Leibniz’ Monads: A Heritage of Gnosticism and a Source of Rational Science

  • Graham Solomon
Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 65)


A typical view of Leibniz’ extraordinary metaphysical and methodological views is to regard them as having appeared by certain “applications” of his mathematical and physical discoveries. If we believe Couturat and Russell the monadology is largely only the expression of certain logically formal relationships: it is the logic of Leibniz that is basic to his mature metaphysics.2 Even more typical is the view that Leibniz’ work in mathematics, especially his work on the calculus, is the source of the key ideas in his metaphysics. J. M. Child, the translator of the early mathematical manuscripts, says it straight out: “... the main ideas of [Leibniz’] philosophy are to be attributed to his mathematical work, and not vice versa.” 3 In a philosophically much more interesting way Paul Schrecker argues that what he calls Leibniz’ “infimitesimal method,” a method obviously derived from his mathematical work, pervades all of the important basic contributions ofboth his metaphysics and methodology. The infinitesimal method involves a rationalist postulate expressing the view that ordinary modes of thought (and ordinary modes of language) be replaced by rigorous formal systems of expression and calculation. his work in logic, especially symbolic logic, and his mathematical investigations led him to seek to extend this postulate to the entire area of scientifiic endeavor. For science to progress, this postulate must be adopted in order to conquer the unfortunate excesses of intuition and imagination.


Mathematical Work Simple Substance Positive Science Ordinary Mode Metaphysical View 
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  1. 1.
    [Previously published in Canadian Journal of Philosophy 10 (1980): 47–62.] An earlier form of this essay was read at a workshop in history and philosophy of science held at Benmiller, Ontario, in May 1977. The workshop was supported by the Department of Philosophy, the University of Western Ontario, the Canada Council, and the Division of Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Science. Further work on the material was encouraged by Jürgen Mittelstrass, Thomas Lennon, and John King-Farlow. I owe much to former teachers: Paul Schrecker, Francis Clarke and Milton Williams, immortal monads who have found new places in Being.Google Scholar
  2. 2.
    Louis Couturat, La Logique de Leibniz d’après documents inédits (Paris, 1901); Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz, 2nd ed. (London, 1949).Google Scholar
  3. 3.
    J. M. Child, trans., The Early Mathematical Manuscripts of Leibniz (Chicago and London, 1920), p. iii.Google Scholar
  4. 4.
    Thus see Nicholas Rescher: “In mathematical analysis the continuity properties of functions play an important role, and there is little doubt that it was his mathematical studies which suggested to Leibniz the philosophic potentialities of the continuity concept.” The Philosophy ofLeibniz (Englewood Cliffs, N. J., 1967), p. 51, n. 9. Couturat, Russell, Schrecker, rescher, Mittelstrass, Aiton: one must be very bold indeed to oppose the authority of such a group of Leibniz scholars! As will be seen, I do not so much offer opposition as gentle insinuation. It is enough to trouble the sleep of the giants; I cannot expect to match their readings of Leibniz text-by-text and argument-by-argument.Google Scholar
  5. 5.
    Paul Schrecker, “The Unity of Leibniz’ Philosophic Thought,” in Leibniz, Monadology and OtherPhilosophical Essays, trans. Paul and Anne Schrecker (Indianapolis and New York, 1965), p. xv.Google Scholar
  6. 6.
    Jürgen Mittelstrass and Eric J. Aiton, “Leibniz: Physics, Logic, Metaphysics,” in Dictionary of Scientific Biography ed. C. C. Gillispie (New York, 1972–75), vol. 8, p. 157.Google Scholar
  7. 7.
    Gerd Buchdahl, Metaphysics and the Philosophy of Science (Oxford, 1969), p. 407–8.Google Scholar
  8. 8.
    Metaphysics may be seen as a nest of more and more inclusive motivations, and the more inclusive the motivation, the more diffiicult it is to psychoanalyze it away: the motivation to seek maximum clarity about certain problems, and maybe to solve them; the motivation to explain problem solving methods by inclusion in more sweeping, deeper, epistemological or “metaphysical” networks; the motivation to “take up a question” in the first place, to put a certain premium on finding an answer, and to place greatest emphasis upon certain ways of “seeing” or structuring understanding of the world. Clarity motivations led to Leibniz’ science; depth motivations produced his “public” metaphysics. The question why he found any of this interesting is only answered by reference to motivations at the third level, the level at which one asks himself: why on earth would Leibniz have thought of replacing physical atoms with spiritual ones? why must everything be thought of as being alive? why are there no gaps in being(after all, we find what appear to be such gaps all the time)? Just try the following exercise: how does one make Leibniz believable to late 20th century undergraduate students?Google Scholar
  9. 9.
    The literature of gnosticism and Neoplatonism (not to speak of that of much of Christian theology as well) is full of discussions of limits. Why has no one suggested that it is this metaphysical concept of the limit that motivates acceptance of the calculus? Might it be that we are inclined to read the success of that part of mathematics back into the work of Leibniz?Google Scholar
  10. 10.
    In discussion of this paper at Benmiller, Adolph Grünbaum correctly pointed out that my account in this paragraph and the one j ust before it leaves out of consideration most of the more intricate philosophical problems of space. I concede his point. I do believe that what I have said is, however, a sketch of a successful reading of the first three paragraphs of the Monadology. In part I am prompted to read Leibniz in this way because of certain suggestions in Husserl’s discussion of the whole/part logic, suggestions too complex to discuss here. See Husserl’s analysis of “foundation” and “dependent” and “independent” parts in Logische Untersuchungen, vol. 2, part 1, p. 111. ZurLehre von den Ganzen und Teilen (Halle a. d. S., 1928), 4th ed.Google Scholar
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    Consider just one of the many texts: Principles of Nature and of Grace, Based on Reason (1714), para. 3: “All nature is full [a plenum] ... and because of the plenitude of the world everything is connected ...”.Google Scholar
  12. 12.
    If the calculus were liable to metaphysical interpretation only in terms of Leibnizian continuity, what fools Newton and Berkeley must have been!Google Scholar
  13. 13.
    A. O. Lovejoy, The Great Chain of Being (Cambridge, Mass., 1936), surely the locus classicus for understanding the history of the concept of continuity; Lewis White Beck, Early German Philosophy: Kant and his Predecessors (Cambridge, Mass., 1969). Beck suggests a thematic connection between Leibniz and the mystic Nicholas of Cusa (71), notes Leibniz’ admiration of the even more mystical Jakob Böhme (156), and in many places is fully aware that Leibniz lived and learned in Germany, a country with a rich and influential mystical and occultist background. Beck understands that the historical move toward rationalism as Aufklärung in Germany is rather different from that in Britain or in other parts of continental Europe. The transition from 14th century German piety (the devotio moderna of the Imitation of Christ and Theologica Germanica) to Kant’s assertion of Aufklärung as “... man’s release from his self-incurred tutelage” is historically unique, and such patterns of difference and diversity are not frequently noted in standard works in the history of philosophy.Google Scholar
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    William Shea has pointed out to me that Leibniz could not have been a Rosicrucian because there were no (empirically ascertainable) Rosicrucians. Whenever one of them was about to be detected, he became invisible ! Such is the power of the Black Arts. Even contradictions in being are tolerated and pragmatically carried out.Google Scholar
  15. 15.
    It may be intriguing to consider: how does the attempt to discover the number of the Beast of the Apocalypse differ in any important way from the attempt to give mathematical grounds for computing that mysterious entity known as an instantaneous rate of change of speed? When, exactly, did alchemy become chemistry and geomatria modern mathematics? Was it not part of the endeavor of the medieval astrologer to have us “sit down and calculate”?Google Scholar
  16. 16.
    Leibniz, Critical Remarks Concerning the General Part of Descartes’ Principles (1692), “On Article 64”, Schrecker & Schrecker, op. cit., 78, emphasis added. That Leibniz’ crucial point is methodological rather than substantive is brought out later in the passage: At the same time [as one seeks to eliminate resort to substantial forms and souls] one will understand that in former times the Schoolmen erred not so much in dealing with the indivisible forms, but in applying this theory in places where the question concerned rather the modes and operations of substance and its forms of action, that is, when the question dealt with mechanism. Nature contains, so to speak, an empire within an empire, or a double government: the government of reason and the government of necessity [compare Kant: the causality of freedom and the causality of necessity], or the empire of forms and that of material particles. Just as all is full of souls, all is also full of organic bodies. These two realms remain distinct, each one being governed by its own law (ibid., p. 79; emphasis added). It appears that one is free to adopt essentially gnostic themes without thereby committing oneself to a misplaced methodological employment of such topics.Google Scholar
  17. 17.
    Kant’s discussion of the dialectical clash between teleology and mechanism in the Critique ofJudgment pits one regulative principle against another. That, for Kant, the teleology/mechanism issue is one concerning the preferred methodological employment of certain principles as demands ofreason, is a point often neglected in accounts of Kant. Some students of Kant wonder why he was even interested in the problem. Because he was a Leibnizian, that’s why, and hence the philosophical role of the supersensible (briefly, the hermetical) was of deep concern to him. The “Critique of the Teleological Judgment” is, after all, an essay on the role and status of the supersensible.Google Scholar
  18. 18.
    Again the line from Leibniz to Kant can be drawn with complete assurance. Leibniz lists the following as ideas only inappropriately applied in mechanical science: the Archeus (an occult vital principle animating and perfecting individual substances), occult fertility and production virtues, substantial forms, souls, and “the simple will of the deus ex machina” (ibid.). Kant’s list includes: circulating humours in organic bodies, a supersensible Being, and thinking spirits without bodies. Kant lists as “things of opinion” (hypotheses appropriate in mechanical explanation) subterranean fire as the cause of earthquakes and volcanoes, rational inhabitants of other planets, and “the ether of the new physicists.” (Critique ofJudgment, “Methodology of the Teleological Judgment,” sections 90–91.) That Kant’s impulse to discuss methodological problems at length stems from his acceptance of a “transcendental” strain in Leibniz may be surprising to some; unfortunately for them, this impulse may be the central philosophical anxiety for Kant. [For discussion of Kant’s Leibnizian theory of hypothesizing see my “Kant on Hypotheses in the ‘Doctrine of Method’ and the Logik,” Archiv für Geschichte der Philosophie 44 (1962), especially pp. 197–200.]Google Scholar
  19. 19.
    From Lessing’s Über die Erziehung des Menschengeschlechtes; my reference is to Etienne Gilson’s citation, The Spirit of Medieval Philosophy (New York, 1940), p. 19.Google Scholar
  20. 20.
    Leibniz, Discourse on Metaphysics, trans. Peter Lucas and Leslie Grint (Manchester, 1953), p. 22. The suggestion that our thoughts are always parts of us is typical of Leibniz. Connectedness, continuity, harmony: the themes are repeated over and over again. Later the archrationalist gnostic Hegel will suggest that our possessions are only extensions of our personalities, and we will begin to understand a man by what he buys and builds, not by what he dreams and by his romances. Man is what he makes and what he pays for. From the point of view ofpsychohistory, is rationalism the basic human pathological state?Google Scholar
  21. 21.
    Buchdahl, op. cit., p. 395.Google Scholar
  22. 22.
    Monadology, trans. Schrecker and Schrecker, op. cit., p. 155.Google Scholar
  23. 23.
    Ibid., para. 67, p. 159. Not unlike Spinoza: the attributes are after all only ways in which we conceive the one substance. It is standard to point out that this fantasy originates from observations made with a good microscope. Perhaps. But compare the section with the rest of the Monadology and it will emerge as the poetic expression of a tightly connected vision of the nature of things, a vision so powerfully primal as to give informed sight to the microscope. Galileo is a good case of one who realized that one must be independently motivated to believe what one “sees” by means of an optical instrument.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Graham Solomon
    • 1
  1. 1.Wilfrid Laurier UniversityWaterlooCanada

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