SCIENCE - Circling Leibnitz

 Circling Leibniz

 Gottfried Wilhelm Leibniz (1646-1716) is not recognised as readily as one might expect given that he is one butt of Voltaire’s 1759 novella Candide where, along with Rousseau, he is caricatured as Dr Pangloss who responds to each new disaster by assuring his travelling companions that theirs is the best of all possible worlds, a maxim popularised by Leonard’s Bernstein 1956 eponymous musical.

Literary theorist Erich Auerbach warns that the brilliance of Voltaire’s satire means that

calm reflection is drowned in laughter, and the amused reader either never observes, or observes only with difficulty, that Voltaire in no way does justice to Leibnitz’s argument and in general to the idea of a metaphysical harmony of the universe, especially since so entertaining a piece as Voltaire’s novel finds many more readers than the difficult essays of his philosophical opponents, which cannot be understood without serious study.

What follows is not the best of all possible understandings of Leibniz but offers enough background to approach his thoughts by circling his life, ideas and mathematics.

 Six pillars of wisdom

 1. Neither clear nor distinct

Even those who have devoted their careers to Leibniz admit to being in what he calls ‘confusion’. While a deal of his output is puzzling to read, the paradox is that no less a barrier is that his two key essays are conversational in tone as shown by these two sentences:

Composites or bodies are multitudes; and simple substances – lives, souls, minds – are unities. There must be simple substances everywhere, because, without simples, there would be no composites.

One more trap for the reader is that the meanings that Leibniz gives to his terms are remote from their current usage. Substance, for instance, does not mean something we can touch. According to Leibniz: ‘A substance is a being capable of action. ‘ In addition, he coins terms for his concepts, notably ‘monad’ and ‘appetitions’. He also gives a special meaning to common words such as ‘awareness’ and ‘perception’. Finally, he adds his own twist to philosophical concepts such as ‘entelechies’. This extract illustrates the difficulties:

Monas is a Greek word signifying unity, or what is one ... Since the monads have no parts, they can neither be formed nor destroyed. They can neither begin nor end naturally, and consequently they last as long as the universe, which will be changed but not destroyed. As a result, a monad, in itself and at a moment, can be distinguished from another only by its internal qualities and actions, which can be nothing but its perceptions (that is, the representation of the composite, or what is external, in the simple), or its appetitions (that is, its tendency to go from one perception to another) which are the principles of change. For the simplicity of a substance does not prevent a multiplicity of modifications, which must be found together in this same simple substance.

Seeking clarification of Leibniz’s terminology is but a start towards overcoming the problems that we nowadays face in being even halfway sure that we know what he was getting at. The major barrier is Leibniz’s worldview. On some days he seems to be as much a ‘mentalist’ as Bishop Berkeley for whom the world is but representation. On other days, he can sound like Sam Johnson stubbing his toe on a stone to rebut the good Bishop by showing that there is a world outside our heads.

Leibniz can strike us as otherworldly, and never more so than in his efforts to rehabilitate Mediaeval forms. No glossary can bridge the gulf between his outlook and the ways in which most of us now assume that our world works. His mind was a mixture of Cartesian mechanism and Aristotelian Scholasticism. He was at once a mathematical genius and the founder of theodicy. That combination, of course, is not out of the ordinary. As both savant and proponent of whacky ideas, Leibniz matched his contemporary and rival Isaac Newton who devoted years to distilling the mind of God from the Book of Revelation.

 2. The lickspittle

Leibniz sought to console not to divide. He wished to overcome the schisms in Christianity – perhaps even to encompass Judaism. He therefore pitched his evidence and reasoning to make his beliefs palatable to those whose theologies he did not share. Admirable as such openness might be in debate, it is nonetheless a burden to those of us now trying to distill the essentials from special pleadings cast in a prose designed to maintain dialogue.

Less admirable factors contributed to the uncertainties that confront anyone trying to grapple with Leibniz’s contribution to Western thought. In Men and Mathematics, E.T. Bell painted a widely held view of the great man’s personality:

In the case of Leibniz the greed for money which he caught from his aristocratic employers contributed to his intellectual dalliance: he was forever disentangling the genealogies of the semi-royal bastards whose descendants paid his generous wages, and proving with his unexcelled knowledge of the law, their legitimate claims to duchies into which their careless ancestors had neglected to fornicate them. But more disastrously than his itch for money, his universal intellect, capable of anything and everything had he lived a thousand years instead of meager seventy, undid him … Leibniz squandered his splendid talent for mathematics on a diversity of subjects in all of which no human being could hope to be supreme, whereas … he had in him supremacy in mathematics. But why censure him. He was what he was, and willy-nilly he had to ‘dree his weird’  … Leibniz’s tragedy was that he met the lawyers before the scientists.

Despite Leibniz’s exercise of his genealogical efforts to help his prince, the Elector of Hanover, onto the throne of the United Kingdom and Ireland in 1714, George left his servant behind because of his brawl with the Newtonians.

            Bertrand Russell accused Leibniz of having

[h]ad a good philosophy which (after Arnauld’s criticisms) he kept to himself and a bad Philosophy which he published with a view to fame and money. In this he showed his usual acumen: his bad philosophy was admired for its bad qualities, and his good philosophy, which was known only to the editors of this MSS., was regarded by them as worthless, and left unpublished …. I think it probable that as he grew older he forgot the philosophy which he had kept to himself, and remembered only the vulgarised version by which he won the admiration of Princes and (even more) of Princesses.

In A History of Western Philosophy, Russell repeats both his low opinion of Leibniz as a man and his tributes to him as ‘one of the supreme intellects of all time’.

Evaluating Leibniz’s position on most matters has been complicated by his compulsion to chase hares and his failure to cross a finishing line. He wondered whether Adam and Eve had spoken Chinese and how Europeans should respond to an inundation of indigenous Australians. He never published a statement of his views comparable to Spinoza’s anonymous Tractatus and his posthumous Ethics, or Kant’s Critiques. Instead, he bequeathed piles of drafts for scholars to burrow through. Across the past forty years, Leibniz has received renewed attention as more of his manuscripts appeared in scholarly editions, throwing up mountains of commentary, with two learned journals - Studia Leibnitiana (1969 - ) and Leibniz Review (1991 - ) - devoted to these academic endeavours. The former launched itself with a Latin Praefacit in a hint to where Leibniz’s reputation then stood at a time when even the Vatican had been converted to the vernacular.

 3. The logician

At short notice during the summer of 1898, Bertrand Russell had to prepare a series of lectures on Leibniz for Cambridge. Russell was perplexed until he hit upon logic as the thread out of the labyrinth. This solution completed Russell’s rejection of Hegelianism. The privileging of logic extended the struggle he was to face with age-old contradictions in mathematics. Wrestling with the latter provoked his dismissal of metaphysics. A reading of Hegel’s comments on mathematics in his Logic struck Russell as little more than a proliferation of ‘puns’. Philosophy had to be based on logic as did mathematics, freed from arithmetic and number. Russell’s study of Leibniz laid one foundation for the work that occupied him until the publication, co-authored with Alfred North Whitehead, of Principia Mathematica in 1911.  

Although Russell’s book made Leibniz respectable for English empiricists, his explication is no longer accepted. Metaphysics have regained center stage while the calculus makes but fleeting appearances. This absence is in contrast to writers on Descartes who at least acknowledge how his concept of extensions in space is linked to his integration of geometry and algebra. The 1954 volume on Leibniz for the Pelican Philosophy series devoted chapters to monads, god, moral theory, the theory of knowledge and logic, but not to mathematics.

Generations of experts admit to not being sure whether their interpretations of Leibniz hit the mark. Writing in 1967on ‘Monadology’ Montgomery Furth begins by noting that

at various times Leibniz held various other views, and that many of his statements of the view that interests me are not completely clear or else conflate it with others … I have so far failed to understand ‘appetition’ in monads – introduced by Leibniz as if co-ordinate with ‘perception’ – as capable of being anything but confused perception of future states.

Half way through Furth’s exposition, he feels obliged to repeat how uncertain he is of his subject. The tentativeness with which Furth treats his subject fits with one of Leibniz’s precepts. Not convinced by Descartes’ reliance on ‘clear and distinct’ ideas as a guide to truth, he proposed that we proceed through levels of confusion towards degrees of clarity. This condition is the inevitable consequence of the complexity of creation against the limited intelligence of we poor creatures. Leibniz also rejected Locke’s notion of the mind as a blank slate. That we can know anything is innate, a gift from the ‘Author of nature’. How well we understand the world and our position in it depends on our efforts. That Leibniz is neither Rationalist nor Empiricist perplexes adherents of both convictions but can make his legacy even more appealing to the mumbo-jumboists.

 4. The mentalist/materialist

How Does Leibniz see the corporeal? Is there a world that is not a mental construct? Daniel Garber overturned one scholarly consensus in the 1980s by contending that Leibniz had been some kind of realist before the 1690s. On this reading, he did not become a fully-fledged Idealist/mentalist until the 1700s. Only then did he play Gabriel to the ‘monad’. Garber’s chronology helps, yet the dividing line remains fuzzy.

Glenn A. Hartz seeks a resolution by proposing that Leibniz adopts ‘a sophisticated, rhetorically nuanced blending of elements of both’ idealism and realism. If that is the case, ‘Theory-Pluralism is the most fruitful way to interpret’ the shifts in Leibniz’s thinking. Thus,  the Idealist and Realist strands need not refute each other. Rather, they are conceptualisations of however much – or little - we know about the world. Hence, they are not necessarily conclusions about how that world is.

These readings and extracts warn of the hazards in wait for anyone hoping to adapt Leibniz’s notions - ‘relational’, ‘monad’, ‘appetitions’ and ‘awareness’ - to current social domains. A safer path is to locate his outlook within the flowering of mathematics and the emergence of mechanical materialism in the seventeenth century.

  5. The mathematician

The 300-year dispute about whether Leibniz nicked his ideas about the calculus from Newton has been settled in favour of their having developed their ideas independently. Leibniz, however, introduced symbols – “f” and “d” – for summation and difference, a system which allowed for the adoption of analysis on a wide scale: ‘The explicit rules of Leibniz’s calculus enabled less privileged investigators to avail themselves of the knowledge of a select few and to use these methods in practice.’  This facility provided lesser minds with a way of keeping abreast. Leibniz’s notation meant that ‘[o]ne could learn to become a scientist, but not to make discoveries.’ Moreover, making the calculus accessible to professionals, notably engineers, helped mathematics to become an academic discipline in schools as well as universities. By contrast, sticking to Newton’s representational form had been ‘devastating for mathematics in England throughout in the eighteenth century. After 1812, Cambridge undergraduates Charles Babbage and John Herschel set up an Analytical Society to replace the Newtonian dots with the letters in Leibnitz. Babbage joked that he had promulgated D-ism over Dot-age.

 6. The ethicist

Those who bother to go beyond Voltaire will find that Leibniz’s ‘best of all possible worlds’ has two aspects. One refers to the natural order. Here, Leibniz is not saying that this universe is the best that we can dream up. It is the best only from among those that are possible. Take away the natural disasters that we know - earthquakes, floods and volcanoes - and you would get a world that is worse, or perhaps no world. Since the god of Leibniz is all-Knowing and all Good, it has put together the best cosmos that could work at all. Leibniz accepts limits to divine omnipotence, for instance, it cannot create another version of itself.

Before we find Leibniz’s claim to be off the planet, consider two alternatives to his position. First, if the world does not conform to the laws of physics then it must be miracles all the way. That would mean that divine interventions could have us breathing oxygen one day and sulfur the next. If anything and everything is possible then no patterns operate from which explain the physical world.

The second way around the bar that Leibniz places on his god’s being swayed by our prayers to stop an earthquake is the doctrine known as Occasionalism. The term is itself misleading. The Occasionalist does not say that god can or does intervene ‘occasionally’. Quite the reverse. The claim is that god is directly involved on every occasion, no matter how microscopic. Into the 1700s, Malebranche defended a Cartesian dualism by representing every human action as the creator’s bridging of mind and body. If that were the case, no patterns or laws of physics need operate. God takes direct charge of each micro-move, the ‘sparrow’s fall’, as Jesus said.

Experience suggests that humankind’s attempts to take God’s place in touching up nature to suit our interests is no more likely to result in ‘the best’, as Engels cautions:

Let us not, however, flatter ourselves overmuch on account of our human victories over nature. For each such victory nature takes its revenge on us. Each victory, it is true, in the first place brings about the results we expected, but in the second and third places it has quite different, unforeseen effects which only too often cancel the first … Thus at every step we are reminded that we by no means rule over nature like a conqueror over the foreign people, like someone standing outside nature – but that we, with flesh, blood, and brain, belong to nature, and exist in its midst, and that all our mastery of it consists in the fact that we have the advantage over all other creatures of being able to learn its laws and apply them correctly.

Even this advantage is qualified: we are able to learn. That we will do so is far from certain.

Since the law-bound realms of nature do not apply to social action, Leibniz’s reasons for denying miracles in regard to physics need not apply to human behaviour. According to Leibniz, Jehovah could have stopped the Nazis from exterminating his chosen people but he could not prevent the effects of poisonous gases on human physiology.

If we accept that this cosmos is the best one that is possible according to the laws of physics, must we also accept that any prevailing socio-economic order is the best on offer? Was Thatcher right to declare that “There Is No Alternative”? Again, TINA is not claiming that this social order is as fine as we can imagine. TINA requires only that neo-liberal  capitalism is the sole one that works. It can be appalling. But all the rest are worse, or impossible. For socialists to reply that ‘we can do better’ sounds like a school report card.

As with Leibniz’s understanding of the natural order, his best of all possible human worlds has to be understood in terms of his theodicy. Much as we might prefer to live in a world where child murder is impossible, would we call that social order perfect if it meant surrendering free will?

Candide concludes with the survivors digging in their garden. Is Voltaire telling us to focus on our own patch and forget the wider world? Or is it that we should cast aside speculative philosophising in favour of useful toil? In 1968, Russell declined to read a manuscript on Leibniz ‘because of my belief that the survival of the human species is more important than the question of whether all propositions have the subject-predicate form’.

Engels and Marx plumped for changing the world as the path to gaining more relative knowledge about it. Leibniz seems likely to have tailored his response to his audience.

See also History

See also Philosophy