De arte characteristica ad perficiendas scientias ratione nitentes

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.