In this preface to “General Science”, Leibniz argues that science is necessary for true happiness as it provides assurance about the future based on knowledge of God and the soul. He also argues that the true method for science is unknown and only exists in mathematics, but it is still imperfect. Leibniz believes that finding characters or signs suitable for expressing all our thoughts would be the solution to the problem. This language would be difficult to create but easy to learn, and it would serve as an instrument of reason. Leibniz considers this project to be the last effort of the human mind and believes that it would depend only on men to be happy once completed.
Félix Alcan, Paris, 1903 — Phil., VI, 11, a (3 p. in-folio.)1
Since happiness consists in contentment, and lasting contentment depends on the assurance we have of the future, founded on the knowledge we must have of the nature of God and the soul; it follows that science is necessary for true happiness.
But science depends on demonstration, and the invention of demonstrations requires a certain method that is not known to everyone. Although any person is capable of judging a demonstration, since it would not deserve that name if all those who consider it carefully were not convinced and persuaded by it, not every person is capable of finding demonstrations on their own or of clearly proposing them when they are found, due to a lack of leisure or method.
The true method, taken in its entirety, is, in my opinion, something completely unknown until now and has only been practiced in mathematics. Even in mathematics, it is still very imperfect, as I have had the good fortune to demonstrate to some (: who today are considered to be among the foremost mathematicians of the century :) through surprising proofs. And I hope to provide examples that may not be unworthy of posterity.
However, if the mathematicians’ method has not been sufficient to discover everything that could be expected of them, it has at least been able to protect them from errors; and if they have not said everything they should have, they have said nothing that they should not have said.
If those who have cultivated other sciences had at least imitated mathematicians in this respect, we would be very fortunate, and we would have had an assured metaphysics, as well as the morality that depends on it, for a long time, since metaphysics contains the knowledge of God and the soul, which should regulate our lives.
Furthermore, we would have the science of motion, which is the key to physics and consequently to medicine. It is true that I believe we are now in a position to aspire to it, and some of my earliest thoughts were received with such tremendous applause by the most learned men of the time, due to their marvelous simplicity, that I believe all that is left for us to do now is to deliberately conduct certain experiments and not rely on chance and groping, as is commonly done, in order to establish the foundation of a secure and demonstrative physics.
However, the reason why the art of demonstrating is only found in mathematics has not been well understood by anyone, because if we had known the cause of the problem, we would have found the solution long ago. The reason is that Mathematics carries its own proof with it: for when I am presented with a false theorem, I do not need to examine it or even know its demonstration, since I will discover its falseness afterwards through an easy experiment, which costs nothing but ink and paper, that is, through calculation, which will reveal the error however small it may be. If it were as easy in other subjects to verify reasoning through experiments, there would not be such different opinions. But the problem is that experiments in physics are difficult and expensive, and in metaphysics they are impossible, unless God performs a miracle for us to make us understand distant immaterial things.
This problem is not without a remedy, although at first it may seem that there is none. But those who will consider what I am about to say will soon change their minds. We must therefore note that the ⟨proofs or⟩ experiments we do in mathematics to protect ourselves from false reasoning (: such as the proof by the novenary rejection, the calculation of Ludolph of Cologne concerning the size of the circle; the tables of sines or others :) are not done on the thing itself, but on the characters that we have substituted in place of the thing. For to examine a calculation of numbers, for example, such as 16772 taken 365 times3 612,105, we would never have done it if we had to make 365 heaps and put 1677 small stones in each one, and count them all in the end to know if the aforementioned number is there. That is why we content ourselves with doing it with the characters on paper by means of the novenary proof, or some other means. Likewise, when a supposedly exact squaring of the circle is proposed, we do not need to make a material circle to tie a string around it, and to see if the length of this string or circumference has the proportion to the diameter that we have been proposed: this would be painful, for when the error is one thousandth or less ⟨part of the diameter⟩, a large circle worked with great precision would be needed. However, we still refute this false Quadrature, by experiment, and by the result of the calculation or proof in numbers. But this proof is only done on paper, and consequently on the characters that represent the thing, and not on the thing itself.
This consideration is fundamental in this matter and although many very clever people, especially in our century, have claimed to give us demonstrations in physics, metaphysics, morality, and even in politics ⟨in jurisprudence⟩ and medicine: nevertheless, they have either been mistaken, because every step is slippery, and it is difficult not to fall when one is not guided by some [experiences or proofs] ⟨sensible directions⟩; or even if they have succeeded, they have not been able to make their reasoning accepted by everyone, because there has not yet been a way to examine reasoning [in metaphysics] by some easy proofs that everyone could understand.
From this it is clear that if we could find characters or signs that are suitable for expressing all our thoughts as clearly and exactly as arithmetic expresses numbers, or as [algebra] geometric analysis expresses lines, we could do in all subjects as far as they are subject to reasoning everything that can be done in Arithmetic and Geometry.
For all inquiries that depend on reasoning would be done by the transposition of these characters, and by a kind of calculation; which would make the invention of beautiful things quite easy. For we would not have to break our heads as much as we are obliged to do today, and yet we would be assured of being able to do everything that is feasible, ⟨ex datis.⟩
Furthermore, everyone would agree on what we had found or concluded, since it would be easy to verify the calculation either by redoing it or by trying some proofs similar to that of the novenary abjection in arithmetic. And if anyone doubted what I had advanced, I would say to him: let’s count, sir, and thus taking pen and ink, we would soon be out of trouble.4
I always add: as much as one can make reasoning speak, ex datis. Because although certain experiences are always necessary to serve as a basis for reasoning, nevertheless, once these experiences are given, one would derive from them everything that anyone else could ever derive, and one would even discover those that remain to be done, for the clarification of all remaining doubts. This would be of admirable help even in politics and medicine, to reason about the given symptoms and circumstances in a constant and perfect way. For even when there are not enough given circumstances to form an infallible judgment, one can always determine what is most probable ex datis. And that is all that reason can do.5
Now, the characters that express all our thoughts will compose a new language, which can be written and spoken: this language will be very difficult to create, but very easy to learn. It will soon be received by everyone because of its great use and its [amazing] ease [surprising] and it will wonderfully serve the communication of several peoples, which will help to make it received. Those who write in this language will not be mistaken as long as they avoid ⟨ calculation errors and ⟩ barbarisms, solecisms, and other grammatical and construction mistakes; furthermore, this language will have a wonderful property, which is to close the mouths of the ignorant. For one cannot speak or write in this language except about what one understands: or if one dares to do so, one of two things will happen, either that the vanity of what one advances will be manifest ⟨ to everyone ⟩, or that one will learn by writing or speaking. As in effect those who calculate learn by writing, and those who speak sometimes have encounters that they did not think of, lingua præcurrente mentem. This will happen especially in this language, because of its accuracy. Since there will be no equivocations or amphibologies; and everything that is said intelligibly will be said appropriately. [This language will be the greatest instrument of reason.6]
I dare to say that this is the last effort of the human mind, and when the project is executed, it will depend only on men to be happy since they will have an instrument that will serve not less to exalt reason than the telescope serves to perfect vision.7
It is one of my ambitions to bring this project to completion, if God gives me life. I owe it only to myself, and I had the first thought of it at the age of 18 as I testified [then] ⟨a little after⟩ in a printed discourse8. And as I am certain that there is no invention that approaches this one, I believe that there is nothing so capable of eternalizing the name of the inventor. But I have much stronger reasons for thinking about it, for the religion that I follow strictly assures me that the love of God consists in an ardent desire to promote the general good, and reason teaches me that there is nothing that contributes more to the general good of all men than what perfects it.
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This passage is a preface to the General Science. It can be conjectured that it dates from 1677, according to an index noted below (p.154 note i). Cf. Phil. VI, 12, e.↩
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This number should be the date of this fragment.↩
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Here, a word is missing (fait). In the margin, we see the multiplication, crossed out.↩
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Cf. Phil. VIII, 26, 64-65, 125, 200; Letter to Placcius, 1678 (Dutens, VI, 1, 22); and Phil., V, 6, f, 19 (ap. Bodemann, p. 82).↩
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Cf. Letter to Galloys, 1677 (Phil., VII, 21, Math., I, 181).↩
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Cf. Letter to Oldenburg (Phil., VII, 11; Briefwechsel, I, 100); Letter to Galloys, December 1678 (Phil. VII, 23, Math., I, 187) and Phil., VII, 201, 205.↩
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Cf. Phil., VII, 14, 17, 20, 27, 32, 174, 187, 202, 205, and Letter to Bourguet, 1709 (Phil. III, 545).↩
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Allusion to the De Arte combinatoria (1666).↩
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