The History of Philosophy, page 31
It was another philosopher who sought to argue that the existence of these imperfections shows that the world is in fact ‘the best possible world there could be’, since a perfect world would not be the best world for us. That philosopher is Leibniz.
LEIBNIZ (1646–1716)
Gottfried Wilhelm Leibniz was recognized in his own day, and is regarded still, as a genius. His contributions to mathematics, logic and philosophy are technical in the way that twentieth-century Analytic philosophy is technical. It might be regretted that he was born when he was – in the middle of the seventeenth century, when the conflicts between Protestant and Catholic Christianity had exhausted themselves on the battlefields of Europe after more than a century – because he peace-mindedly felt a need to try to reconcile Christian with Christian and humankind with the deity, devoting time and great mental powers to this unavailing ambition that might have been more fruitfully employed on other things.
Leibniz was born in Leipzig in 1646 into a highly educated family of Lutheran lawyers and academics. His father was a professor of philosophy at Leipzig University, his maternal grandfather was the university’s Professor of Law. He was educated at home until matriculating at the university in 1661, aged fifteen. He studied philosophy and mathematics, like everyone else at the time taking the Aristotle-based Scholastic philosophy curriculum.
A summer spent in Jena while an undergraduate brought him into contact with the mathematician Erhard Weigel, who made him interested in the concept of proof as applied to both logic and philosophy. For his habilitation thesis in philosophy he wrote a highly original logical essay, On the Art of Combinations, in which he set out the idea of a logical language, a ‘universal characteristic’, in which all problems could be stated clearly and solved.
Leibniz moved to Altdorf University for his doctorate in law, and was offered a position in its law department, but by that time he had secured a post as secretary to Baron Johann von Boineburg, a Protestant convert to Catholicism who encouraged Leibniz’s interest in achieving reconciliation between Catholics and Protestants. Accordingly Leibniz wrote a series of monographs on the various topics of dispute between the confessions. At the same time he maintained his wide and varied interests in science, law and literature (he wrote poetry in Latin), and added to them a scheme for a calculating machine.
Boineburg introduced Leibniz to the Elector of Mainz, in whose service he went to Paris as a diplomat. In this capacity he lived there for four years, coming to know leaders in the world of science and philosophy, among them Nicolas Malebranche, Antoine Arnauld and Christiaan Huygens. The last became his mentor, teaching him more mathematics and physics, and giving him unpublished manuscripts by Descartes and Pascal to read. Leibniz said that it was when reading some of Pascal’s work that the ideas for differential calculus and infinite series came to him.
In 1673 Leibniz went to London to present his idea for a calculating machine to the Royal Society. There he met Robert Boyle, Robert Hooke and John Pell. The last told him that his ideas about infinite series had been anticipated by the French cleric-scientist Gabriel Mouton – Leibniz checked, and found that this was right – and Hooke showed him that his calculating machine had flaws. He returned to Paris chastened but determined.
The controversy over who was first to invent calculus, whether Newton or Leibniz, started immediately and has continued since. The truth appears to be that they each devised a version of it independently, though Newton invented his version earlier than Leibniz did, and both delayed publication, though Newton delayed longer than Leibniz. The dispute grew bitter, and cast its shadow over the later part of Leibniz’s life because the powerful and influential Royal Society, in somewhat biased fashion it has to be said, decided in favour of Newton and as good as accused Leibniz of plagiarism.
Leibniz’s other contributions to mathematics included a binary arithmetic, methods of solving linear equations, treatises on dynamics, and logic as a ‘universal algebra’. One positive outcome of the dispute with Newton was that Leibniz had a long and interesting correspondence with Samuel Clarke, a follower of Newton, on space, time, gravitation, free will and other subjects. Leibniz’s relativistic conceptions of space and time, for one example, have advantages over Newton’s absolutist conceptions of both.
Leibniz became librarian to the court at Hanover, whose duke was heir to the throne of Great Britain. He would therefore have accompanied the Duke to England in 1714 when the latter succeeded Queen Anne, but his reputation in London was bad as a result of the Newton controversy, and he did not do so. He died two years later, leaving behind him an enormous body of unpublished work, an extensive correspondence in German, French and Latin with scholars and scientists across Europe, and – not least among his legacies – the Academy of Berlin, whose founding he had promoted.
Apart from his monographs on matters of religious doctrine, Leibniz wrote only two books: New Essays on Human Understanding (completed 1704, first published in 1765) and Theodicy (1710). His philosophical work otherwise appears as essays in journals, letters and unpublished manuscripts. Among the most important of the unpublished works were the Discourse on Metaphysics, a relatively early work, and the later Monadology. His thinking evolved over time, and the complicated editorial task of dating his many unpublished writings has made understanding his development more difficult.
He said of himself (in a letter to a friend written in 1714, two years before his death) that he had learned much from the Aristotelian, Scholastic and Platonic traditions, and had been stimulated by the discovery as a teenager of the ‘moderns’ (the philosophers and scientists of the seventeenth century) which led to his work in mathematics and mechanics. As with his reconciliatory efforts in religion, he wished to find the truth in all these different perspectives and thereby ‘to uncover and unite the truth buried and scattered’ among them all.
Among the moderns who influenced him were Descartes and Locke, who prompted his thinking about physical nature, and Hobbes and Spinoza, whose atheism and materialism troubled him, not least in connection with the question of free will and the relation of God to the world. He said his reasoning was based on what he described as ‘two great principles’: the Principle of Non-Contradiction (‘not both A and not-A’) and the Principle of ‘Sufficient Reason’, which can be expressed either as ‘there is a reason for everything’ or ‘every effect has a cause’. The first is a principle of logic, the second is a principle of metaphysics. His work displays commitment to several other principles, however: another logical principle, ‘the identity of indiscernibles’, a semantic principle stating that all truth is ‘analytic’, a metaphysical principle stating that nature is a continuum, and a theological principle claiming that everything God does is for the best.
The principle of ‘the identity of indiscernibles’ says that ‘there cannot be two things possessing exactly the same properties yet differing only in number’; that is, if two things have exactly the same properties, they are not two things but one and the same thing. The significance of the principle becomes more apparent when restated thus: no two or more distinct things exactly resemble each other. Note that this is not the same thing as ‘the indiscernibility of identicals’, which is trivially true: when putatively two things are in fact identical – there are not two things, but just one thing – then the putatively two things cannot, obviously, be told apart. Combining the two principles gives ‘Leibniz’s Law’: x and y are identical if and only if for every property F, x has F if and only if y has F.
The principle of analyticity says that in all true affirmative propositions the concept referred to by the predicate term is already contained in the concept of the thing referred to by the subject term. In later philosophy such propositions were dubbed ‘analytic’ because their truth-value can be determined solely by analysing the meanings of the subject and predicate terms; an example is ‘all bachelors are unmarried men,’ or (more obviously) any tautology, such as ‘all tall men are tall.’ Leibniz’s claim about this immediately looks questionable, for it implies that all apparently empirical propositions are not what they seem. Such assertions as ‘Paris is the capital of France’ or ‘rain sometimes falls in Canada,’ described in later philosophy as ‘synthetic’ propositions because they synthesize or join together unrelated concepts in the subject and predicate, would seem to have to turn out to be analysable in such a way that we find that the concept of being the capital of France is already ‘contained’ in the concept of Paris, or that ‘falling in Canada’ is somehow already ‘contained’ in the concept of ‘rain’. But in fact Leibniz had a different and deeper account to give of why he made this claim, explained below.
Leibniz’s own statement of the principle of continuity is that ‘nature never makes leaps’; all change happens continuously through a series of intermediary steps from the starting state to the end state. And his ‘principle of the best’ says that everything God does is for the best, so childhood cancer, and whole populations being wiped out in earthquakes, is for the best in the light of some greater ultimate plan. This is how Leibniz can claim that this highly imperfect and suffering-filled world can be ‘the best of all possible worlds’. Summarily put, the argument is that God is wholly good, so nothing that happens can be without a good eventual purpose; and therefore if there is much that seems bad in the world, it is because bad things are ultimately good for us, and a perfect world would not be the best possible world because it would provide no opportunity for us, with our free will, to choose to act in ways that earn either the reward or the punishment of the deity.
With these theoretical commitments, all but the last of them of great philosophical interest, Leibniz elaborated a striking metaphysical view, intended to answer what he took to be the fundamental philosophical question: What exists? What is there? ‘I consider the notion of substance to be one of the keys to the true philosophy,’ he wrote, and proceeded to argue throughout his life – though with changes to the detail of the view – that reality ultimately consists in simple substances, individual entities which, coining a term derived from the Greek prefix mono- meaning ‘one’, he called monads. Some of the natural philosophers – scientists – of the seventeenth century had coined the term ‘corpuscle’ meaning ‘little body’ to denote the tiny components of physical things; by choosing not to call them ‘atoms’ they were not committing themselves to the ultimacy or indivisibility of these particles. But Leibniz conceived of monads as indeed being foundational to reality as it appears to us.
The theory begins with Leibniz’s concept of ‘substance’. A substance is a thing that has a ‘complete individual concept’, that is, is such that the concept of it contains within itself all the things that can be said about it (predicated of it). This is what he meant by claiming that all true propositions are analytic: the predicate concept in every true affirmative proposition is contained in the concept of the subject. The concept of that substance completely ‘individuates’ that substance, that is, marks it out uniquely from the infinity of other substances. Since everything that can be said of a substance includes all its past, present and future properties, the only mind that can grasp the concept of it is God’s mind. The idea of a completely individuating concept is the same as that of the substance’s essence, for it is what makes it the unique thing it is.
There is an interesting corollary of this idea, which is that if you consider what God knows of any individual soul, then because that soul will contain the ‘marks and traces’ of everything that is or will be true of it, together with traces of everything else that has happened everywhere in the universe, God will be able to read off, from viewing that one individual soul, everything there is to say about the universe in its entirety and in all its history.
Leibniz concludes from the principles he set out, together with this doctrine, that no two substances can be completely indistinguishable but distinct (this is the principle of the identity of indiscernibles at work); that substances are indivisible and forever separate as existents; and that each substance is a complete world in itself and ‘mirrors’ all the other substances from its own unique perspective on them. It is accordingly a mind-like entity, ‘simple’ in the logical sense of being ‘non-complex’, and the most fundamental thing there is. These simple substances are the monads.
Monads are not in space; the properties that uniquely distinguish each one from all the others do not include spatial location. The properties that individuate them are ‘perceptions’, mental states, including the perceptions each has of all the others. These are not conscious perceptions; only ‘rational souls’ have conscious perceptions, which Leibniz calls ‘apperceptions’. Monads can come into existence or leave it only by an act of explicit creation or annihilation by God. And monads are what everything consists of, which means that they are the constituents of bodies; so even a lump of stone is made up of monads, and indeed an infinity of monads. The answer to the question of how non-spatial entities can constitute spatial or spatial-seeming ones turns on the nature of their mutual perceptions; this is an unclear aspect of Leibniz’s doctrine, but if it is really a form of idealism in which a spatial material world is a projection from the mental activity and relationships of monads, it could avoid the obvious objection. In his Principles of Nature and Grace Leibniz said that everything in nature is ‘full of life’, meaning thereby that everything is made of monads.
At this juncture a complication enters, which is that it appears that Leibniz came to think that monads contain monads within themselves, that each indeed is an infinity of monads; if so, this controverts the idea that each is a simple substance and an ultimate constituent of the order of being. His account of how the phenomenal world – the world that appears to us – is constituted by things which conform to his elaborate metaphysical picture of substances is confusingly at odds with itself in the different manuscripts and letters in which he set out his views. The clearest version of it is the relatively early one, in the Discourse on Metaphysics, in which the universe and all its parts are seen as a continuous ‘emanation’ from God, who in his omniscience can see every angle and aspect of how the universe can appear. So the monads, as emanations of the deity, are as it were particular instances of these perspectives, each one its own unique viewpoint on everything else.
Leibniz’s version of the traditional arguments for God’s existence has his stamp on them. He accepts the ontological argument, saying not only that the concept of a perfect being must necessarily be the concept of an existing being, but also that because this being is perfect, it can contain nothing negative within it that contradicts any of its perfections. He uses the ‘principle of sufficient reason’ to say that contingent things cannot have a ground of existence which is itself contingent, for that would be insufficient for their existence; and therefore they can exist only because there is a necessary being to serve as the sufficient ground for their existence – this being God.
From this deterministic picture of the universe, in which God knows everything even about the future, it is difficult to see how Leibniz could think that human beings have free will. And if they do not, where is there a role for ideas of sin and moral obligation? Yet he both wants and needs humans to have free will, because without that notion it would be impossible to justify God’s arrangement of things in the world, most especially the presence of suffering and evil. For the apparent evil in the world to be good, at least part of the reason has to be that it is formative for humans, who can earn their place in bliss by their response to it.
Leibniz’s attempt to make room for free will is neither clear nor, as far as it goes, convincing. He says that humans are ignorant of the future, and that is to all intents and purposes – and maybe even logically – the same thing as freedom. This limitation on human capacities goes further than that, of course, for we cannot know even a fraction of all the predicates that apply to anything in the present or past either. Therefore, he implies, ignorance is tantamount to freedom.
He tries a different tack when he says that intelligent beings are not bound by the ‘subordinate’ laws of the universe – the kind that we describe in talking about how the physical world, as it appears to us, works – and that therefore they can act ‘as it were by a private miracle’. This move is not quite without a ground in the context of his views, for if everything is an emanation from the deity – which in different words and from a different approach is what Berkeley thought, and indeed what much theology thinks – then there is a way one could argue that the deity’s great miracle is devolved or delegated in tiny ways to some of what emanates from it; though this reintroduces, with added force, the problem that all defenders of theistic viewpoints have to face: making the deity the ultimate author of evil.
So copious was Leibniz’s output, so general his genius and so unfinished and still in development were his philosophical views that it is hard to give a neat summary of them. He is like twentieth-century Analytic philosophers in the detail and technicality of his work; unlike them he sought to build a system out of the technical details; he would have needed more time to see if they could be worked out consistently.
