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On Leibniz

On Leibniz: Expanded Edition

Nicholas Rescher
Copyright Date: 2013
Pages: 320
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    On Leibniz
    Book Description:

    Contemporary philosopher John Searle has characterized Gottfried Wilhelm Leibniz (1646-1716) as "the most intelligent human being who has ever lived." The German philosopher, mathematician, and logician invented calculus (independently of Sir Isaac Newton), topology, determinants, binary arithmetic, symbolic logic, rational mechanics, and much more. His metaphysics bequeathed a set of problems and approaches that have influenced the course of Western philosophy from Kant in the eighteenth century until the present day.On Leibniz examines many aspects of Leibniz's work and life. This expanded edition adds new chapters that explore Leibniz's revolutionary deciphering machine; his theoretical interest in cryptography and its ties to algebra; his thoughts on eternal recurrence theory; his rebuttal of the thesis of improvability in the world and cosmos; and an overview of American scholarship on Leibniz.Other chapters reveal Leibniz as a substantial contributor to theories of knowledge. Discussions of his epistemology and methodology, its relationship to John Maynard Keynes and Talmudic scholarship, broaden the traditional view of Leibniz. Rescher also views Leibniz's scholarly development and professional career in historical context. As a "philosopher courtier" to the Hanoverian court, Leibniz was associated with the leading intellectuals and politicians of his era, including Spinoza, Huygens, Newton, Queen Sophie Charlotte, and Tsar Peter the Great.Rescher extrapolates the fundamentals of Leibniz's ontology: the theory of possible worlds, the world's contingency, space-time frameworks, and intermonadic relationships. In conclusion, Rescher positions Leibniz as a philosophical role model for today's scholars. He argues that many current problems can be effectively addressed with principles of process philosophy inspired by Leibniz's system of monadology.

    eISBN: 978-0-8229-7814-5
    Subjects: General Science

Table of Contents

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  1. 1 Leibniz on Possible Worlds
    (pp. 1-44)

    Leibniz’s theory of possible worlds, elaborated and explained by him over many years in many writings, constitutes an interesting but rather complicated doctrine that goes to the very heart of his metaphysical system. The present discussion will provide a compact but synoptic sketch of its principal components.

    The doctrine that necessary propositions are those truths that obtain in all possible worlds establishes an important linkage between logic and metaphysics in Leibniz’s thought. For the principles of logic will, on this basis, be necessary truths that are established as such by virtue of this feature of possibility-pervasive validity. And the fundamental...

  2. 2 Contingentia Mundi: Leibniz on the World’s Contingency
    (pp. 45-67)

    From the earliest days of his philosophizing Leibniz insisted upon the contingency of the world. It was always one of his paramount aims to avert a Spinozistic necessitarianism, and he regarded the contingency of the world’s constituents and processes as an indispensable requisite towards this end, one in whose absence the idea of divine benevolence would be inapplicable.

    At first thought, it might seem that Leibniz’s teaching that this actual world is only one among many alternative possibilities automatically provides for the contingency needed to escape from necessitarianism. For it might seem that necessity cannot enter in where other alternatives...

  3. 3 Leibniz on Intermonadic Relations
    (pp. 68-91)

    His theory of relations represents a crucial component of Leibniz’s philosophy. It is one of those many points of fertile concurrence where logic and metaphysics come together in fruitful symbiosis. But the theory confronts many problems. One of the gravest of these is the question, Are intermonadic relations real, or are they matters of mere seeming? It is sometimes said that for Leibniz, relations are mere creatures of the mind: That they are “our own creation” and “not in nature,” and so forth. This is indeed the doctrine of Spinoza,¹ and is approximated by such nominalist and materialist thinkers as...

  4. 4 Leibniz and the Plurality of Space-Time Frameworks
    (pp. 92-105)

    Leibniz advocated a theory of space (and time) as “relative”—that is, as relative to the physical things ordinarily said to be locatedwithinspace (and time). He opposed the doctrine of Newton’sPrincipiawhich cast space and time in the role of empty containers existing on their own and having a makeup that is indifferent to the things emplaced in them. For Leibniz, space and time are simply relational orders of being. Owing to the general tenor of his theory, Leibniz is sometimes seen as a precursor of Einstein and modern relativity theory. But this view is mistaken or,...

  5. 5 Leibniz and the Concept of a System
    (pp. 106-116)

    The aim of this essay is to examine the role of the systems concept in Leibniz’s thinking. It addresses the questions, Whence did Leibniz obtain the idea of system? How did he develop it? What sort of role did it play in his philosophy?

    While the underlying idea of what we nowadays call a “system” of knowledge was certainly alive in classical antiquity—with the Euclidean systematization of geometry providing a paradigm for this conception—actual use of the term “system” in this connection is of relatively recent date. In fact, as we shall shortly see, Leibniz was the first...

  6. 6 Leibniz and Issues of Eternal Recurrence
    (pp. 117-135)

    In the extensive philosophical literature that the Church Fathers devoted to the issue of “eternal recurrence,” three significant distinguishable ideas came to be conflated, namely:

    I.Eternal recommencement: the unending succession of destructions and re-creations of the world over an ongoing series of cosmic phrases or cycles of world annihilation and rebirth (palingenesis).¹

    II.Eternal recurrence: the unending reappearance of certain event-occurrence patterns as per Wagnerian leitmotivs or recurrently served menus (partial apokatastasis).

    III.Eternal repetition: the cyclic repetition at the cosmic level of exactly the same overall sequence of events, with cosmic history akin to a movie that is...

  7. 7 Leibnizian Neo-Platonism and Rational Mechanics
    (pp. 136-145)

    One of the saliently definitive doctrines of Neoplatonism issues from the teaching of Plato’sTimaeus(29D–30C) that intelligence, reason, and value are the crucial factors for explaining and understanding the nature of the universe.

    In no other major thinker in the Western tradition did this line of thought play a more central, determinative, and ultimately influential role than in the philosophy of G. W. Leibniz, who often avowed himself to be a follower of Plato and who, in turn, passed his Platonic vision of things on to a long-continuing tradition. In this brief chapter I can do no more...

  8. 8 Leibniz and the World’s Improvability
    (pp. 146-169)

    Until quite recently, no philosopher since Leibniz’s day has grappled seriously with the question of whether it is feasible to see the actual order of nature as the optimal resolution of the problem of world realization underplausibleconstraints—constraints, that is, which could reasonably be seen as appropriate requirements for realizing a coherent universe.¹ After all, the Leibnizian claim that this is the best possible world may seem to be absurd because so much appears to be amiss with the world. Yet the idea that the world is improvable is not without its problems.

    Since classical antiquity, theorists of...

  9. 9 The Epistemology of Inductive Reasoning in Leibniz
    (pp. 170-179)

    Philosophers naturally think of Leibniz as first and foremost a metaphysician: the author of theMonadologyand the founder of the “new system of preestablished harmony.” From this perspective, Leibniz’s ideas regarding the theory of knowledge fade into the background. In the common way of thinking among philosophers, Leibniz is not a substantial contributor to the theory of knowledge. Nevertheless, it is in this somewhat unaccustomed role that he will be presented in this present discussion.

    Epistemology is—to be sure—negligible if we assume the standpoint that is standard in the articulation of Leibniz’s metaphysics. Everything here turns on...

  10. 10 Leibniz, Keynes, and the Rabbis
    (pp. 180-200)

    Leibniz’s fascination with difficult legal issues dates from his early years and found expression in the doctoral dissertationDe casibus perplexis in jure, which he presented to the University of Altdorf at the age of twenty in 1666. This interest in law intersected with his concern for combinatorics and probability when, in a 1687 letter to Vincentius Placcius, one of his longest-term correspondents,¹ he wrote as follows:

    If two litigants lay claim to a sum of money, and if the other claim of the one is twice as probable as that of the other, the sum should be divided between...

  11. 11 Leibniz and Socialized Medicine
    (pp. 201-204)

    In the autumn of 1688 Leibniz at last realized his long-standing aspiration for an audience with the ruling prince of the Holy Roman Empire, Leopold I. He nursed the hope of persuading the emperor to appoint him as an advisor for projects of public interest, and in the course of this audience he made many proposals along these lines.

    Leibniz went to extraordinary lengths to plan for this meeting, drafting not just one but four preparatory memoranda for his presentation. The two longest of them, written in Latinate German, occupy more than fifty closely printed pages,¹ and they give a...

  12. 12 The Contributions of the Paris Period (1672–1676) to Leibniz’s Metaphysics
    (pp. 205-218)

    This essay seeks to elucidate the biographical background of the preceding discussion of Leibniz’s recourse to the idea of perfection maximization through infinitistic comparisons. In pursuing this goal, it will assess the extent to which the philosophical and mathematical work of Leibniz’s Parisian period contributed to the formation of his entire metaphysical system.¹

    To determine the extent to which a part contributes to a whole we must begin by setting before our minds just what this whole actually is. In the present case, this is by no means all that simple. For there can be considerable dispute as to just...

  13. 13 Leibniz Finds a Niche (1676–1677)
    (pp. 219-255)

    On 1 November 1675 the royal treasury of Louis XIV paid out the sum of 100,000 livres in gold coinage to Christophe Brosseau, representative in Paris of John Frederick of Hanover, duke of Brunswick-Lüneburg and premier member of the house of Brunswick, which ruled various principalities in the Lower Saxon region of Germany. After deductions for the usual gratuities to the royal treasurer and other officials involved, this handsome treasure was placed for safekeeping in the vaults of the Jesuit order in the Rue St. Antoine. Its ultimate transmission to Hanover—at the usual charge of 5 percent—lay in...

  14. 14 Leibniz Visits Vienna (1712–1714)
    (pp. 256-288)

    Vienna, capital of the Holy Roman Empire, had long been a focus of Hanoverian interest in connection with not only the elevation of the dukedom to an electorate in the imperial system, but also the Grand Alliance’s war against France. Then too the “princely conspiracy” had led to the exile of Prince Maximilian Wilhelm from Hanover to the imperial service.¹ And, of course, Vienna had great appeal for Leibniz as a center of culture and power. Over many years he had made several visits, and he had assiduously cultivated relationships at the imperial court. And now in projecting yet another...

  15. 15 Leibniz Crosses the Atlantic
    (pp. 289-299)

    In 1967 Kurt Müller published a comprehensive survey of the Leibniz literature.¹ It is striking that in this inventory of some 3,400 items, no more than a handful issued from North America. It will seem unbelievable to contemporary North American Leibnizians that one can count on one’s digits the North American scholars who had published on Leibniz in the period up to 1956, when L. E. Loemker’s monumental English-language Leibniz anthology first appeared and an upsurge of Leibniz studies got under way.²

    The earliest North American scholarly publication on Leibniz was what Max Fisch has called “a masterly review article...

  16. 16 Leibniz and American Philosophy
    (pp. 300-312)

    In these deliberations I propose to sketch a small chapter of the large story of Leibniz’s vast influence upon subsequent philosophizing. The protagonists of this story are four American thinkers whose work was significantly prominent in the first half of the twentieth century, namely C. S. Peirce (1839–1917), John Dewey (1859–1952), A. N. Whitehead (1861–1947), and Kurt Gödel (1906–1978).

    To an immigrant like myself, it does not seem an undue stretch to characterize Whitehead and Gödel as American thinkers since, after all, virtually the whole of theirphilosophicalwork was done during their years on this...

  17. 17 Leibniz and Cryptography
    (pp. 313-351)

    It is unquestionably an exaggeration to say, with Voltaire, that men use speech only to conceal their thoughts from the view of others. But it is certainly the case that they sometimes do so.

    The symbolic encoding of information and its concealment and revelation was of paramount interest to Leibniz throughout his entire career from beginning to end, and it was a topic that stimulated his mind in many directions. And cryptography, so Leibniz tells John Bernoulli, is a part of this project that is well deserving of the attention of a mathematician.¹ The “art of decipherment is something virtually...

  18. 18 Leibniz’s Machina Deciphratoria: A Seventeenth-Century Proto-Enigma Machine
    (pp. 352-368)

    G. W. Leibniz (1646–1716) was the quintessential Renaissance man, a German Leonardo da Vinci but with a difference. For instead of focusing on the plastic arts like Leonardo, Leibniz worked more abstractly—with mathematics. He invented the calculus, topology, determinants, binary arithmetic, symbolic logic, rational mechanics, and much else besides. But like Leonardo, Leibniz also constructed machines: wheels that ran on treads, windmills that worked by scoops, and an arithmetical machine that was—and still is—one of the wonders of the world of geared engineering. A great deal is known about Leibniz’s amazing achievements, but there are still...

  19. 19 Process Philosophy and Monadological Metaphysics
    (pp. 369-378)

    Monadological metaphysics is intimately bound up with a process-philosophical perspective. And from the days of Leibniz and Boscovitch process-oriented thinking has figured prominently in monadological philosophizing. After all, the term “monad” has both a physical and a metaphysical sense. Physically, monads are centers of force or activity—loci characterized by a dynamic impetus to change. Metaphysically, monads are particulars—items existing as units of reality—whose identity lies in their descriptive uniqueness. One of the prime objects of this discussion is to show how these two seemingly discordant factors are interrelated.

    Monadological metaphysics pivots on the idea that concrete particulars...

  20. 20 Was Leibniz Ennobled?
    (pp. 379-384)

    Leibniz’s earliest biographers unhesitatingly considered him ennobled and even sometimes spoke of him as Baron von Leibniz. Guhrauer conjectures (vermuthet) in his 1846 pioneering Leibniz biography that he was ennobled in January 1690, on the occasion of the crowning of Joseph I as King of the Romans.¹ But a careful search of the imperial archives in Vienna gave no sign that a letter patent of ennoblement had ever been issued. For, as Guhrauer rightly says, “we are unable to specify this ennoblement [Standeserhöhung] of Leibniz’s with exactness as to the year and day. For a certifying document [Diplom] has not...

  21. 21 Leibniz Disillusioned: Parting Ways from J. D. Crafft
    (pp. 385-396)

    Johann Daniel Crafft or Krafft and sometimes Kraft (1624–9 April 1697) was for many years Leibniz’s collaborator and business partner. And not just that—he was as close a personal friend as Leibniz ever had.

    By profession Crafft was a chemist, alchemist, and scientific entrepreneur. The two had been in touch ever since Leibniz’s mid-twenties when, like Crafft, he was in the service of the Elector of Mainz. Their regular, extensive, and long-enduring correspondence dates back to the summer of 1671, when they began to scout out opportunities for using science to make money.¹ They soon even agreed on...

    (pp. 397-400)

    This inventory of my Leibnizian writings merits a brief preliminary account of the history of my concern with the work of this fascinating and many-sided thinker, whose influence has been a recurrent leitmotiv in my life. Indeed, our initial contact dates from a development of merely symbolic importance—seeing that it occurred in 1928 when I was only four or five months old—namely, my parents’ move to the house of my early childhood at No. 3 Leibnizstrasse in the Westphalian town of Hagen.

    Though I had certainly encountered Leibniz in undergraduate history of philosophy courses, and had been intrigued...