De arte characteristica ad perficiendas scientias ratione nitentes Let Us Calculate: On the Art of Characters Gottfried Wilhelm Leibniz (1646–1716) c. 1688; printed 1890 Cold Library · Open Stacks · S-007212 · https://coldlibrary.com/s/007212 Rights: Leibniz died in 1716; the Latin text was printed in 1890 by C. I. Gerhardt, who died in 1899. Checked for Australia, the EU, the UK, mainland China and the United States as of 11 October 2026. Guidance, not legal advice. Source: Internet Archive, Die philosophischen Schriften von G. W. Leibniz, ed. C. I. Gerhardt, vol. 7 (1890), https://archive.org/details/11172348bsb (retrieved 2026-10-11) English translation: Claude (an AI), 2026 · CC0 1.0 Generated 2026-10-14 from https://coldlibrary.com/en/open-stacks/leibniz-let-us-calculate ---- Omnia quae certo cognoscimus, vel demonstrationibus vel experimentis constant. Et in utroque dominatur ratio. Nam ipsa ars instituendi experimenta iisque utendi certis rationibus nititur, quatenus scilicet a casu sive fortuna non pendet. Missis nunc experimentis, quippe quae sumtibus et apparatu et tempore indigent, quin et fortuna adjuvantur, dicamus tantum de perficiendis scientiis quatenus ratione nituntur. Progressus Artis inventoriae rationalis pro magna parte pendet a perfectione artis characteristicae. Causa, cur non nisi in solis numeris et lineis, et rebus quae his repraesentantur, demonstrationes quaeri ab hominibus soleant, nulla alia est, quam quod characteres tractabiles notionibus respondentes extra numeros non habentur. Quae causa est etiam, cur ne Geometria quidem hactenus analytice tractata sit, nisi quatenus ad numeros revocatur per analysin speciosam, in qua numeri generales literis designantur. Datur tamen alia analysis geometriae sublimior per proprios characteres, qua multa pulchrius breviusque quam per Algebram praestantur, cujus et specimina habeo. Et dari demonstrationes etiam extra magnitudines, vel Logicorum formae documento esse possunt, quin et ICti in Digestis quaedam exhibent vere demonstrata, cujus rei specimina produxi dissertatione de Conditionibus, et Joh. Suisset, dictus Calculator, aliique post ipsum, etiam in Metaphysicis, dedere demonstrationes de gradibus intensionibusque formarum; et quaedam a Platonicis et Aristotelicis dicuntur, quae non difficulter demonstrationis forma indui possunt. Si daretur vel lingua quaedam exacta (qualem quidam Adamicam vocant) vel saltem genus scripturae vere philosophicae, qua notiones revocarentur ad Alphabetum quoddam cogitationum humanarum, omnia quae ex datis ratione assequi, inveniri possent quodam genere calculi, perinde ac resolvuntur problemata arithmetica aut geometrica. Atque ea vera foret sive Cabbala vocabulorum mysticorum, sive Arithmetica numerorum Pythagoricorum, sive Characteristica Magorum hoc est Sapientum. Rei tantae suspicionem aliquam hausi paene adhuc puer, et qualemcunque descriptionem obiter inserui libello ab adolescente olim edito de arte Combinatoria. Possibile esse, imo facile et intra aliquot annos ab aliquot intelligentibus conspirantibusque pro suo primo gradu absolvendum, geometrica sane certitudine possum demonstrare. * * * Sed ut redeam ad expressionem cogitationum per characteres, ita sentio nunquam controversias finiri neque sectis silentium imponi posse, nisi a ratiocinationibus complicatis ad calculos simplices, a vocabulis vagae incertaeque significationis ad characteres determinatos revocemur. Id scilicet efficiendum est, ut omnis paralogismus nihil aliud sit quam error calculi, et ut sophisma, in hoc novae scripturae genere expressum, revera nihil aliud sit quam soloecismus vel barbarismus, ex ipsis grammatices hujus philosophicae legibus facile revincendus. Quo facto, quando orientur controversiae, non magis disputatione opus erit inter duos philosophos, quam inter duos Computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo (accito si placet amico) dicere: calculemus. Ne quis autem a me impossibilia jactari aut sperari putet, sciendum est, hac arte ea tantum (convenienti studio adhibito) posse obtineri, quaecunque ex datis quantocunque ingenio possint elici, sive quae ex datis sunt determinata, prorsus ut in problematibus Geometriae; quae vere facti sunt, et a fortuna vel casu pendent, eatenus ad artem inveniendi non pertinere manifestum est. Et ne quis porro post hanc limitationem existimet, exigui igitur usus hanc artem fore in illis omnibus, ubi opus est conjecturis, ut in indagationibus historiarum civilium vel naturalium, in arte examinandi corpora naturalia vel personas intelligentes, adeoque in vita communi, in medicina, jure, militaribus et reipublicae gubernatione — sciendum est: quantum in illis omnibus valet ratio (valet autem plurimum), tantum et multo magis posse hanc artem, quae nihil aliud est, quam summa quaedam exaltatio, et compendiosissimus per symbola notasve usus humanae rationis. Itaque, quando ex datis quaesitum non est determinatum aut exprimibile, tunc alterutrum hac analysi praestabimus, ut vel in infinitum appropinquemus, vel, quando conjecturis agendum est, demonstrativa saltem ratione determinemus ipsum gradum probabilitatis, qui ex datis haberi potest, sciamusque quomodo datae circumstantiae in rationes referri debeant, et quasi in bilancem, acceptis expensisque similem, redigi queant, ut quod maxime rationi consentaneum sit eligamus. In quo etsi fallamur aliquando, ut is qui perfectissime etiam mistos rationi aleae ludos novit, agemus tamen quicquid ratio jubet, et plerumque optatum consequemur, quemadmodum boni lusores fortunaeque ipsius fabri, quos ut proverbio dicitur, pilae talique quaerunt. Et hoc ipsum judicabimus quod non tantum verisimilius sed et tutius sit, et quatenus conveniat spem pretio emere periculove. Quibus sane nihil majus ab humana ratione postulari potest. Itaque inter caetera molior ego Logicae partem quandam, hactenus prope intactam, de aestimandis gradibus probabilitatis et statera probationum, praesumtionum, conjecturarum, indiciorum. Possum etiam ostendere, quomodo non minus in calculo generali quam in calculo numerico examina sive indicia veritatis excogitari possint abjectioni novenariae talibusque aliis similibus respondentia, prorsus quemadmodum abjectio haec per me a numeris communibus ad Algebram translata est. * * * Et ut finiam, si inventio Telescopiorum et Microscopiorum tantum cognitioni naturae lucis attulit, facile intelligi potest, quantum praestare debeat novum hoc organon, quo ipse mentis oculus, quantum in humana potestate est, instruetur. Equidem temerarium foret promittere a primis aggressionibus postremam tantae artis perfectionem, quae crescet cum ipsa hominum experientia, prout (ipsa hac arte manuducente) plura semper et potiora Data eruentur. Quemadmodum tamen apud Sinenses ferunt, qui aliquot characterum millena norit, eum potissima scribere posse, caeteris magis reconditis vel cuique proprio artifici vel majori Magistro servatis, ita hic quoque, proportione progressuum sive hominis cujusque sive totius generis humani, fructus quoque artis unius major sentietur. Interim hoc consequemur, ut semper certa serie progredi valeamus quantum in potestate est, et quod hactenus minime factum est, ex datis quicquid fieri potest elicientes, thesauris jam repertis ac divinis beneficiis ad sanitatem corporis ac perfectionem mentis utamur et fruamur, quantum fas est. ---- English translation by Claude (an AI) Everything that we know with certainty rests either on demonstrations or on experiments. And in both, reason rules. For the very art of setting up experiments and of using them rests on definite reasons, so far, that is, as it does not depend on chance or fortune. Leaving experiments aside for now, since they need expense and equipment and time, and are helped along by fortune as well, let us speak only of perfecting the sciences in so far as they rest on reason. The progress of the rational art of discovery depends in great part on the perfection of the art of characters. The reason why people usually look for demonstrations only in numbers and lines, and in the things that these represent, is none other than this: outside numbers, we have no manageable characters corresponding to notions. That is also why not even geometry has so far been treated analytically, except in so far as it is brought back to numbers by the specious analysis, in which general numbers are designated by letters. There is, however, another and higher analysis of geometry by means of its own characters, by which many things are done more elegantly and more briefly than by algebra, and of which I have specimens. And that there are demonstrations outside magnitudes as well, the forms of the logicians can serve as proof; indeed the jurists in the Digest set out some things that are truly demonstrated, of which I gave specimens in my dissertation on Conditions; and John Suisset, called the Calculator, and others after him, gave demonstrations even in metaphysics about the degrees and intensities of forms; and some things said by the Platonists and Aristotelians can without difficulty be put into the form of a demonstration. If there were some exact language (such as some call the Adamic), or at least a kind of truly philosophical writing, by which notions were brought back to a kind of alphabet of human thoughts, then everything that reason can reach from what is given could be found by a kind of calculation, just as arithmetical or geometrical problems are solved. And that would be the true Cabbala of mystical words, or Arithmetic of Pythagorean numbers, or Characteristic of the Magi, that is, of the wise. I caught some suspicion of so great a thing when I was still almost a boy, and put in passing some description of it, such as it was, into a little book I published long ago as a young man, On the Combinatorial Art. That it is possible, indeed easy, and that its first stage could be completed within a few years by a few intelligent people working together, I can demonstrate with geometrical certainty. * * * But to return to the expression of thoughts by characters: I think that controversies will never be ended, nor silence imposed on the sects, unless we are brought back from complicated reasonings to simple calculations, and from words of vague and uncertain meaning to determinate characters. That is, it must be brought about that every fallacy is nothing but an error of calculation, and that a sophism, once expressed in this new kind of writing, is in truth nothing but a solecism or a barbarism, easily refuted by the very laws of this philosophical grammar. Once this is done, when controversies arise, there will be no more need for disputation between two philosophers than between two accountants. It will be enough for them to take their pens in hand, sit down at their counting boards, and say to one another (calling in a friend, if they like): let us calculate. But lest anyone think that I am boasting of impossible things, or hoping for them, it should be understood that by this art only those things can be obtained (with suitable study applied) that could be drawn from the data by any intelligence, however great, that is, those that are determined by the data, exactly as in the problems of geometry; things that are truly matters of fact, and depend on fortune or chance, plainly do not belong to that extent to the art of discovery. And lest anyone further think, after this limitation, that the art will then be of little use in all those matters where conjectures are needed, as in inquiries into civil or natural history, in the art of examining natural bodies or intelligent persons, and so in ordinary life, in medicine, law, military affairs and the government of the state, it should be understood that as much as reason avails in all these things (and it avails very much), so much and far more can this art, which is nothing but a kind of supreme elevation of human reason, and its most compendious use by means of symbols or signs. So when what is sought is not determined by the data, or cannot be expressed, we shall achieve one of two things by this analysis: either we shall come ever closer to it without end, or, when we must act on conjectures, we shall at least determine by demonstrative reasoning the very degree of probability that can be had from the data, and know how the given circumstances are to be entered in the accounts and brought, as it were, to a balance like that of receipts and expenses, so that we may choose what is most consistent with reason. In this, even if we are sometimes mistaken, as is someone who knows perfectly well even the games in which chance is mixed with reason, we shall still do whatever reason commands, and for the most part we shall get what we hoped for, like good players, who make their own fortune and whom, as the proverb says, the ball and the dice come looking for. And we shall judge this very point too: what is not only more probable but also safer, and how far it is wise to buy a hope at some cost or risk. Nothing greater, surely, can be asked of human reason. And so, among other things, I am at work on a part of logic so far almost untouched, on estimating degrees of probability, and on a balance for proofs, presumptions, conjectures and indications. I can also show how, in the general calculus no less than in numerical calculation, checks or tests of truth can be devised that correspond to casting out nines and to other methods like it, just as I have myself carried this casting out over from ordinary numbers to algebra. * * * And to finish: if the invention of telescopes and microscopes has brought so much light to the knowledge of nature, it is easy to understand how much this new organon must achieve, with which the very eye of the mind will be equipped, as far as is in human power. It would indeed be rash to promise from the first attempts the final perfection of so great an art, which will grow with human experience itself, as (with this very art leading the way) more and more important data are brought to light. But just as they say among the Chinese that whoever knows some thousands of characters can write the most important things, the rest, which are more recondite, being kept for each particular craftsman or for a greater master, so here too the fruit of this one art will be felt the more, in proportion to the progress made, whether by each person or by the whole human race. Meanwhile we shall achieve this: that we can always advance in a sure order, as far as is in our power, and, what has so far hardly been done at all, draw from the data whatever can be drawn, and so use and enjoy the treasures already found and the gifts of God for the health of the body and the perfection of the mind, as far as is right.