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SCIENCE - Circling Leibnitz |
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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. 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. 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. 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. 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. 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. |
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| See also Philosophy |