad, C. D. Leibniz. An introduction,p.27) He claims that most singular propositions about individuals don’t fulfil these conditions; individuals don’t have ‘definitions’ or ‘descriptions’ as such thereby rendering both the first and second condition unfulfilled. Though this might be the case, however, this is simply a way in which Leibniz can be interpreted to satisfactorily account for contingency by redefining his theory. It is more helpful to return to Leibniz’s response.

It seems, as demonstrated earlier, that Leibniz’s own worry about the effect of the Predicate in Notion Principle on the idea of contingency prompts him to offer a solid theory of how contingency can exist in tandem with it. This theory itself, however, carries numerous points of contention which require examination. Perhaps one of the most poignant worries is the maintenance of the freedom of God. It seems that, in postulating a world where all predicates are contained in all subjects and therefore all is determined, God’s freedom is substantially limited. Arnauld famously expresses this concern in a letter to Leibniz : ‘I thought that we might infer that God was free to create or not create Adam, but assuming that he wanted to create him, everything that has happened to humankind had to happen, or ought to happen, by a fatal necessity, or at least, I thought that, assuming he wanted to create Adam, God is no more free, with respect to all this, than he would be not to create a creature capable of thought, assuming that he wanted to create me.’ (Leibniz, ‘Extracts from the letters to Arnauld’ in G. W. Leibniz: Philosophical Essays ed. Ariew and Garber) Leibniz offers rebuttal to Arnauld’s criticism which I think seem generally cogent. Firstly, he points out that God, when deciding to create Adam, would resolve to create a very specific version of Adam, the consequences of the creation of which would be consequences that God wills to happen. God considers the whole picture of the world before creating an Adam with the specific attributes to allow this world to be actualized. Leibniz states that God ‘takes into consideration all the resolutions he has concerning the whole series of the universe; this is somewhat like a wise man who, making a decision about one part of his plan and having the whole plan in view, would decide so much the better, if his decision could settle all the parts at once.’ (Leibniz, ‘Extracts from the letters to Arnauld’ in G. W. Leibniz: Philosophical Essays ed. Ariew and Garber) This does seem to preserve divine freedom since God is so omniscient that he can perceive the consequences of everything that will ever occur and determines them all at once in order to arrive at the best possible world. This idea of God generating a plan in its entirety for the world and its inhabitants also serves to counter the worry that God, if he does determine all of our actions, also pre-determines sin. For example, it seems that God created an Adam naturally pre-determined to disobey him. The idea that God generates a plan for the universe which results in the most overall good, the best possible world, offers justification of this. Broad puts the point succinctly: ‘he had to choose between a total state of affairs containing disobedient Adam, and other states of affairs containing no Adam or an obedient one. As he saw that the former was on the whole better than any of the latter, his consequent volition was for a disobedient Adam.’ (Broad, C. D. Leibniz. An introduction,p.27) Admittedly, human freedom emerges a little battered from this idea of a divine plan but it is perhaps questionable whether Leibniz even wishes to maintain human freedom; it certainly seems as if he is espousing a deterministic world view and talks frequently of the ‘certainty’ of our actions.

This reply, however, gives rise to a further objection from Arnauld. Leibniz maintains that the specific Adam determined ‘with respect to all these circumstances’ is an Adam chosen from an array of possible Adams. Arnauld claims it difficult to conceive of a number of Adams existing potentially since Adam is a particular individual with particular predicates, the collection of which determine ‘Adam.’ As Russell points out, ‘a subject is defined by its predicates, and therefore, if the predicates were different, the subject could not be the same.’ (B. Russell, A Critical Examination of the Philosophy of Leibniz chapter 3) Surely, the alteration of predicates means that a collection of possible Adams would not exist, only a collection of particular people all different from Adam; ‘ it is as difficult to conceive of several Adams, taking Adam as a particular nature, as it is to conceive of several mes.’ However, it is perhaps debatable whether this would really make a difference to the overall coherency of Leibniz’s theory; if I have understood the problem correctly, it seems to me to be one of terminology i.e. claiming that we cannot claim that person A is the same as person B because they have slightly different predicates. This would certainly be the case for Leibniz but it doesn’t seem obvious that he is claiming that these so-called ‘possible Adams’ are actually the same person, they are merely potential people. Leibniz, reasserting the worry of Arnauld, states that there could be a multiplicity of Adams who share the same predicates as the Adam we know and who fit the description of the Adam we are familiar with. However, Leibniz points out that this simply serves to demonstrate the importance of an individual having a complete and determinate nature. The Indentity of Indiscernibles Principle states that it is impossible for two individuals to be completely alike; ‘therefore, we must not conceive of a vague Adam, that is, a person to whom certain attributes of Adam belong, when we are concerned with determining whether all human events follow from positing his existence; rather, we must attribute to him a notion so complete that everything that can be attributed to him can be deduced from it.’ (Leibniz, ‘Extracts from the letters to Arnauld’ in G. W. Leibniz: Philosophical Essays ed. Ariew and Garber)

Still, even if Leibniz can satisfactorily counter objections against his theory of contingency, there remains the problem of God and the predicates which, according to the Predicate in Notion Principle, are supposedly contained within him. For example, if the notion of God contains within it the predicate that ‘God will actualize the best possible world’, then it seems that God has no freedom in this regard and it follows, since the contingency of the world and its inhabitants depends on the contingent decision of God, that nothing can be said to be truly contingent. The criticism, then, seems to be a powerful one. However, it seems that Leibniz’s idea that all subjects contain their predicates in some way, is the case because God created beings this way. Individuals can be said to contain all of their predicates because God pre-determines, like Leibniz says, everything that will ever occur in the world. God is perhaps not subject to the same law since it is a law which he generated in his creation of a world in which everyone is determined. In addition, though some might suggest that God’s nature means he will necessarily have to choose to actualize the best possible world, this doesn’t necessarily have to be the case. The perfection of God means that it is impossible that he would will a world lesser than the best possible world to come into existence. This world is not necessary because God chose to bring this world into existence as opposed to others; it was contingent upon the free choice of God. However, this does not entail that he is necessarily bound to choose a particular world. God has all perfections including perfect goodness; in his perfect goodness he will want to actualize the best world; his bringing about a lesser world, however, does not necessarily imply a contradiction, simply a falsity.

In conclusion, Leibniz’s conception of contingency and necessity is open to a number of criticisms. However, it does seem that in the majority of cases, Leibniz manages to counter his critics in a cogent manner. I am not convinced that any of the aforementioned concerns about the preservation of contingency within Leibniz’s framework are particularly fatal to his theory.

The Conception of God in Descartes and Leibniz

René Descartes and Gottfried Leibniz both espouse belief in a God that is infinitely powerful, infinitely knowledgeable and infinitely benevolent. Nonetheless, Descartes and Leibniz differently structure the hierarchy of those three defining traits as they determine God’s actions. Descartes’ God is a Voluntarist, meaning that God has absolute freedom of indifference. Power is supreme for Descartes. Leibniz objects to the arbitrariness of goodness and truth that arises from Descartes’ conception. In response, Leibniz chooses to depict a God whose power is constrained by a dominant intellect and benevolence. However, in Leibniz’s attempt to find absolute truth and goodness outside of God’s power, he limits God’s power to such an extent that the nature of God is fundamentally altered from the all-powerful, all-knowing, all-benevolent conception that Leibniz claims to believe in. Ultimately, Descartes’ view of God, though problematic, is more convincing because it does not involve the paradox of a God with limited freedom. For Descartes, God’s power is primary. God can will anything to exist. Descartes writes that “every single moment of my entire existence depends on him.” God has complete freedom of discretion in choosing what to create and what not to. Descartes “cannot deny that many other things have been made by him, or at least could have been made.” God could have created any kind of world, or no world, if he wanted, and as one of God’s creations, Descartes has “no right” to question way God chose to create the world and his unique role in it. Although Descartes has no right to question God’s choice, he does not need to worry that God’s choice is not the best or most perfect because God is infinitely benevolent. Benevolence is a form of perfection and because God is all perfect, he is by definition benevolent. Descartes explains the imperfections in the world by asserting that there is a larger perfection achieved by having some parts of the world imperfect, like humans. As an imperfect human he cannot hope to comprehend that larger perfection. Fundamental for Descartes is the fact that God cannot be a deceiver because it would be an imperfection. He makes sure to emphasize that God does have the power to deceive, but he just does not have the will to deceive because that would be a flaw. Descartes believes that God is not a deceiver because it would compromise his infinite goodness, but even the idea of what is good or not remains under God’s control. “The nature of all goodness and truth is already determined by God.” It is vital for Descartes that God is not a deceiver because God determines what people believe to be truth, so a non-deceiving God ensures that what people clearly and distinctly perceive to be true really is. But not only does God determine what people believe to be true, God determines truth itself. There is no absolute truth outside of God. As Gary Hatfield writes, even the mathematical and logical truths are “established by God and are entirely dependent on him, just as are all his other creations.” God could have created other mathematical truths. Two plus two could equal five if God wanted. Thus although the mathematical truths seem to be absolutely true, they are not. They could be otherwise. God is infinitely knowledgeable and infinitely benevolent but the truths that he knows and the goodness that he abides by were first decided on by he himself. God is not held to any external standards. As Hatfield articulates, “nothing about the current set of essences required God to create them instead of others.” Descartes’ depiction of God is unsettling because it makes goodness and truth completely arbitrary. The ultimate standards by which we judge all our actions and beliefs seem to carry less weight if they were chosen at God’s whim. There is nothing inherent in God’s concepts of truth and goodness that mandated that God chose them. We are God’s pawns, believing whatever he says to believe, and we have no external standard by which we know that it is correct to believe him. Descartes ensures us that God is not a deceiver, but that becomes less of a consolation if we know that God himself determined what deceit is. It seems less important to say that God is all-good and all-knowing because the terms good and knowing have been relativized. The sole meaningful definition of God becomes that he is all-powerful.Leibniz is troubled by this picture of God. He seeks to solve the problem of the arbitrary nature of goodness and truth that arises from Descartes’ theory of power as God’s supreme defining trait. Leibniz sets himself directly up against Descartes: “I am far removed from the opinion of those who maintain that there are no rules of goodness and perfection in the nature of things or in the ideas God has of them.” Leibniz believes that the notion that things are good because God made them is not enough. It undermines God’s magnificence. “Why praise him for what he has done if he would be equally praiseworthy in doing the exact opposite?” Leibniz’s God, unlike Descartes’ Voluntarist, is an Intellectualist. His infinite intellect and benevolence reign in his infinite power. Leibniz believes that there are standards for truth and goodness that exist outside of God’s will. Leibniz believes that there is an infinity of possible worlds that exist in God’s intellect and God chose to create the one that exists because it is the best. There are certain necessary truths, such as the laws of mathematics, which exist in every single world. The opposite of these truths would be a contradiction. God simply cannot will two plus two to equal five. In addition to necessary truths, there are contingent truths specific to each possible world. The opposite of these truths does not imply a contradiction, because they could be otherwise, for example if God had chosen to create a different world than he did. However, Leibniz’s God has less power than Descartes’ even over the contingent truths. God had to accept the truths that exist in our world when he chose to create our world. He could not create our world and then choose to change some of the laws of our world. Our world existed in God’s intellect as it is, with all the truths that hold in our world and all the events that have ever happened and will ever happen. Once he chose our world, there was nothing he could do to change it. “God foresees things as they are and does not change their nature.” The truths exist independent of his will to bring them into realization through creation.By dividing truths into contingent and necessary, Leibniz hopes to preserve some of both divine and human freedom. If things could have been otherwise, they are not fated and God and people retain choice over their actions. However, God’s infinite benevolence causes a large problem for such reasoning. Because God is infinitely good, he had to choose the best possible world. Leibniz claims that “notions possible in themselves do not depend upon God’s free decrees.” However, it is hard to believe that other notions and other worlds are truly possible if God was forced by his benevolence to create our world and our world only. Leibniz thinks he has retained God’s freedom by making a distinction between metaphysical or absolute necessity and moral necessity. God’s choice of this world was not metaphysically necessary because there were other worlds he could have chosen. However, when his benevolence is accounted for, it is clear that he really could not have chosen other worlds. His moral necessity is de facto metaphysical necessity. It would be a logical contradiction of his benevolence if he did not follow the moral necessity. Leibniz’s God is constrained by his own benevolence and knowledge to the point that he loses all freedom of creation. It may be self-constraint but it is a crippling constraint nonetheless. Allowing God the power to act otherwise than he did forces a contradiction in his own nature because it goes against his benevolence. “God cannot will voluntarily…rather we must say that God wills the best through his nature.” Leibniz has created a solution to the arbitrariness of goodness and truth but in doing so he has eliminated one of God’s defining faculties, that of infinite power. Leibniz’s depiction of God is contradictory. God cannot be both infinitely powerful and completely constrained by de facto metaphysical necessity. Descartes’ conception of God is problematic but it is not contradictory. Consequently, Descartes’ God is ultimately more compelling. If people accept that God creates and defines their existence, it is a natural leap to believe that God creates and defines everything else, including the notions of goodness and truth. A person is already taking a gigantic leap of faith in believing that there is a God and that God is infinitely benevolent, powerful, and knowledgeable, when the existence and nature of God are phenomenologically completely unknowable to us. In such circumstances it seems inappropriate to make arguments about arbitrariness. Descartes’ God is magnificent just for being God, for being infinitely powerful and creating the world and the people that live in it. This alone merits their devotion. Leibniz strives to define standards of goodness and truth, but in trying to preserve the traditional concept of God at the same time, he creates a contradictory argument. Despite his claim otherwise, Leibniz limits God, and this is counter to the concept of God as an infinite being. Leibniz tries to challenge Descartes’ hierarchy of God’s three defining traits, but in placing God’s infinite power below his intellect and benevolence, Leibniz undermines God’s infinite power and thus the entire notion of God he claims to subscribe to. Descartes’ model of God is more persuasive because he is able to preserve the limitless nature of God with all three characteristics intact.