On the General Characteristic

by Gottfried Wilhelm Leibniz

There is an old saying that God created everything according to weight, measure, and number. But there are things which cannot be weighed, those namely which have no force or power. There are also things which have no parts and hence admit of no measure. But there is nothing which is not subordinate to number. Number is thus a basic metaphysical figure, as it were, and arithmetic is a kind of statics of the universe by which the powers of things are discovered.

Men have been convinced ever since Pythagoras that the deepest mysteries lie concealed in numbers. It is possible that Pythagoras brought over this opinion, like many others, from the Orient to Greece. But, because the true key to the mystery was unknown, more inquisitive minds fell into futilities and superstitions, from which there finally arose a kind of popular Cabbala, far removed from the true one, and that multitude of follies which is falsely called a kind of magic and with which books have been filled. Meanwhile there remained deep‑rooted in men the propensity to believe that marvels can be discovered by means of numbers, characters, and a certain new language, which some called the Adamic language; Jacob Böhme called it the Natursprache.

But perhaps no mortal has yet seen into the true basis upon which everything can be assigned its characteristic number. For the most scholarly men have admitted that they did not understand what I said when I incidentally mentioned something of the sort to them. And although learned men have long since thought of some kind of language or universal characteristic by which all concepts and things can be put into beautiful order, and with whose help different nations might communicate their thoughts and each read in his own language what another has written in his, yet no one has attempted a language or characteristic which includes at once both the arts of discovery and of judgment, that is, one whose signs or characters serve the same purpose that arithmetical signs serve for numbers, and algebraic signs for quantities taken abstractly. Yet it does seem that since God has bestowed these two sciences on mankind, he has sought to notify us that a far greater secret lies hidden in our understanding, of which these are but the shadows.

Some unknown fate has brought it about, however, that when I was a mere boy I became involved in these considerations, and as first inclinations usually do, they have remained strongly fixed in my mind ever since. Two things which are otherwise of doubtful merit and are harmful to many people, proved wonderfully useful to me: first, I was self‑taught, and second, I looked for something new in every science when I first studied it, often before I even understood its already established content. But so I gained a double reward: first, I did not fill my head with empty and cumbersome teachings accepted on the authority of the teacher instead of sound arguments; second, I did not rest until I had traced back the tissues and roots of every teaching and had penetrated to its principles. By such training I was enabled to discover by my own effort everything with which I was concerned.

When I turned, therefore, from the reading of history, which had delighted me from my earliest youth, and from the cultivation of style, which I carried out with such ease both in prose and in more restricted forms that my teachers feared that I might remain stuck in such frivolities, and took up logic and philosophy and had barely begun to understand something about these fields, what a multitude of fancies came to birth in my brain and were scratched down on paper to be laid before my astonished teachers. Among other things I once raised a doubt concerning the categories. I said that just as we have categories or classes of simple concepts, we ought also to have a new class of categories in which propositions or complex terms themselves may be arranged in their natural order. For I had not even dreamed of demonstrations at that time and did not know that the geometricians do exactly what I was seeking when they arrange propositions in an order such that one is demonstrated from the other. My question was thus superfluous, but when my teachers failed to answer it, I pursued these ideas for the sake of their novelty, attempting to establish such categories for complex terms or propositions. Upon making the effort to study this more intently, I necessarily arrived at this remarkable thought, namely that a kind of alphabet of human thoughts can be worked out and that everything can be discovered and judged by a comparison of the letters of this alphabet and an analysis of the words made from them. This discovery gave me great joy though it was childish of course, for I had not grasped the true importance of the matter. But later, the more progress I made in my thinking about these things, the more confirmed I was in my decision to carry the problem further. It happened that as a young man of twenty I had to prepare an academic treatise. So I wrote a Dissertation on the Art of Combinations, which was published in book form in 1666, and in which I laid my remarkable discovery before the public. This dissertation was in fact such as might be written by a youth just out of the schools who was not yet conversant with the real sciences. For mathematics was not cultivated in those parts; if I had spent my childhood in Paris, as did Pascal, I might have advanced these sciences earlier. There are two reasons, however, why I do not regret having written this dissertation; first, it pleased many very gifted men greatly; and second, in this dissertation I already then served notice to the public of my invention, so that it will not look as if I had thought of it only recently.

Why, within the memory of mankind as preserved by records, no mortal has ever essayed so great a thing—this has often been an object of wonder to me. For to anyone who proceeds according to an order in thinking, these considerations should have occurred from the very first, just as they occurred to me as a boy interested in logic, before I had even touched on ethics, mathematics, or physics, solely because I always looked for first principles. The true reason for this straying from the portal of knowledge is, I believe, that principles usually seem dry and not very attractive and are therefore dismissed with a mere taste. Yet I am most surprised at the failure of three men to undertake so important a thing—Aristotle, Joachim Jung, and René Descartes. For when Aristotle wrote the Organon and the Metaphysics he laid open the inner nature of concepts with great skill. Joachim Jung of Lübeck is a man not well known even in Germany but of such rare judgment and breadth of mind that I cannot think of anyone, not even excepting Descartes himself, from whom a great revival of science might better have been expected, if only he had been known and supported. He was already an old man, however, when Descartes began his activity, and it is regrettable that these men could not have known each other. As for Descartes, this is of course not the place to praise a man the magnitude of whose genius is elevated almost above all praise. He certainly began the true and right way through the ideas, and that which leads so far; but since he had aimed at his own excessive applause, he seems to have broken off the thread of his investigation and to have been content with metaphysical meditations and geometrical studies by which he could draw attention to himself. For the rest, he set out to discover the nature of bodies for the purposes of medicine, rightly indeed, if he had completed the task of ordering the ideas of the mind, for a greater light than can well be imagined would have arisen from these very experiments. His failure to apply his mind to this problem can be explained by no other cause than that he did not adequately think through the full reason and force of the thing. For had he seen a method of setting up a reasonable philosophy with the same unanswerable clarity as arithmetic, he would hardly have used any way other than this to establish a sect of followers, a thing which he so earnestly wanted. For by applying this method of philosophizing, a school would from its very beginning, and by the very nature of things, assert its supremacy in the realm of reason in a geometrical manner and could never perish nor be shaken until the sciences themselves die through the rise of a new barbarism among mankind.

As for me, I kept at this line of thought, in spite of the distraction of so many other fields, for no other reason than that I saw its entire magnitude and detected a remarkably easy way of following it through. For this is what I finally discovered after most intent thought. Nothing more is necessary to establish the characteristic which I am attempting, at least to a point sufficient to build the grammar of this wonderful language and a dictionary for the most frequent cases, or what amounts to the same thing, nothing more is necessary to set up the characteristic numbers for all ideas than to develop a philosophical and mathematical 'course of studies', as it is called, based on a certain new method which I can set forth, and containing nothing more difficult than other courses of study, or more remote from use and understanding, or more alien to the usual way of writing. Nor would it require more work than is already being spent on a number of courses, or encyclopedias, as they are called. I think that a few selected men could finish the matter in five years. It would take them only two, however, to work out by an infallible calculus the doctrines most useful for life, that is, those of morality and metaphysics.

Once the characteristic numbers for most concepts have been set up, however, the human race will have a new kind of instrument which will increase the power of the mind much more than optical lenses strengthen the eyes and which will be as far superior to microscopes or telescopes as reason is superior to sight. The magnetic needle has brought no more help to sailors than this lodestar will bring to those who navigate the sea of experiments. What other consequences will eventually follow from it must be left to the decree of the fates; however, they cannot be the great and good. For men can be debased by all other gifts; only right reason can be nothing but wholesome. But reason will be right beyond all doubt only when it is everywhere as clear and certain as only arithmetic has been until now. Then there will be an end to that burdensome raising of objections by which one person now usually plagues another and which turns so many away from the desire to reason. When one person argues, namely, his opponent, instead of examining his argument, answers generally, thus, 'How do you know that your reason is any truer than mine? What criterion of truth have you?' And if the first person persists in his argument, his hearers lack the patience to examine it. For usually many other problems have to be investigated first, and this would be the work of several weeks, following the laws of thought accepted until now. And so after much agitation, the emotions usually win out instead of reason, and we end the controversy by cutting the Gordian knot rather than untying it. This happens especially in deliberations pertaining to life, where a decision must be made; here it is given to few people to weigh the factors of expediency and inexpediency, which are often numerous on both sides, as in a balance. The more strongly we are able to present to ourselves, now one circumstance and now another, in order to balance the varying inclinations of our own minds, and the more eloquently and effectively we can adorn and point them out for others, the more firmly we shall act and carry the minds of other men with us, especially if we make wise use of their emotions. There is hardly anyone who could work out the entire table of pros and cons in any deliberation, that is, who could not only enumerate the expedient and inexpedient aspects but also weigh them rightly. Thus two disputants seem to me almost like two merchants who are in debt to each other for various items, but who are never willing to strike a balance; instead, each one advances his own various claims against the other, exaggerating the truth and magnitude of certain particular items. Their quarrel will never end on this basis. And we need not be surprised that this is what has happened until now in most controversies in which the matter is not clear, that is, is not reduced to numbers.

Now, however, our characteristic will reduce the whole to numbers, so that reasons can also be weighed, as if by a kind of statics. For probabilities, too, will be treated in this calculation and demonstration, since one can always estimate which of the given circumstances will more probably occur. Finally, anyone who is certainly convinced of the truth of religion and its consequences, and so embraces others in love that he desires the conversion of mankind, will surely admit, if he understands these matters, that nothing will be more influential than this discovery for the propagation of the faith, unless it be miracles, the holiness of an apostle, or the victories of a great monarch. Where this language can once be introduced by missionaries, the true religion, which is in complete agreement with reason, will be established, and apostasy will no more be feared in the future than would an apostasy of men from the arithmetic or geometry which they have once learned. So I repeat what I have often said: that no man who is not a prophet or a prince can ever undertake anything of greater good to mankind or more fitting for the divine glory.

But we must go further than words! Since the admirable connection of things makes it most difficult to give the characteristic numbers of a few things separated from others, I have thought of an elegant device, if I am not mistaken, by which to show that ratiocination can be proved through numbers. Thus I imagine that these most remarkable characteristic numbers are already given, and, having observed a certain general property to be true of them, I set up such numbers as are somehow consistent with this property, and applying these, I at once demonstrate through numbers, in wonderful order, all the rules of logic and show how we can know whether certain arguments are in good form. But the material soundness or truth of an argument can be judged without much mental effort and danger of error only when we have the true characteristic numbers of things themselves.

SOURCE: Leibniz, Gottfried Wilhelm. “On the General Characteristic” (circa 1679), Philosophical Papers and Letters, selection translated and edited with an introduction by Leroy E. Loemker, 2^nd ed. (Dordrecht, Holland; Boston: D. Reidel Pub. Co., 1976 [1969, 1^st ed. 1956]), pp. 221-225. (Synthese Historical Library; v. 2)

This is part I of this selection. Footnotes are omitted here, as well as the introductory paragraph. Part II + references: pp. 225-228. This selection can be considered to belong to the introductory section of Leibniz’ planned work Plus ultra, with the sectional title ‘Initia et specimina scientiae generalis’. The German original given for this selection is Philosophische Schriften, ed. C. I. Gerhardt, 7 vols., VII, 184-89.

This volume may still be the most comprehensive selection (xii, 736 pp.) of Leibniz’ papers in English. Other relevant selections are listed below.

Dissertation on the Art of Combinations (1666), pp. 73-84. With alleged applications in every field. Note reference to Lully's Ars Magna, with diagram (p. 83).

On Universal Synthesis and Analysis, Or the Art of Discovery and Judgment (1679?), pp. 229-234. Probably belongs to Plus Ultra.

Two Studies in the Logical Calculus (1679), pp. 235-247.

Studies in a Geometry of Situation with a Letter to Christian Huygens (1679), pp. 248-258. On the application of a general characteristic to geometry, analysis situs, et al.

A Study in the Logical Calculus (early 1690s), pp. 371- 382.