SCIENCE - Leibnitz and the Labyrinth

 Leibniz and the labyrinth

 The name and opinions of Gottfried Wilhelm Leibniz (1646-1716) are 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.[1]

What follows is not the best of all possible understandings of Leibniz but hopes to come up with enough background to make sense of how Marxists have treated him Leibniz.

I understand enough Marx to be confident about what debates around his concepts are about and where my grasp of them is weakest. That awareness makes me alert to how far I am from a comparable level of competence in regard to Leibniz. Even those who have devoted as much attention to Leibniz as I have to Marx admit to being in what Leibniz calls ‘confusion’.  This essay moves through seven levels of understanding about Leibniz, his life, ideas and mathematics. In preparation is a literature survey of a motley of Marxists who have responded to his thought, in particular, to the monad and dialectics.

 Seven pillars of wisdom

 Neither clear nor distinct

A deal of Leibniz’s output is puzzling to read. No less a barrier to understanding is that his two key essays are conversational in tone as in 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. It is simple or composite. A simple substance is that which has parts. A composite substance is a collection of simple substances …

In addition, Leibniz 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 next extract introduces several of these terms and illustrates the difficulties alluded to above:

Monas is a Greek word signifying unity, or what is one … Since 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 restful, 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 substances does not prevent a multiplicity of modifications, which must be found together in this same simple substance.[2] 

Seeking clarification on Leibniz’s terminology is only 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 asserting that all we can know are our sensations. On other days, he can sound like Sam Johnson stubbing his toe on a stone to rebut the good Bishop by howing that there is a world outside his head.

Leibniz can strike us as ‘otherworldly’, says Garber,[3] 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 today’s Europeans 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 preeminent theodicean. That combination, of course, is not out of the ordinary for mathematicians.[4] Leibniz was a match for his contemporary and rival Isaac Newton both as a savant and a proponent of whacky ideas.[5] Newton devoted years to distilling the mind of God from the Book of Revelation.[6]

 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 them 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. 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 know ledge 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. As Gauss blamed him for doing, 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 – according to Gauss – 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.[7]

Leibniz exercised his genealogical efforts to help his prince, the Elector George of Hanover, onto the throne of the United Kingdom and Ireland in 1714. George left his servant behind because of the brawl with the Newtonians. Newton’s probity was scarcely better. He played the perfect hypocrite about his heretic Arianism in order to retain his £2,000 a year as Master of the Mint.[8]

            Bertrand Russell hardened his dislike for Leibniz’s character  In the ‘Preface’ to the 1937 reissue of his 1900 study he 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.[9]

Eight years later, 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’.[10] As we shall see, Russell concedes some value to the theory of monads.

Evaluating Leibniz’s position on most matters has been complicated by his failure to finish anything. 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 ‘Preface’ (“Praefacit’) in Latin, a hint as to where Leibniz’s reputation then stood at a time when even the Vatican had adopted the vernacular Mass.

 The quasi-Cartesian

Whatever sense I have been able to make of Leibniz is based on the attention I have paid to Descartes since 2004 when I heard a doctoral student introduce her findings with the claim that the oppression of women and the despoliation of the natural world were the result of Descartes’ splitting mind from body, his dualism. At the time, I knew no more about Descartes than that such allegations were conventional wisdom. My historical materialist outlook, however, meant that I also knew that whatever had caused sexism and the plunder of nature was more than an idea. I have learned that Descartes did not separate mind from body but rather said that they were different kinds of substances, which interacted.[11]

As is the case with vulgarisations of Leibniz, too many readers of Descartes equate mind with soul so as to evade the latter which is incomprehensible, not to say embarrassing, in this secular age.[12] One way back into that mentality is through A History of Philosophy by the Jesuit Frederick Copleston.[13]

Descartes in the 1640s got out from under the repression of the Church by proposing a line between using mathematics to investigate extensions in space (bodies) but not thoughts, which were unquantifiable. He gave the body, including the brain and the pineal gland, to scientists but left the ‘rational soul’ to the Inquisitors.[14] Several commentators suspect that this ‘dualism’ was a maneouvre to avoid his being sent to the stake as a libertine as much as it was an ontological or epistemological conviction.[15]

The notion of ‘soul’ has dropped out of fashion. Those philosophers who compile a Syllabus of Descartes’ Errors rarely consider his views in relation to the theological discourse of the seventeenth century.[16] They ignore the doctrine of transubstantiation; do not care whether God had created the body and the soul out of utterly distinct substances as Descartes maintained in arguing for the latter’s immortality;[17] sideline disputes over whether the resurrections of the body and of the soul were coterminous or had the corporeal shell to wait until the Last Judgement.[18] Understanding Leibniz is made harder because not even the most hardened Idealists can now see the world in the ways that he did. His deity is pretty much dead.

 The logician

At short notice during the summer of 1898, Bertrand Russell had to prepare a series of lectures on Leibniz for Cambridge. By 1900, Russell had turned his notes into a book which he supplemented with extracts from fugitive texts.[19] He had been perplexed until he hit upon logic as the thread out of the labyrinth. This solution completed Russell’s rejection of the Hegelianism he had taken in from ???? McTaggart. A reading of Hegel’s comments on mathematics in his Logic struck Russell as little more than a proliferation of ‘puns’.[20] The privileging of logic extended the struggle that Russell was to wage with age-old contradictions in mathematics. Wrestling with the latter provoked his dismissal of all he saw to be metaphysical. 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.[21]

Although Russell’s book made Leibniz respectable for English empiricists, his explication is no longer accepted.[22] The metaphysics have regained center stage while the calculus makes but fleeting appearances. This absence is contrast to writers on Descartes who at least acknowledge how his concept of extensions in space are linked to his integration of geometry and algebra. The rebalancing found voice in Ruth Lydia Saw’s 1954 volume on Leibniz for the Pelican Philosophy series which devotes 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’ for the leading US journal, Philosophical Review, 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.[23]

Half way through Furth’s scholarly exposition, he feels obliged to stress once more how uncertain he is of his subject:

That the view here called Leibniz’s is by no means to be found unalloyed throughout his writings. Even the reductionist character of the monadism is not consistently maintained, this even in his latest writings, and where it is maintained the reduction is not always this one. Several causes are responsible: the surreptitious influence of earlier but abandoned view of his, his practice of shaping a given discussion to a given issue without sufficient attention to its consistency with his remarks (often to a different correspondent) on a different issue, and his notorious habit of writing in a simpliste fashion when he believes that the immediate occasion calls for popularisation.[24]

The tentativeness with which Furth treats his subject fits with one of Leibniz’s precepts. He was not convinced by Descartes’ reliance on ‘clear and distinct’ ideas as a guide to truth. Instead, he proposed that we proceed through levels of confusion towards degrees of clarity. This condition is the inevitable consequence of the complexity of God’s creation against the limited intelligence of his creatures. He 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 appeal to putative dialecticians.[25]

 The mentalist/materialist

The more I read of and about Leibniz the less confident I become about my understanding of how he sees the corporeal. Is there a world that is not a mental construct? Daniel Garber overturned the 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 in the 1700s. Only then did he play Gabriel the ‘monad’. Garber’s chronology helps, yet the line remains fuzzy.

Glenn A. Hartz finds a resolution by proposing that Leibniz adopts ‘a sophisticated, rhetorically nuanced blending of elements of both’ idealism and realism.[26] If that is the case, ‘Theory-Pluralism is the most fruitful way to interpret’ the shifts in Leibniz’s thinking. Hartz contends that 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. Hartz’s approach is feasible if realism is distinguished from the materialism that Leibniz identified with Descartes. Cartesian principles apply to physics but not to metaphysics.

Margaret Wilson traces Leibniz’s efforts to refute Cartesian explanations of ‘Perception… by mechanical reasons, that is by figures and motions’ (Monadology #17). She proceeds through his criticism of previous attempts to defend metaphysics:

Leibniz seems to hold, then, that in analyzing conscious perception we must take account of both the ‘true unity’ of the perceiving ‘I’ and a manifoldness or variety in object or content. To return to the passage quoted from the ‘Monadology’, his point seems to be (very roughly) that a materialist explanation of perception is impossible because perception does essentially involve the ‘true unity’ of the perceiving self, while material mechanisms are always divisible into parts. What will be missing is the observer’s description of hypothetically perception-producing machine is just the essential ‘unity’ of consciousness, or anything from which an understanding of that unity could be derived.[27]

Wilson’s resort to ‘seems’ and ‘very roughly’ is more tentative than in many philosophical presentations. Here too, the impediments to her explication inhere in Leibniz.

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

  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.[28] However, Leibniz 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 ‘One could learn to become a scientist, but not to make discoveries.’ Moreover, institutionalising the calculus for professionals, notably engineers, allowed mathematics to become an academic discipline in schools as well as universities.[29] By contrast, sticking to Newton’s representational form had been ‘devastating for the development of English Mathematics 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. [30]

 The ethicist

Those who bother to go beyond Voltaire 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 is all Knowing and all Good, he 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.

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

The second way around the bar that Leibniz places on his God’s being swayed by our prayers to stop earthquakes etc. is the doctrine known as Occasionalism. The term is itself misleading. The Occasionalist does not say that God intervenes only ‘occasionally’. Quite the reverse. The claim is that God is directly involved on every occasion, no matter how microscopic. If that is the case, no patterns or laws of physics need operate.[31] God is in charge of each micro-move, the ‘sparrow’s fall’, as Jesus said.

Experience suggests that attempts by our species to take God’s place in touching up nature to suit our interests is no easy task, as Engels reminds us:

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.[32]

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

The law-bound world of nature does 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. He could not prevent the effects of bullets or 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 capitalism is the best socio-economic system 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 capitalism is the sole one that works. It can be very bad. But all the rest are worse, or incorporate. For socialists to reply that ‘we can do better’ sounds like a school report card. Socialists need to do better in the quality of our refutation.

As with Leibniz’s understanding of the natural order, his best of all possible social world 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. There is much debate over Voltaire’s intention. Is he 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? Engels and Marx went for the latter as the path to gain relative knowledge about things. Leibniz is likely to have sounded that he favoured both.

[1] Erich Auerbach, Mimesis, The Representation of Reality in Western Literature, Princeton University Press, Princeton, 1953, p. 408.

[2] Leibniz, ‘Principles of Nature and Grace Based on Reason’, Roger Ariew and Daniel Garber (eds), Leibniz Philosophical Essays, Hackett Publishing,  Indianapolis, 1989, p. 207.

[3] Daniel Garber, ‘Gottfried Wilhelm Leibniz’, Routledge Encyclopedia of Philosophy, volume 5, Routledge, London, 1998, p. 542.

[4] Margaret Wertheim, Pythagoras’ Trousers, God, Physics and the Gender Wars, Times Books, New York, 1995; for a recent exchange see Jean-Pierre Changeux and Alain Connes, Conversations on Mind, Matter, and Mathematics, Princeton University Press, Princeton, NJ, 1996.

[5] Ernst Cassirer, ‘ Newton and Leibniz’, The Philosophical Review, 52 (4), July 1943, pp. 366-91; Larry Stewart, ‘The Selling of Newton: Science and Technology in Early Eighteenth-Century England’, Journal of British Studies, 25 (2), April 1986, pp. 178-92.

[6] Richard S. Westfall, Never at rest: a biography of Isaac Newton, Cambridge University Press, Cambridge, 1980, pp. 344-57.

[7] E.T. Bell, Men of Mathematics, volume one, Penguin, Harmondsworth, 1953, pp. 130-1 and 132.

[8] Westfall, Never at rest, pp. 351, 814-5 and 829.

[9] Bertrand Russell, Leibniz, George Allen & Unwin, London, 1937, p. vi.

[10] Bertrand Russell, A History of Western Philosophy, Simon & Schuster, New York, 1945, pp. 581-96.

[11] To dissociate dualism from Descartes wee Stephen Gaukroger, Descartes an intellectual biography, Clarendon Press, Oxford, 1995, pp. 388-94; Thomas Fuchs, Mechanisation of the Heart, Harvey and Descartes, University of Rochester Press, Rochester, 2001, especially pp. 122-5; John Cottingham, ‘Cartesian Trialism’, Mind, 94, April 1985, pp. 218-230; Daniel Garber, Descartes Embodied, Cambridge University Press, Cambridge, 2001, pp. 257-273.

[12] In Margaret Dauler Wilson, Descartes, Ego Cogito, Ergo Sum, Routledge & Kegan Paul, London, 1978, the index entry for ‘soul’ says ‘see mind’, which reads ‘mind/soul’ as if there were no distinction, or at least none so far as Descartes was concerned; Deborah J. Brown, Descartes and the Passionate Mind, CUP, Cambridge, 2006, discusses the differences between the three kinds of soul but her vocabulary slips between ‘soul’, ‘mind’, ‘brain’ and ‘will’ without defining each, pp. 34-35; John Cottingham argues that Descartes uses mind and soul interchangeably but provides only one debatable quotation as evidence, ‘ “l’esprit ou l’ame de l’homme (ce que je ne distingue point).” This interchangeability of ‘mind’ and ‘soul’ appears in the 1647 French version of the Meditations, while the original 1641 Latin text refers to the mind (mens), ‘Cartesian dualism: theology, metaphysics, and science’, John Cottingham (ed.), The Cambridge Companion to Descartes, Cambridge University Press, Cambridge, 1992, pp. 236 and 253n.; for Abraham Gorleaus as a precursor of some Cartesian thinking on these matters see Helen Hattab, Descartes on Form and Mechanism, CUP, Cambridge, 2009, pp. 158-9 and 174-6; for a later critic, Charles Perrault, who brought out the centrality of the soul in Descartes’ alleged dualism, see John P. Wright, ‘Perrault’s criticisms of the Cartesian theory of the soul’, Stephen Gaukroger et al. (eds), Descartes’ Natural Philosophy, Routledge, London, 2,000, pp. 680-96.

[13] Frederick Copleston, A History of Philosophy, volume 4, Modern Philosophy, Descartes to Leibnitz, Image Books, New York, 1963, chapters XV – XVIII.

[14] Descartes needs to be read as if in dialogue with Aristotle and Aquinas, see F.C. Copleston, Aquinas, Penguin, London, 1955, pp. 156-98; Anthony Kenny, Aquinas, OUP, Oxford, 1980, pp. 46-9; Nicholas Jolley, ‘Malebranche on the Soul’, Steven Nadler (ed.), The Cambridge Companion to Malebranche, CUP, Cambridge, 2000, pp. 31-58.

[15] Gaukroger, Descartes an intellectual biography, pp. 290-2.

[16] Antonio R. Damasio is another who gives no indication of having studied Descartes let alone any of the commentaries, Descartes’ Error, Emotion, Reason and the Human Brain, Papermac, New York, 1994.

[17] Daniel P. Walker, ‘Medical Spirits and God and the Soul’, Spiritus, Edizioni dell’Ateneo, Roma, 1984, pp. 223-44.

[18] Marcia B Hall, ‘Michelangelo’s Last Judgement as Resurrection of the Body: The Hidden Clue’, Michelangelo’s ‘Last Judgement’, Cambridge University Press, Cambridge, 2005, pp. 95-112; Fernando Vidal, ‘Brains, Bodies, Selves, and Science: Anthropologies of Identity and the Resurrection of the Body’, Critical Inquiry, 28 (4), Summer 2002, pp. 930-74; Bernadine Barnes, ‘Skin, Bones, and Dust: Self-Portraits in Michelangelo’s “Last Judgment” ‘, The Sixteenth-Century Journal, 35 (4), Winter 2004, pp. 969-86.

[19] Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz, The University Press, Cambridge, 1900.

[20] Ray Monk, Bertrand Russell, The Spirit of Solitude, Jonathan Cape, London, 1996, pp. 113-8.

[21] In 1968, Russell declined to read a primer 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.’ Russell to F.R. Cowell, 15 May 1968, quoted Walter H. O. Briant, ‘Russell on Leibniz’, Studia Leibnitiana, 11 (2), 1979, p. 221.

[22] O’Briant, pp. 159-222.

[23] Montgomery Furth, ‘Monadology’, Philosophical Review, 76 (2), April 1967, pp. 169-70, 172n.

[24] Furth, pp. 186-7.

[25] Franklin Perkins, Leibniz, A Guide for the Perplexed, Continuum, New York, 2007, chapter 4; Nicholas Rescher, ‘Leibniz’s Quantitative Epistemology’, Studia Leibnitiana, 36 (2), 2004, pp. 210-31; Ruth Lydia Saw, Leibniz, Penguin, Harmondsworth, 1954, chapter 7; Alison Simmons, ‘Changing the Cartesian Mind: Leibniz on Sensation, Representation and Consciousness’, Philosophical Review, 110 (1), January 2001, pp. 31-75.

[26] Glenn A. Hartz, Leibniz’s Final System. Monads, Matter and Animals, Routledge, London, 2006, pp. 21-27. 

[27] Margaret D. Wilson, ‘Leibniz and Materialism’, Canadian Journal of Philosophy, 3 (4), June 1974, p. 508; cf. her Descartes, Ego Cogito, Ergo Sum, Routledge & Kegan Paul, London, 1978.

[28] Westall, Never at rest, pp. 514-20, 712-31 and 761-92.

[29] Skuli Sigurdsson, ‘Equivalence, Pragmatic Platonism, and Discovery of the Calculus’, Mary Jo Nye et al. (eds), The Invention of Physical Science, Intersections of Mathematics, Theology and Natural Philosophy Since the Seventeenth Century, Kluwer Academic Publishers, Dordrecht, 1992, pp. 101-11.

[30] W.V. Wilkes, ‘Herschel, Peacock, Babbage and the Development of the Cambridge Curriculum’, Notes and Records of the Royal Society of London (N&RRSL), 44 (2), July 1990, pp. 212-4.

[31] Steven Nadler, ‘Malebranche on Causation’, Steven Nadler (ed.), The Cambridge Companion to Malebranche, Cambridge University Press, Cambridge, 2000, pp. 112-138.

[32] Frederick Engels, The Dialectics of Nature, Progress Publishers, Moscow, 1964, pp. 182-3.

See also HISTORY