Leibniz Selection, ed. Philip P. Wiener (1951)


I am indebted to Professor Arthur O. Lovejoy for his; incisive view of Leibniz's development of the principles: of plenitude, continuity, and gradation presented in the fifth chapter of his authoritative study of the history of the idea of The Great Chain of Being, the William James Lectures delivered at Harvard University, 1933, and published by the Harvard University Press in 1936, with whose kind consent I have used that part of the text which translates Leibniz's utterances on the subject.

I wish to thank Professor Albert R. Chandler, Chairman of the Philosophy Department of Ohio State University, for his kind permission to use his revised translation of Dr. George Montgomery's version of Leibniz's Discourse on Metaphysics, first published by the Open Court Publishing Co. in 1902 and reprinted with Professor Chandler's revision in 1924.

Professor Donald Lach has kindly permitted me to use in my Introduction a quotation from his article on "Leibniz and China" which appeared in the Journal of the History of Ideas 6 (1945), pp. 436-455.

The Philosophical Review has co-operated also in permitting the use, in Part II of the Introduction below, of parts of my article, "Notes on Leibniz's Conception of Logic in its Historical Context," which appeared in that journal in November, 1939, pp. 567-586; however, these notes have been largely revised.

To Professor Paul Schrecker of the University of Pennsylvania, and the leading editor of many of Leibniz's unpublished writings, I owe some important suggestions in the choice of selections. Professor Leroy E. Loemker, former Dean of Emory University, has courteously and cooperatively shown me the table of contents of his two-volume edition and translation of Leibniz's Philosophical Papers and Letters (University of Chicago Press, 1956), which the advanced student will surely wish to consult.

Dr. Huntington Cairns has in his writings indicated the historical significance of Leibniz as a legal philosopher, and kindly permitted me to draw on his expert knowledge of the subject.

Finally, the form in which I have chosen to acknowledge many suggestions from fellow-teachers of the history of philosophy has been to include as large a diversity of selections as they have proposed. Thus there should be enough source-material here to meet the needs of many kinds of students who do not have access to the original Latin, French, and German texts (see pp. 601-606). About half of these selections have never been translated into English, and the extant translations have had to be revised for accuracy.

Emile Ravier's Bibliographic des Oeuvres de Leibniz (Paris, F. Alcan, 1937) is the most exhaustive bibliography to date of all the known writings and editions of Leibniz's work. It has been used to supply the dates for the selections given here.

Thanks to Professor Paul O. Kristeller's meticulous critical reading of the first printed version of my Leibniz Selections, I have been able to incorporate many of his suggested corrections in the present text, declining only his preference for literal translation.


Philip P. Wiener


Alfred North Whitehead, whose Universal Algebra and organic view of nature owe much to Leibniz, has placed him in "the century of genius." Gottfried Wilhelm Freiherr von Leibniz (1646-1716) belonged not only to that century but exemplified also the Renaissance ideal of the universal man in his many-sided activities, and ushered in the Age of the Enlightenment as well. He was a lawyer, scientist, inventor, diplomat, poet, philologist, logician, moralist, theologian, historian, and a philosopher who religiously defended the cultivation of reason as the radiant hope of human progress.

In order to place Leibniz's life in chronological relations to the great seventeenth-century philosophers, we may recall that Newton was born in the same year Galileo had died (1642), Robert Boyle was born in the same year Francis Bacon had died (1626), and that in the year of Leibniz's birth (1646), Descartes was fifty, Hobbes fifty-eight, Locke and Spinoza were only fourteen. In the natural sciences, then advancing rapidly, Leibniz corresponded with experimenters in physics, Huyghens. Von Guericke. Boyle. Newton. Papin, Perrault, Mariotte, and with biologists like Leeuwenhoek. In mathematics, Leibniz knew thoroughly the works of Pascal, Fermat, Descartes, Roberval, and corresponded with the Bernouillis, Sturm, Goldbach, Wallis, Wren, Varignon, Tschirnhaus (friend of Spinoza), and Newton. It was as a result of his correspondence with Newton that Leibniz was falsely charged with plagiarism in the discovery of the infinitesimal calculus. In the social sciences (as we now call them), among Leibniz's contemporaries were the founders of statistics, Graunt, Petty, and De Witt, the legal philosophers of "natural law," Grotius and Pufendorf; and finally, a group of Catholic and Protestant theologians, Arnauld, Malebranche, Clarke, De Volder, et al. discussed with Leibniz important questions of science, philosophy and religion which were not then studied as separate disciplines.

The wide range of Leibniz's intellectual interests was not unusual for the scientists and philosophers of his time, but few thinkers since Aristotle ever produced writings on so vast and varied a scale. They include thousands of letters and innumerable essays, finished and fragmentary, long and short, most of them posthumously published and many still unpublished. They deal with special and general topics in logic, mathematics, mechanics and mechanical inventions, biology and medicine, psychology and epistemology, metaphysics and theology, ethics and jurisprudence. There are also military and diplomatic plans and proposals, philological theories, documented researches in the medieval history of the Holy Roman Empire and the genealogy of the royal family of Hanover, projects for the reunion of the Protestant and Catholic Churches and for perpetual peace, and for the founding of academies of arts and sciences all over Europe on the model of the British Royal Society and the French Academy to which Leibniz had been elected. Only a few of the forty large volumes planned by the Prussian Academy as a definitive edition have appeared, and it is unlikely that the task will be completed in this century.

Leibniz's writings are both the delight and despair of students of his many-sided thought. They are a delight to a wide variety of scholars because they contain brilliant apercus suggestive of many new ideas in the development of modern scientific and philosophic thought. However, the advanced character of his scientific thinking did not affect Leibniz's conservative respect for older, scholastic traditions and distrust of radical innovations, especially in ethics and theology. Still the mathematical student will admire his invention of determinants, non-metrical geometry (analysis situs), and the calculus (superior in its notation to Newton's), but will despair of Leibniz's unproved claims to deduce all the axioms of geometry and rules of algebra by means of a universal, logical language. The symbolic logician like C. I. Lewis, who has gone into the history of his science, will credit Leibniz with having taken the first steps toward a logical calculus, but will be disappointed by Leibniz's unrealized proposals. The experimentalist like Huyghens would have loved to see the possible experiments and inventions claimed by Leibniz, but was skeptical of his a priori rules for the art of discovery. The historian like Gibbon will admire Leibniz's labors in ransacking the medieval archives of feudal Germany, but will be cold to Leibniz's defense of his patron's feudal rights. The philosopher of science will admire Leibniz's acute analyses of the foundations of science or its first principles, but will wonder at the strange pre-established harmony of mind and body, of monads "without windows" reflecting each other's inner nature but opaque to external influences. He may with Bertrand Russell suspect that Leibniz sacrificed much of his logical rigor when he essayed to provide room in the foundations of science for extra-scientific value-judgments based on the traditional teleological conceptions of divine creation and planning. In any case it was natural for Leibniz to defend certain traditional ideas of God, freedom of the will, and immortality of the soul in the context of his own intellectual history, to which we now turn.

His father was a professor of moral philosophy at the University of Leipzig, and died when Leibniz was only six. The boy, precocious in learning things by himself, taught himself enough Latin (with the aid of Comenius' Orbis Pictis) to peruse the volumes of his father's library well stacked with classical and scholastic books on literature, history, and philosophy (Plato, Xenophon, Herodotus, Aristotle, Cicero, Quintilian, Polybius, Augustine and the other Church Fathers, Thomas Aquinas). But there were also the exciting modern books of Francis Bacon and Rene Descartes whose Discourse on Method might be compared with one of Leibniz's autobiographical accounts: "At school before I came to the grade in which Logic was taught, I had immersed myself in the historians and poets, having begun to read the historians almost as soon as I was able to read at all, and in verse I found great pleasure and ease; but as soon as I began to learn Logic, I found myself greatly fascinated by the division and order of thoughts which I was able to follow, and soon observed, as far as a boy of thirteen could, that there must be much more to the subject. I was most of all delighted with the Categories (Predicaments) which seemed to me to call the roll of all the things in the world, and I read Logic books of all sorts in order to find the best and most detailed account of the list of categories. I used to ask myself and my schoolmates to which category and subcategory anything that came up belonged." (Letter to Wagner, 1696).

This early fascination for such diverse subjects as history and logic is symptomatic of his intellectual versatility and, to a certain extent also, of his originality. His infinitesimal calculus was a masterly method for measuring rates of change, absent in the prevailing Cartesian theory that matter is extension or timeless spreadoutness. Leibniz, by insisting on the failure of Cartesian physics to include temporal, dynamic properties, provided physical nature with a historical dimension. And in his Discourse on Metaphysics there is a bold attempt to include the history of each individual substance within a "real definition" of its logically determined nature.

At the age of fifteen Leibniz was already preoccupied with the ancient problem of universal ideas: did they exist apart from changing particular things and processes (as Plato and the medieval realists like Anselm believed), or in the particular observations which are prior to the abstraction of general properties (as Aristotle and the nominalists maintained)? Leibniz took up the question in his baccalaureate thesis (Disputatio metaphysica de Principio Individuo, Leipzig, 1663), and argued in true scholastic style for a principle of individuation which would preserve the independence of universals with respect to ephemeral sensations, and yet embodied universal ideas in the eternal natures of individuals. In his youthful philosophizing, he thought, under the influence of Gassendi, that the essences of things were inseparable from the properties of material atoms and their motions. But this materialistic atomism was soon abandoned in favor of a scholastic principle of individuation, namely, that an individual is a determinate unity of form and matter, created by God. Leibniz was then ready to revert to the doctrine of substantial forms or embodied souls as the ultimate realities. The soul was understood in Aristotelian fashion as the "form" of the body, but "form" was not to be interpreted in a static, geometrical sense; this was the error of the Cartesians. Their two substances of thought and extension also left the relation of mind and body and the problem of personal immortality ungrounded; but the true interpretation of "substantial form" would do justice to the eternal purposive nature, final cause, or entelechy of each creature. Physics could then rid itself of the lifeless, purposeless motions of atoms in the void, and base its mechanical laws on the internal dynamic actions of groups of centers of energy. These substantial centers of living energy he called (following Augustine and Bruno) "monads." In them the spiritual and physical live in a pre-established harmony with one another.

On behalf of his substantial forms or monadic souls, Leibniz argues that he is only asking that they be considered to have the same sort of eternal existence which the atoms of Democritus already were presumed to have, and the same tendency or exigency to exist that the atoms had to move.

Not only does nature then do nothing in vain, but it operates in the most economical fashion according to the simplest laws, permitting no waste of space or identical empty spaces. For similar reasons, Leibniz opposed the Newtonian assumption of "action at a distance," for it violated the smooth continuity of causal action: "Nature makes no leaps" is Leibniz's favorite principle of continuity, and he applied it everywhere.

The economy and implied teleology of natural processes were illustrated in the laws of optical reflection and refraction where light always chooses the minimum path. Descartes' laws of motion preserved the quantity of motion (we should say momentum today), whereas Leibniz showed that there was also conserved a quantity of living force (we should say energy today). Finally, even Newton confessed that he was not satisfied with the action at a distance of gravitation, the universal force of attraction, and hoped that its underlying nature could some day be discovered.

So far as the purely scientific questions are concerned, the difference between the Cartesians and Leibniz is settled by crediting the former with the law of the conservation of momentum and the latter with the law of the conservation of energy. The difference between Newton's and Leibniz's views of space and time, discussed in the extensive correspondence with Samuel Clarke (a friend of Newton), is still of interest to students of the evolution and logic of modern physics. But there are also questions of broader philosophical import in these controversies. Leibniz challenged the adequacy of the mechanical conception of nature in both the Cartesian and Newtonian world-views. That conception seemed to Leibniz to fail to do justice to the organic, dynamic, and purposive features of life and thought. The idea of purposive activity provided Leibniz with a unifying principle for physical, biological, and psychological phenomena. It is historically relevant to note that he had come to the problems of the natural sciences only after deep absorption in humanistic studies, metaphysics, theology, and law.

Leibniz received his bachelor's and master's degrees at Leipzig in 1664-1666 for two theses on jurisprudence, and then moved to Altdorf nearby to receive a doctorate in law with a dissertation On Perplexing Cases in Law (De casibus perplexis in jure, 1666). This was followed a year later by an essay On a New Method for the Study and Teaching of Jurisprudence (Nova methodus discendae docendaeque jurisprudentiae, 1667) which secured him a position as legal adviser to the Elector of Mainz and Archbishop of Frankfurt. Now Huntington Cairns has observed in his authentic account of Leibniz as a legal philosopher that Leibniz's "early writings on jurisprudence, a field with which he began to occupy himself when he was eighteen years old, reveal clearly the mixture of scholasticism, novelty of insight, and scientific analysis that was to characterize his mature studies. . . . The doctrine of law is to be treated rigorously, beginning with definitions and proceeding syllogistically to the deductions and theories of law." [ H. Cairns, Legal Philosophy from Plato to Hegel (Baltimore, 1949), pn. 297, 299.]

Leibniz's success in applying his logical genius to the human questions of law opened a career for him in the diplomatic world; he refused an offer of a professorship in order to seek his fortune in the larger world of affairs.

When he arrived in Paris in 1672 on a diplomatic mission but fell in with the great mathematical scientists, he was caught between his wordly ambitions and his great admiration for the new developments in mathematical and physical sciences. An important clue to his philosophical development consists in observing how in nearly all of his writing he tried to accommodate traditional philosophy with its Platonic ideas, Aristotelian categories, spholastic substantial forms, to the new concepts and methods of the rapidly growing sciences.

While working on his doctorate, at the age of twenty, Leibniz had struck off an essay on the art of combining concepts (De ars combinatoria, 1666). It adapted the scholastic work of Lully, Ars magna, in the form of a universal ideographic language for symbolizing abstract concepts like Justice, Courage, etc. What Leibniz attempted was a universal method of analyzing concepts by means of numerical characters. Though he later confessed to the mathematical immaturity of this essay, he seems never to have abandoned the Pythagorean and semi-cabalistic notion of penetrating the mysteries of nature, man, and God by means of an esoteric universal language. Exaggerated as most of his claims for his ''universal characteristic" seem to us today, the fact remains that in Leibniz's own opinion it led him to the discovery of the infinitesimal calculus as well as to "the true method of metaphysics and theology." It is therefore central to an understanding of Leibniz's contribution to philosophy to examine his conception of the function of logic.


Leibniz himself more than once actually identified the basis of his new logic ("universal characteristic") with that of metaphysics and natural theology. "It is sufficient at present for me to notice that the foundation of my universal characteristic is the same as the demonstration of the existence of God." (Letter to Princess Elisabeth, 1678). But he also claimed repeatedly that his logic was the mother of all his discoveries in mathematics, physics, geology, philology, law and technology. Hence, for Leibniz, logic had to serve a double function; it had to offer proofs for the existence and structure of the divine source of all things, and also to further the arts and sciences.

These two functions of logic, bearing on theology and the sciences, vied with each other in Leibniz's thought with such equal force that it is often impossible to say which of them is more characteristic of his many logical writings, or how clearly he distinguished them in his own conception of logic. The rivalry in his orientation of logic between its theological uses, on the one hand, and its scientific function on the other, seems to be correlated with the changing intellectual traditions and social structure of his times. Although the foundations of the social order of seventeenth-century Europe rested on theological, legal and political traditions, the rise of the modern states, of experimental science, and of commerce displaced the feudal structure, and its scholasticism was confronted by far-reaching cultural changes. The development of more exact methods of measuring time, latitude and longitude, interest and insurance rates, and new techniques of agriculture, mining, shipbuilding, transportation, sanitation, medicine and accountancy required an intellectual reorientation and instruments which the traditional logic and science were unable to supply so long as they were subservient to theology.

The instrumental role which Leibniz assigned to his more general symbolic logic can be illustrated from his many concerns with the invention of adding machines for banks, of ready-reckoners for commerce, of submarines and magnetic compass for shipping, water-pumps for mines, telescopes, and microscopes for war and medicine, etc.:

"In natural philosophy, I have been the first, perhaps, to have completely demonstrated that the earth moves, and that the vacuum does not exist; this I have shown not through experiments, for they do nothing, but by geometrical demonstrations. . . . . In Mathematics and Mechanics I have by means of the Combinatory Art found several things which in practical life are of no small importance: first of all, an arithmetic machine which I call a Living Bank-clerk . . . of many uses in Business, military affairs, surveying, sine-tables and astronomy. Another instrument of mine which I call a Living Geometer, mechanically -- for nothing exists in nature otherwise than mechanically -- provides a way to resolve all conceivable lines and figures. . . . In Optics I have first of all men discovered (1) a certain kind of tube or lens which I call Pandochas because it makes the whole object uniform. . . . (2) Catadroptic tubes, for in one tube are juxtaposed a mirror and perspective . . . (3) a means, much sought until now, of measuring from a given position in perspective . . . which I found through the Art of Combinations. In nautical things . . . on procuring sufficient data from a few experiments . . . I will demonstrate how to find longitudes completely, and provide a way for a person on a ship to know with certainty what his location is without the help of the sun, moon and stars which cannot always be observed (yet Huyghens' famous invention depends on them alone). In Hydrostatics I have restored the lost invention of Drebel that enables one to go with a ship under the surface of the water during a storm (for it is tranquil enough under water) or during an attack by sea-robbers, and then to come up again; and this is what Mersenne wanted so much to do. In Pneumatics . . . I have compressed air into a box 1000 times normal pressure which can exert terrific force on water . . . like a cannon shot." (Letter of Leibniz to Herzog Johann Friedrich, Oct. 1671).

In hundreds of such letters written by Leibniz to all the corners of scholarly Europe, our philosopher, inspired by his vision of the universal logical language, claimed for his art d'inventer a power which taxes our credulity. Almost all the mechanical, military, religious, legal, and political phases of the life of his country and age, were in Leibniz's mind to be benefited by his vision. The universal characteristic deciphered the book of nature and revealed for him every link in the whole great chain of being: the water that needed to be pumped out of the Harz mines, the fossils in the mountains which had to be described not as "sports of nature" but as Nature's historical record of her illustrious works, the physical phenomena of gravitation, elasticity, and magnetism which Leibniz thought he could deduce from the purely geometrical laws of light.

"I assumed that the motion of the ether came from the daily motion of light around the earth, without bothering to ask whether the sun or earth turns. . . . All the phenomena of gravitation, magnetism, electricity, and light are explicable by the resolution of a few problems of pure geometry: so much so that I believe I can be satisfied concerning the laws of motion by demonstrations entirely geometrical, without using any assumptions or principles from experience; and that whatever we will be able to say about these things, henceforth, will be only a matter of calculation and geometry (res calculi et geometriae)". (Letter to Ferrault, 1676).

The problems of medicine, of morals, of law, of theology and of metaphysics were all in Leibniz's mind to be duly resolved by the new symbolism. Thus logical rigor was important to him not merely for abstract theoretical reasons; it was necessary also, he thought, for the most practical interests of the seventeenth century, technological, medical, moral, legal, political, or religious. For example, Descartes is criticized by Leibniz not only for having failed to give a sufficiently rigorous proof of God's existence (a failure which weakens the defense of religion), but also because Descartes "of all men excelled in speculations, but has found nothing useful in life which falls under the senses and which may serve in the practice of the arts." (Letter to Philip, 1679).

It is in his correspondence concerning the experimentalists of the Royal Society of England (whom he had visited in 1673) that Leibniz reveals most clearly what he thought his logical instrument could do, and what the plain empiricists were not doing, namely, to elicit all the knowledge deducible from, a given number of presuppositions. Lack of a proper art of demonstration had made it necessary, in Leibniz's opinion, for Baconian experimental philosophers like Boyle to resort to many observations in order to find out what Galileo and Descartes were able to know by reasoning. Some years after visiting the Royal Society in London, Leibniz reports: "For they confessed to me in England that the great number of experiments they have amassed gives them no less difficulty than the lack of experiment gave the ancients." (Letter to Herzog Friedrich, 1679).

More than once does Leibniz take his experimental friends of the Royal Society to task for not having deduced more than they have from their many experiments. He and Huyghens admire the work of Robert Boyle, but find the Honorable Gentleman lacking in "application," or powers of generalization and inference. What Leibniz most admired in Boyle was his search for the simples or alphabetic elements of chemistry. Now Boyle thought his mechanical philosophy merely probable or no more true than his experimental observations, and reserved for theology a supernal place in "Things above Discourse," outside of science and logic. But Leibniz with his ambitious logical apparatus hoped to prove the teleological fitness of the grand laws of mechanics, so that the conservation of energy was a consequence of the continuity and universal harmony in all of nature.

In the physical sciences, what Hertz recognized in his Principles of Mechanics as the symbolic function of hypotheses, was first expressed by Leibniz as follows: "Ars characteristica is the art of so forming and arranging characters, in so far as they refer to thoughts, that they have among them those relations which the thoughts have among themselves: so that out of the ideas composing the idea expressing things, an expression of the things is composed out of characters of those things."

Leibniz constantly strove to reconcile the a priori elements of demonstrative reasoning with the more empirical side of scientific method. This stands out clearly if we compare the quotation just given with the empiricism in the following remark:

"It is my habit to list a catalog of Experiments to do, when I examine some matter of Physics. And usually, I make such an enumeration of them that can assure me that by means of these experiments one will be able to find the cause or rule of what is in question through demonstration and not through Hypothesis. . . . In no wise content with the physical principles of Mons. des Cartes, I see that there is a way of establishing by means of experiments already done or easy to do, a Physics that is solid and without Hypothesis." (Letter to Berthey, 1677).

Thus a "solid Physics without Hypothesis" meant for Leibniz a more purely deductive logical system than either Descartes or Newton was prepared to offer. Leibniz had in mind apparently a postulational method for testing the compatibility or "compossibility" of the first principles or basic assumptions of any science. Compatibility of postulates in physics, for example, was demonstrable by experimental instances on the principle that what is actual is also possible, as in establishing the consistency of an axiom-set, we seek "interpretations." The superiority of the postulational treatment lay in the possibility of using the universal characteristic as a means or instrument for deriving new laws.

The criterion of "compossibility" -- the compatibility of existing things -- was also important in metaphysical theology, for Leibniz's main objections to Descartes' and Spinoza's proofs of God's existence rested on the logical point that their proofs had not established the compossibility of the attributes in the definition of God. Metaphysics or natural theology yields certainty because reference to empirical instances is not necessary in order to prove the consistency of the idea of God, the simplest of all ideas. Experimental physics can yield only probabilities because it is humanly impossible to refer all experimental laws to the logically simplest terms.

If adequate notice is taken of the postulation of hypotheses or logically probable constructions, there will be more progress in Physics than if experiments alone are devised:

"I agree with you, Sir, that it is necessary to follow the plans of Verulam in Physics, by adding to them, however, a certain art of conjecturing (art de deviner), for otherwise we shall hardly advance. I should be astonished if Mr. Boyle, who has so many fine experiments would not come to some theory of chemistry after meditating so long on them. Yet in his books, and for all the consequences that he draws from his observations, he concludes only what we all know, namely, that everything happens mechanically. He is perhaps too reserved. Excellent men should leave us even their conjectures; they are wrong if they wish to give us only those truths that are certain." (Letter to Huyghens, Dec. 29, 1691).

Was Leibniz merely catering in his diplomatic way to the empiricism of his correspondents? Not if we consider the many times Leibniz reports his own empirical procedure; for example: "What made me believe that the variation of the compass-needle follows some rule (although still unknown) is the fact that I have seen some journals or log-books of long voyages in which it was often recorded as not changing by leaps but little by little." (Letter to Huyghens, Nov. 1690). Or again: "Is there nobody in philosophy at present who thinks about medicine? The late Mr. Crane was at home in it, but Messieurs les Cartesiens are too much preoccupied by their hypotheses. I prefer a Leeuwenhoek who tells me what he sees to a Cartesian who tells me what he thinks. It is however necessary to add reasoning to observations." (Letter to Huyghens, Feb. 1691).

Despite the traditonal text-book opposition of rationalists to empiricists, it is interesting to note that Hume in the next century claimed that he had the same interest as Leibniz in formal demonstrations to empirical matters of probability.

"The celebrated Monsieur Leibnitz has observed it to be a defect in the common systems of logic, that they are very copious when they explain the operations of the understanding in the forming of demonstrations, but are too concise when they treat of probabilities, and those other measures of evidence on which life and action entirely depend, and which are our guides even in most of our philosophical speculations." (Hume's Abstract of a Treatise on Human Nature, p. 7).

There was, then, a significant oscillation in Leibniz's writings between his a priori system of irreducible real definitions and the experimental aspect of his program for the use of logic as an instrument of discovery and invention. The task of reconciling the two aspects of Leibniz's logical theory was not successfully met by Leibniz nor by his successor, the dogmatic rationalist Wolff. A much more important attempt to resolve this old problem of rationalism and empiricism was made by Kant. Kant was greatly influenced by Leibniz's Nouveaux Essais (which was not published until 1765) with its point by point criticisms of Locke's Essay Concerning the Human Understanding.

There are two parts to Leibniz's universal characteristic: one is the system of primitive characters that stand for the irreducible simple concepts, the alphabet of the universal script; the other is the calculus of reasoning (calculus ratiocinator) which contains the rules of reducing all composite ideas to the simple ones and of combining the simple characters into composite ones. The former supplies the ultimate premises of all the sciences; the latter, the rules for combining concepts and propositions. Thus Leibniz's universal characteristic was both a metaphysical system and an instrument of demonstration and invention. It was not a novelty to conceive of logic as both a part of philosophy and an instrument. Boethius in the sixth century argued for this dual function of logic, comparing it to the eye which is both a part of the body and an aid to its orientation.

Nor was it a novelty to conceive of a universal language as the basis for the unification of the sciences. Since Lully's and Kircher's efforts, Jungius, the teacher of Leibniz, and various British philosophers known to Leibniz (Dalgarno, Wilkins, Hobbes, and Locke), had worked at the problem of simplifying language and logic on an international plane. In Bishop Wilkins' Essay towards a Real Character and a Philosophical Language, printed for the Royal Society in London, 1668, the following advantages of a universal language are cited in the Epistle Dedicatory:

"More easy conversing with those of other nations . . . facilitating mutual commerce amongst the several nations of the world, and the improving of all natural knowledge; it would likewise very much conduce to the spreading of the knowledge of Religion . . . and contribute much to the clearing of some of our modern differences in Religion by unmasking many wild errors, that shelter themselves under the disguise of affected phrases; which being Philosophically unfolded, and rendered according to the genuine and natural importance of Words, will appear to be inconsistencies and contradictions. And several of these pretended, mysterious, profound notions, expressed in great swelling words, whereby some men set up for reputation, being this way examined, will appear to be, either nonsense, or very flat and jejune."

Leibniz approved of Locke's view, expressed in the last chapter of the Essay Concerning Human Understanding, that the study of Semiotics or the Doctrine of Signs "would afford us another sort of logic and critic than we have been hitherto acquainted with." But neither Locke nor his British compatriots had the mathematical training or skill to develop as Leibniz did the beginning of a symbolic logic through the generalization of algebraic and geometric reasoning.

Leibniz's aim was to find a common logical basis beyond the syllogism for algebraic, geometric, and theological reasonings. That he was not absolutely insistent that all science was completely reducible to an "alphabet of human thought" is intimated by such fragmentary notes of his as: "However, we must not imagine that we can always complete analysis to the first possibles, for that is not necessary for science." "Necessary" here can mean only "empirically possible," for it would take God's eternity to reveal the infinite number of absolute simples or compossibles.

It is not surprising therefore that the empiricist in Leibniz should have so frequently in his writings stressed the logical problem of estimating probabilities in matters of fact: "It is astonishing that the science of estimating probabilities is almost unknown, and that Logicians have not yet examined the degrees of probability or of likelihood that exist in conjectures or proofs . . . not in order to arrive at certainty, which is impossible, but in order to act as reasonably as possible on the facts and knowledge given us."

Thus, according to Leibniz, demonstrative certainty is impossible in matters of fact. He conceived the deductive procedure which yields certainty as consisting essentially in transforming one proposition into another by substituting in the former the definition of one or another of its terms. No deductive system was complete or rigorous until its premises (axioms or postulates) were reduced, as Pascal had insisted in De l'Esprit Geometrique, to the form of absolutely simple ideas by definitions. But Leibniz wished Pascal had offered a means of knowing when ideas were absolutely simple apart from conventional definition. Now, just as the prime numbers necessarily determine every composite number, so, Leibniz argued, the "real definitions" of terms would necessarily determine the axioms of any deductive system and vield theorems with a certainty relative to the definitions.

A "real definition" is the best kind of definition (definitio optimi generis) for it decomposes a term into its relatively "simple" constituent notions, e.g., "a parabola is the locus of points equidistant from a straight line and a point" is a real definition because the construction of the subject depends only on notions (point, line, equal distances) and operations known to be possible. A nominal definition, on the other hand, is merely a convenient abbreviation or convention about the use of terms, e.g., "ABC stands for a triangle." Only real definitions guarantee the possibility of things by means of a non-contradictory group of constituent concepts, e.g., "a square is an equilateral rectangle" has a real basis in the elements of equal sides and right angles which constitute the square.

The sciences for Leibniz are a group of real definitions together with all that can be deduced from them by means of the art of combinations. The two parts of the universal characteristic, viz., the inventory of real things and the rules for combining them, go to form a metaphysic and a logic. In practice, Leibniz realized, the number of simple constituent elements in any empirical object is so great that only God can identify them, that is, only God can reduce all empirical predications to simple identities.

Leibniz like Spinoza and Descartes adopted the traditional mode of theology and assumed there was an absolute set of simple ideas in God's mind through which all our knowledge is derived even though it is never complete:

"A primitive concept is one which is not resolvable into others so long as the object which it signifies possesses no other character but is known through itself (sed est index sui). Now such a concept can get its existence only from that which is known through itself; namely from the highest substance, that is, from God. All derivative concepts, however, which we can have, we can possess only through the mediation of these primitive concepts, so that nothing can exist in things without the doing of God, even though we are not allowed to know altogether distinctly in which ways the nature of things depends on God or the ideas of things on the idea of God, wherein ultimate analysis or adequate knowledge of all things through their causes originates."

Now nothing in this theological tradition is more important for the mind of man than to strive toward the knowledge of God. Hence the attempt to demonstrate all axioms by reducing them to absolute primitives or simples is one of the ambitious but dubious metaphysical aspects of Leibniz's logic, at least of one function of logic as Leibniz conceived it.

There is only one language for all the sciences because there is only one God whose ideas are the ultimate simples and whose language is the language of nature. The seventeenth-century book of nature is not as simple as the ancient book. Nature is infinitely complex, for "in every particle of the universe there is contained a world of infinite creatures." Consequently the number of primitive ideas or real definitions must be infinite:

"It is very important to conceive the number of primitive propositions as infinite, for they are either definitions or Axioms. The number of definitions as well as the number of terms is infinite. And so is the number of Axioms. I call an Axiom a proposition that is necessary and indemonstrable. Necessary applies to propositions whose opposite implies a contradiction. Now the only proposition whose opposite implies a contradiction is a formal identity. The latter is evident by itself, hence cannot be demonstrated; to demonstrate means to make evident by reason and Inconsequence. The senses show that 'A is A' is a proposition whose opposite 'A is not A' implies a contradiction. Now what the senses show is indemonstrable. Therefore, the true and indemonstrable Axioms are the identical propositions. . . . If these primitive propositions are infinite, the conclusions will also be so. . . . The primitive indefinables cannot be easily recognized by us, except as prime numbers are. These we have so far been unable to detect except by division by all the smaller numbers. Likewise, irresoluble terms would only be recognized negatively and provisionally. For I have a mark by means of which the resolubility of a term can be recognized. It is as follows: When we meet a proposition which appears to us necessary, and which is not demonstrated, it follows infallibly that there is in this proposition a definable term, provided that this proposition is necessary. Next, we must try to give its demonstration; and this cannot be done without finding the required definition. By this method of not allowing any axiom to pass without proof except the definitions and the identities, we shall come to the resolution of terms and to the simplest ideas." [L. Couturat, Opuscules et fragments inidits de Leibniz. pp. 186-7.]

The most interesting statement in the foregoing is the one that appeals to the senses as part of the proof of the irreducibility of the law of identity and of the reducibility of all other statements to identities. This made it possible to put propositions in the visible form of equations, and to work with propositions as one did algebra, so that in any discussion the reasonings of mem could be exhibited in the form of a calculus. An end would be put to clamorous controversy, claimed Leibniz,, if the disputants would merely stop shouting, take out pencil and paper, and say to each other, "Let us calculate."

Although the operations of algebra (sum, product, factoring) were generalized in Leibniz's logic, the traditional algebraic science of quantity became merely a sample (echantillon) of the more general science and its enlarged field of applications, beyond the traditional limitations of mathematics to size or quantity: "Thus the best advantages of algebra are only samples of the art of characters whose use is not limited to number or size."

La vraie logique, la methode d'universalite, was thus-able to embrace a general geometry (analysis situs) and all the other branches of pure and applied mathematics,, i.e., both necessary and probable reasoning. This theoretical consequence of a logic of contingent truths of fact (verites de fait) had for Leibniz its practical social correlate: "We need a new logic to know degrees of probability in matters of fact, . . . . law, . . . . business." Frequently, prior to this, Leibniz had compared his new logic of estimating probabilities with the methods of bookkeepers. "The general science is to the particular sciences what the science of accounting is to the merchant or banker." In other words, a scientist or philosopher with a faulty logic will be as confused as a business man who does not know how to keep his accounts in order. And the divine order of things will reveal itself only to the philosopher who applies the most exact method of universal logic to his ideas if they are to account adequately for the supreme order of creation.

Leibniz's exacting logic did not meet with any immediate success among either the scientific or metaphysical thinkers of his time. It was not until the middle of the nineteenth century that mathematical logic was applied to the extension of the syllogism and to the calculus of probability in any extensive way by Boole and De Morgan. Boole devoted also a chapter of his Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probability (1854) to refuting in Leibnizian fashion the metaphysics and theology of Spinoza's Ethics. The axiomatic foundations of arithmetic and algebra came even later in the works of Weierstrass, Dedekind, Peirce, Frege, Peano, Whitehead, and Russell. Only in the last generation have applications of symbolic logic to relay-switch circuits, punch-card systems, and calculating machines, and even to biological theory, been made by scientists. They do not seem aware that the immortal spirit of Leibniz is gazing with rewarding delight on their embodiment of his visions. The smile undoubtedly changes to a deep frown when that same spirit contemplates the dismissal of metaphysics by specialists who lack cosmic perspective.


Bertrand Russell in his Critical Exposition of the Philosophy of Leibniz maintains that "Leibniz's system does follow correctly and necessarily from five premises" which he enumerates as follows:

I. Every proposition has a subject and predicate.

II. A subject may have predicates which are qualities existing at various times. (Such a subject is called a substance.)

III. True propositions not asserting existence at particular times are necessary and analytic, but such as assert existence at particular times are contingent and synthetic. The latter depend on final causes.

IV. The Ego is a substance.

V, Perception yields knowledge of an external world, i.e., of existents other than myself and my states.

Russell then finds that the first premise is inconsistent with the fourth and fifth premises, and this constitutes for a him a general objection to Leibniz's monadism.

If we followed Russell's method of logical atomism, we could make short shrift of any system of metaphysics in the history of philosophy. Such analysis, indeed, is not merely an exercise of logic, but is also an invaluable aid for the critical study of the history of philosophy. It ought to produce humility in would-be metaphysicians who believe themselves free of all inconsistencies. Nevertheless, if we depended on that method exclusively, we should be missing the historical vision of Leibniz, his dynamic view of the universe and of man's place in it. We should be forgetting that the human mind is, as it I always has been, influenced by systems of thought which are never completely consistent, and we should thus fail to understand a good many of the pervasive and cumulative ideas that go into the evolution of our continually changing approach to scientific and moral problems. Though Leibniz is not a thoroughgoing experimentalist, his two uses of logic -- to analyze the theoretical foundations of all the sciences and to integrate our scientific knowledge with its human or civilized values -- stand out as the salient features of his rationalism.

Though Leibniz's system of microcosmic mirrors reflecting one another in various grades of energetic scintillation makes a pretty kaleidoscopic image, it is difficult to see how this optical analogy fits into Leibniz's other favorite analogy of the world as a pond teeming with living organisms. Such analogies, however, were illustrations of abstract principles which no thinker can ignore; for example, the interrelatedness and reciprocal causal action of bodies and of life processes as well as the evolutionary continuity of species of graded complexity and internal organization. Leibniz was so impressed with the details of internal structure, partly because of his logical sense of order and partly because of Leeuwenhoek's microscopic discoveries, that he tended to neglect the external factor of environmental interaction with organisms. His evolutionism and monadism are pre-formationist exactly because he regarded all processes and substances as governed by logical principles such as he found in mathematical series and the infinite terms generated by the law connecting them internally. The density of terms in such infinite series was generalized by Leibniz into a metaphysical principle of plenitude. Instead of atoms and empty spaces, swarms of monads fill the world in infinite abundance. One can also find mathematical analogies for Leibniz's hierarchy of monads. Now Professor Lovejoy has shown that the principles of continuity, plenitude, and gradation are the pervasive ideas that enter into the historic idea of "the great chain of being." Though this idea no longer enjoys the vogue it did for so many centuries of the history of thought, there are features of Leibniz's use of it which are still valuable to the modern philosopher, whenever he aims to frame a world-view within the bounds of what is scientifically intelligible and humanly valuable.

We may still appreciate Leibniz's suggestive discussions of the nature of individuals and of their spontaneous internal freedom, his analysis of processes, qualities and objective relations in the spatio-temporal order, his synoptic view of the great chain of being as a continuum of inter-related dynamic centers of energy, his worldly sense of the complexity and contingency of existence, his logical insight into the analytical character of the forms of thought, his epistemological distinctions of the degrees and kinds of knowledge, his psychological postulates of the integrative purposive action of the mind, its inseparability from bodily behavior, and the unconscious myriad of scarcely perceptible effects on the mind (petites perceptions), the possibility of organizing scientific research for peaceful purposes among thinkers in different fields and of different nationalities, and his toleration (without sparing logical criticism) of religious and ethical creeds as far apart as those of the Western and Oriental civilizations. In this summary recital of the high points of Leibniz's contributions to philosophy, we are ignoring for the time being the local and historical conditions in which Leibniz worked out his philosophical principles, though many of the defects in his philosophy may be explained by reference to his frequent concessions to the ruling political and ecclesiastical powers of his time, which we shall discuss later. To the extent that Leibniz formulated principles that are still philosophically important, we are justified in ignoring their immediate historical context.

Furthermore, we have seen that the roots of Leibniz's Weltanschauung are traceable to ideas which long antedate the seventeenth century. An important group of these ideas was developed in Leibniz's philosophy, as Arthur O. Lovejoy has so clearly demonstrated, to be the "most conspicuous, most determinative and most pervasive" conception of the Chain of Being among the great philosophic systems of the seventeenth century: "The essential characteristics of the universe are for him [Leibniz] plenitude, continuity, and linear gradation. The chain consists of the totality of monads, ranging in hierarchical sequence from God to the lowest grade of sentient life, no two alike, but each differing from those just below and just above it in the scale by the least possible difference. Since the metaphysics of Leibniz is a form of idealism, or more precisely, of panpsychism, the gradation is defined primarily in psychological rather than morphological terms; it is by the levels of consciousness which severally connect them, the degrees of adequacy and clarity with which they 'mirror' or 'represent' the rest of the universe, that the monads are differentiated. Nevertheless, the material world also, as a phenomenon bene fundatum, the mode in which these incorporeal entities necessarily manifest themselves to one another, has a derivative and somewhat equivocal, but essential, place in Leibniz's scheme of things; and he habitually employs without hesitation the ordinary language of physical realism, and discusses the problems of physical science as genuine, not as fictitious problems. And in the material world too the same three laws hold good; and they should be used by the investigator of I nature as guiding principles in his empirical researches." [Arthur O. Lovejoy, The Great Chain of Being: A Study of the History of an Idea. The William James Lectures delivered at Harvard University, 1933. Cambridge, Mass.: Harvard University Press, 1936, p. 144.]

This admirably succinct and authentic summary of Leibniz's metaphysics and theory of knowledge should be a valuable guide to the student as he reads through the selections of Parts II and III of this volume. It will be noticed that the principle of plenitude was used by Leibniz to refute the atomists' lifeless and mechanistic view of nature as a fortuitous concourse of particles in empty space. The plethora of real essences which crowd reality for Leibniz is marked by a dynamic propensity within each essence to come into existence in order to cooperate in producing the richest or the greatest possible diversity within the economy of nature's laws. These laws, we have already noticed, are eternal decrees of God who never wills any existence incompatible with his reason. Monads come into existence as "fulgurations" or sparks of the divine, falling within the rational limits of a pre-established harmony. They are spiritual rather than physical points, but aggregations of them make up dynamic bodies in space.

It is remarkable how Leibniz in this principle of the dynamic inclination of essences to realize harmoniously the maximum of existence, unites physical, aesthetic, logical, metaphysical and theological considerations. In any case, what follows from this principle of plenitude is the principle of sufficient reason. The office of this principle is to explain or make rational the essentially contingent nature of existing things, why they should exist rather than remain mere possibilities in the mind of God. It posits that whatever exists has a reason or purpose for existing, derived from the order of creation. The ambiguous use Leibniz makes of this principle of sufficient reason appears in his two-fold way of explaining contingent truths, sometimes referring to God's willing the good in accordance with reason, and sometimes to man's empirical inability to reduce matters of fact to purely logical identities. If theologians did not take to Leibniz's principle of the exigency in essences to exist and the corollary principles of plenitude and of sufficient reason, it was because (as Professor Lovejoy has pointed out) such a principle seemed dangerously close to the materialistic theory of the inherent sufficiency of matter to move itself and to be intelligible without invoking divine decree or assistance.

Leibniz, however, did use his principle of sufficient reason to supplement the principle of contradiction, realizing that empirical science could not proceed by logical analysis alone and had to admit contingency in our knowledge of things, too complex and diverse for any understanding other than God's. This complexity and diversity was subsumed under his principle of the identity of indiscernibles which postulates that no two individuals, for example, two oak leaves, can be exactly alike in all their properties. This is an a priori principle and has ambiguous import also. Logically, it may be used as a definition of identity: two things (or, in logic, two terms) are identical if everything predicable of one is also predicable of the other; in that case, they differ only in their name; and the other meaning is that in observable nature no two things differ only numerically, for there are and must be inherent, individual, qualitative differences. The Cartesians who made extension or space the essence of substance would then be wrong in distinguishing two bodies merely by their geometrical properties or position, for space is homogeneous everywhere, whereas physical bodies being aggregates of living centers of energy have a more qualitative, dynamic basis for differentiation.

One might, as John Herman Randall, Jr. has suggested, derive the whole of Leibniz's metaphysics from his life-long polemic against the Cartesians. Their view of the conservation of motion was attacked by Leibniz because it failed to take into account the internal, dynamic interplay of natural forces. It is certainly true that Leibniz introduced his metaphysical principles of sufficient reason and continuity in defending his own version of the conservation of energy in the collisions of bodies or in their gravitational energy. That all physical bodies are elastic, resist motion, and acquire or expend energy according to the square of their velocity, could only be explained by reference to the internal dynamic essence of each individual substance. The latter is only partly fathomable by the human mind, since the striving effort (conatus) inherent in each ultimate substance is known completely only to God. Whatever manifestations of these essences we observe and measure in physics conform to the continuity we find in our own memories, in motion resolved by mathematical functions, and in the processes of natural growth. Rest is not absolute, but a limiting case of motion.

Furthermore, we cannot, according to Leibniz, explain why some substances act more freely and more powerfully than others unless we introduce the infinite gradations of internal activity characteristic of different grades of monads. As Professor Lovejoy has indicated, when it comes to differentiating the monads, Leibniz shifts from physics to psychology: each monad is graded according to its powers of mental activity, the higher monad perceiving changes within itself more clearly, distinctly, or adequately than the lower ones, and in so doing, "mirrors" more of the objective relations of the entire universe of monads from its point of view. The ensemble of these points of view forms an order of co-existence, and space is nothing but the simultaneous perception of co-existing qualities, as time is nothing but the order of successively perceived qualities. The spaces and times of each monad will be relative to the point of view of each. But there still remains the absolute space and time belonging to the ensemble of all points of view which only God can perceive intuitively, and which would constitute for him the objective relational order of the real universe. Leibniz thus had two orders of space and time, one for man's relative knowledge and one for God.

This ambiguous theory of space and time resembles Berkeley's phenomenal view which also made space an order of co-existing qualities, and time the order of their succession. Yet, though both admit the reality of secondary qualities, Leibniz criticized young Berkeley for denying the physical existence of bodies in space and time: "The man in Ireland who impugns the reality of bodies seems neither to give adequate reasons nor to explain sufficiently what is in his mind. I suspect he is one of those people who seek to become famous bv their paradoxes." (Letter to Des Bosses, 1715).

The inherent effort of each essence to realize the maximum existence is the metaphysical basis for Leibniz's defense of a spontaneous freedom of will (made possible by divine grace) in the case of men's individual essences. The effective power of the will varies with the power of reason in each monad, though it is conditioned by an innumerable host of conflicting inclinations, unconscious perceptions, and unpredictable influences which act on the mind through the pre-established harmony in all things. This internal spontaneity does run afoul of Leibniz's cosmic determinism, but, at least, on the empirical side, it represents an attempt to do justice to the variety, complexity and contingency of human motivation.

The ultimate individuals (monads) of the universe are then active centers of energy containing all that they have been or will be within themselves. "Each monad is burdened by the past and pregnant with the future." The influence of the pre-formationist theory of biology is again very marked here, and again, is not consistent with Leibniz's notion of man's moral freedom. Also, so long as Leibniz explained his notion of an individual by comparing the latter to a place in a mathematical series or continuum, the substance or essential nature of each individual is determined rigorously by the formula of the series which fixes the internal relations of the individuals to one another. God, the king of monads, is not a monad, but the rule which generates the whole hierarchical series. Much of this is from Spinoza.

Leibniz's doctrine of internal relations compelled him logically to deny any external causal interactions among monads, thus paying a rather high premium for insuring their metaphysical individuality and moral privacy. Whatever changes they had to undergo were understood to be internal developments according to their pre-formed natures in the divinely pre-established harmony. The latter guarantees the perfect clock-like co-ordination of mind and body. That is what Leibniz meant when he wrote "the monads have no windows." They can only perceive with various degrees of discernment the changes which tick themselves off mentally in an order co-ordinated with their internal mechanism created by the perfect clock-maker, God.

There are hypothetically various possible alternatives in the varied detail of changes internal to the life of each monad, and an act of free will consists in choosing from among them. Each hypothetical possibility has strictly determined consequences, so that there is no absolute freedom to alter the metaphysically determined system of all compossibilities. Moral choice then rests on the hypothetical order of unrealized possibilities. This is true of man's voluntary actions and of God's choice of "the best of all possible worlds."

The problem of evil arises only because of the limitations of human understanding with respect to God's will whose providence is so often inscrutable. Like the scholastics Leibniz denies the metaphysical reality of evil as incompatible with the divine goodness of creation, and in his Theodicy, the only book published in his life-time, Leibniz prepared a long apologetic for the explanation of physical and moral evil. There are scarcely any new arguments here, and much use is made of the principle of sufficient reason even though man's knowledge is never sufficient to grasp the necessity for the existence of so much apparent evil. Leibniz also frequently indulges in the esthetic analogy of the apparent lack of harmony or beauty in the perception of an isolated piece of work of art, until the rest of it is brought into view. So we are reminded, with some empirical truth, that we often prematurely judge things evil until further consequences reveal a more just outcome to which the apparent evil was evidently a necessary prelude.

W. Somerset Maugham has expressed in a modern pragmatic way the Spinozistic-Leibnizian theory of free will. One of the characters in Of Human Bondage, Philip, says: "The illusion of free will is so strong in my mind that I can't get away from it, but I believe it is only an illusion. But it is an illusion which is one of the strongest motives of my actions. Before I do anything I feel that I have a choice, and that influences what I do; but afterwards, when the thing is done, I believe that it was inevitable from all eternity." -- "What do you deduce from that?" asked Hayward. -- "Why, merely the futility of regret. It's no good crying over spilt milk, because all the forces of the universe were bent on spilling it." [W. Somerset Maugham, Of Human Bondage (New York; Doubleday and Co., 1917), ch. 67.]


Leibniz repeatedly deplored the fact that men, including the most learned and scientific, so often bicker with one another, ridiculing others for holding opinions differing from their own, and refusing to make any compromises in their own views. "The human race, considered in its relation to the sciences which serve our welfare, seems to me comparable to a troop which marches in confusion in the darkness, without any word or other signs for the regulation of their march and the recognition of one another. Instead of joining hands to guide ourselves and make sure of the road, we run hither and yon and interfere with one another." But the reason for this perpetual competition among men lies in the self-assertiveness essential to each individual as a center of active force, which Leibniz himself had insisted on as the ground of all individual existence. It is true that he optimistically and on religious grounds assumed also that all monads fell into a pre-established harmony. If men would follow the right method and use the universal characteristic as a means of expression, all wrangling would cease. Harmony rests on empirical conditions.

The temper of Leibniz's philosophy is not as naively optimistic as Voltaire with his literary wit and acidulous irony made it out to be in Candide. In Leibniz's frequent exhortations to advance the use of a more rational method of inquiry and discussion in scientific, social, philosophical and religious matters, he obviously presupposes that "the best of all possible worlds" does not imply preserving the present discordant appearance of things and the irrational habits of men. His many essays on method imply making fuller empirical use of the active power of reason in order to pursue goals to the best of our ability and knowledge. Whether such a melioristic program for promoting the progress of mankind is compatible with Leibniz's metaphysical theory of a pre-established harmony is, of course, an embarrassing question. Sometimes Leibniz writes optimistically -- usually in order to obtain the support of a princely patron for some scientific or philosophical project -- and sometimes (perhaps, after being turned down or ignored) he writes dourly that his age is not yet ripe for his ideas. In the latter case, we must each be content with adding our mite of creative intelligence, though at other times Leibniz thought it would not require many minds like his own to bring about the millennium of Enlightenment under the benevolent patronage of a heroic prince or princess.

This oscillation of mood in Leibniz between optimism and pessimism concerning the possibility of a life of reason for man reflects the radical dualism running through Leibniz's life and philosophical writing. The optimism runs high in his metaphysical and theodicic theories of our knowledge of the dependence of all things on a divine order and the ultimate reducibility of all phenomena to logical identities expressing the nature of immortal substances (monads) endowed with different grades of active souls (according to their power to form clear, distinct, adequate and intuitive ideas). The pessimism appears in our inability to divine the universal harmony among the apparent physical, moral and metaphysical evils of existence, and in the fact that in three-fourths of our knowledge, as Leibniz put it, we have to be content with indistinct, symbolic, probable approximations to truth. Leibniz's optimism often rested on the Platonic idea of a permanent rational order of justice, truth and beauty lying behind the apparent evils, imperfect knowledge and discordance which marks the finite earthly life of man. This span of man's life is only a small transitory stage of the larger life of the immortal soul, as the life of the caterpillar is only a stage in the life of a butterfly. Such metaphors, borrowed from the biological discoveries in Leibniz's day by Swammerdam, Malpighi, Leeuwenhoek and others, were used by Leibniz as analogical arguments for the immortality of the soul and for the transience of life's ills.

For a philosopher who was so sure of the eternal nature of truth, goodness, justice, and many other Platonic ideas in the sciences of the mind, it is astonishing how many concessions Leibniz made to the temporal order of the semi-feudal princes and ecclesiastical officials of his day. He rarely criticized an established tradition or institution, and in fact warns against innovation in morals, politics or religion as socially disturbing. He thus subscribed to an almost literal interpretation of Christ's dictum: "Render unto Caesar what is Caesar's, and unto God what is God's." His whole philosophy teems with many dualities in addition to and yet in a sense paralleling this one of the temporal and the spiritual: the kingdoms of nature and of grace, the contingent truths of fact and the necessary truths of reason, the mechanical order of efficient causes and the teleological order of final causes, the empirical and the rational elements in knowledge.

But there is no doubt that Leibniz sought by means of his persistent vision of a universal harmony to reconcile logically incompatible elements in the classical, scholastic traditions and in the mathematical, experimental methods of the new or rapidly growing sciences of the seventeenth century to which he himself made such important contributions. The latter were largely a result of his sojourn in Paris among the brilliant mathematical scientists gathered there, though Leibniz, it should be recalled, came to Paris on a diplomatic mission. He had come as an envoy of the German princes to see Louis XIV and persuade him to divert his armies from war-devastated Germany to Egypt. Leibniz did not succeed in either meeting the Roi Soleil or changing the military ambitions of Mars Christianissimus, as Leibniz, smarting with disappointment, bitterly called the prince whom he had at first hailed as the Great Monarch of the age. "In fact to wish to subjugate by arms the civilized nations of Europe who are for the most part also the defenders and lovers of liberty, is not only impious but mad." But Louis XIV's armies proceeded to invade Holland, and Europe was at war until 1714. The German princes on the Rhineland, who were allowed by the Treaty of Westphalia (1648) to make separate treaties, were subsidized by Louis XIV, and thought they could play a double game of catering to France and intriguing for their own interests. Leibniz at first defended his friend and patron, Baron Boineburg, by agreeing with him that it was dangerous to have France for an enemy on the shores of the Rhine. But after Louis XIV's invasion of Holland, Leibniz attacked the French king for ignoring natural law, the law of all peoples (jus gentium), and the very idea of Christianity. He denounced Louis XIV for allying himself with the Turks against Christians and thus violating his vow as a Christian ruler to serve as the vicar of God.

Leibniz's interest in law and government was not confined to academic jurisprudence and its logic, though these were his early interests. He defined the universality of natural law not only in an abstract way but in political pamphlets, attacking the "inexcusable peace of Utrecht" of 1713, and defending the idea of the Holy Roman Empire for preserving on a temporal basis the universal order of peace and law against the aggressive, imperialistic policies of Louis XIV toward Austria, Spain, Holland and England. In Vienna, Leibniz even proposed a mass uprising against France, even as Richelieu had once had Louis XIII order a call to arms against Spain, -- a forgotten fact which Leibniz had brought to light by exhuming the ordinances from the archives during his stay in Paris. But Leibniz was not advocating internal revolution: "As to that large question of the power of sovereigns and the obedience due them by people," he wrote to his friend Boineburg in 1695, "I am wont to say that it would be good for princes to be convinced that people have a right to resist them, and that, on the other hand, people be persuaded to passive obedience. However, I share enough of Grotius' opinions to believe that people ought as a rule to obey, the harm resulting from revolution being incomparably greater than what provokes it." This is a very utilitarian attitude quite separable logically from Leibniz's theodicic view that this is "the best of all possible worlds."

Leibniz aimed to form a single Christian body of European states so that as a result the whole of Europe might cease conspiring against itself. That is why he approved of l'Abbe de Saint-Pierre's project for perpetual peace in Europe on the basis of a sort of holy alliance among the rulers of Europe who would perpetuate peace bv co-operative organization of the arts and sciences. Though he disagreed with that part of the plan which would abolish the Holy Roman Empire and give the Emperor only one vote, Leibniz said: "On the whole it is feasible, and its realization would be one of the most useful things in the world."

There is no explicit political philosophy in Leibniz though he was more politically active than any philosopher ever had been in Europe. The favor he enjoyed among the princes and princesses, church dignitaries and learned men of Europe made him a desirable ally in the religious and national competition of his age. He was offered a position as Chief Librarian of the Vatican, but preferred to keep on friendly terms with both Catholic and Protestant theologians and found it diplomatic not to take sides. This does not seem to be in Leibniz merely a matter of personal expediency, for he had a genuine love of peace and was imbued with the spirit of reconciliation, hoping to reunite the churches and join the cultures of West and East by interchange of ideas and goods with distant China. He was intensely interested, on behalf of Protestant missionary work in China, in the dispute in Rome concerning the modifications of the ritual for conversion proposed by some Catholic missionaries in China. Their purpose was to adapt the sacramental rites to Confucianism which was a state-religion and closely identified with civil service requirements.

There has been recently a growing interest in the intellectual history of China and its relations to Western civilization as the two cultures come into closer communication with each other, as Leibniz anticipated. Here the difficulties of language are very great for Western students, and the need of a universal medium of expression of ideas, such as Leibniz contemplated, is indeed of paramount practical importance. Meanwhile we must draw upon an expert sinologist like Professor Donald Lach who has made a study of "Leibniz and China" in a recent article:

"The influence of Leibniz upon his contemporaries and upon his successors was just as important in the field of Chinese studies as it was in general philosophy and mathematics. Of special significance was the stimulus which his thought gave to men of religion who were interested in opening China as a new field for Protestant missionaries. . . . Leibniz was the only major philosopher of the period to hold that the Chinese possessed a spiritualistic doctrine compatible in some of its aspects with Christianity . . . Leibniz studied Chinese life and institutions, not for themselves alone, but in an effort to corroborate with facts his theory of universal culture. Chinese political and social administration he believed to be far superior to the rule of favorites and the balance-of-power politics common to the monarchies of Europe. . . . It was in this connection that Leibniz felt Europe might learn something of moral philosophy from China. According to Leibniz, China should profit from the revealed theology of Europe as exemplified in the Christian tradition. Chinese philosophy he considered not a foreign system of thought, but simply an alien counterpart of his own monadology and the Christian religion. In his analysis of I Ching's trigrams, he was not only looking for another mathematical device; he hoped also to reveal that the ancient Chinese were a logical and intelligent people. For a time, at least, he considered the Chinese language as a possibility in his search for a universal philosophic language. Moreover, in his consideration of historical subjects Leibniz recognized the necessity of studying Chinese history if the development of mankind is to be adequately co-ordinated and understood. In his great scheme of universal civilization, the philosopher pictured China and Europe, geographical opposites, as intellectual allies. Ideas and philosophies, as well as mechanical contrivances, were to serve as connecting links in the chain which Leibniz visualized and which men had hitherto -- and have even yet -- to forge." [Donald Lach, "Leibniz, and China," Journal of the History of Ideas (1945), pp. 453 f.]

The whole last volume of Foucher de Careil's seven-volume edition of Leibniz's historical, religious and political works is devoted to Leibniz's projects and correspondence on the founding of scientific Academies in Berlin, Vienna, Amsterdam, and finally in Moscow. As his letter to Peter the Great shows, Leibniz in the last year of his remarkable scientific and worldly career, sought to extend the cultivation of science and learning to the vast reaches and primitive life of Russia, and then by way of this vast geographical link to connect the culture of Europe to that of China. Even in this last of his grand schemes, the old duality appears in the form of Leibniz's arguments for the advancement of the sciences including the systematic study of the languages of the peoples of Russia for the purpose of translating the Bible and doing missionary work among them.

Leibniz would have made an ideal Director for an international organization like Unesco whose program in many ways embodies his cosmopolitan ideas, far-sighted spirit of collaboration and co-operation for a more enlightened, peaceful, and morally progressive world civilization. Whether Leibniz was too optimistic about world harmony is no longer a question for academic dispute or literary wit, but one on which the very survival of civilization depends.