Die philophischen schriften von Gottfried Wilheim Leibniz, vol. III
C. I. Gerhardt (ed)
pp 583-586

Date: August 1715

Translated from the French

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[G III p583]

     As I am about to depart for Switzerland, after having returned from a journey to Bologna and Parma, I will not be able to respond to your learned letter as thoroughly as the material it contains deserves. I will have the honour of writing to you from Neufchatel in a way which will be more useful for me, and which will be at the same time more convenient.
     I have passed on to Mr Vallisnieri what it pleased you to tell me concerning him.1 He replied to me that because of his great occupations he [G III p584] is presently unable to answer your question about the rarity of twins in certain species of animals,2 but that with time he will try to clarify this matter as much as will be possible for him; besides, he assures you of his respect and veneration, and that he has given the order for a copy of his latest work to be sent to you, which Mr Zendrini has been charged to do.
     I am very obliged to you, Sir, for what you have deigned to tell me in favour of Mr Leeuwenhoek,3 whom I respect greatly. Besides, I by no means intended to offend him when I treated his opinion on spermatic worms as a hollow story. Nevertheless, I am not persuaded by his hypothesis. If I could have easily enclosed my proofs for the propositions I have the honour of sending to you, you would have found in abbreviated form the answer to the objections you have deigned to make to me.
     With God's help, in the future I hope to have the benefit of conversing with you, Sir, about the sublime matters into which your system offers admirable openings. Nevertheless I will say a word on the notion of instants, which I regard as properly related to a beginning in everything which is successive. I therefore conceive the instant as no more real with regard to time than the point is with regard to extension. The instant is therefore nothing other than the notion of a given state in the relation that changeable beings have between themselves. As you have very well remarked, Sir, this concerns existences, that is, the actual relative state of creatures between themselves. Now two things should be said: either there is no given state of beings that compose the universe, which is not necessarily the result of another preceding state of the same nature, and so on to infinity; or there is some given state which is simply the result of a state of pure possibility, which draws its origin from the eternity of essences which subsist ideally in the understanding of the supreme being. In the first case, we could not demonstrate by reason that the world is not eternal, and all the arguments of our philosophers and theologians against the eternity of the universe would be sophisms. It is true that I remember having noticed something about that in a work of Derodon against atheists.4 Nevertheless I believe, with regard to the second case, that by gathering a great amount of data, one could construct a [G III p585] demonstration of it, in order to prove that the world or the assemblage of contingent beings had a beginning, and that could be done by the lights of reason alone. But in order to succeed in such a worthy aim, one would have to clearly explain, by removing all ambiguities, the notions of the necessary and the contingent. Otherwise one would not do anything worthwhile. And on this matter I have marvelled a thousand times that Spinoza did not dare assert that the world is eternal given that, according to his hypothesis, it has to be as necessary as the cause. There was apparently something political in his work.
     What you propose, Sir, about nature, in the idea of the ordinates of hyperbola B, triangle C and rectangle A,5 is assuredly worthy of your deep penetration, and I consider that this matter is such as to deserve all of the attention of our greatest geniuses. What you add about unity pleased me immensely, and I am happy to have been fortunate enough to use this same distinction between the resolution into notions, and the division into parts, in a discussion I had with a Veronese philosopher during my last journey. This helps to confirm my view, because instants are not true parts of time any more than unity is a true part of number. Both are just assignable notions, either to the changes of relations in beings, or to continuous and discrete quantities. So just as one could not conceive any number without the notion of unity being contained within it, similarly one could not conceive any succession without the notion of a beginning or of a primitive assignable state entering into it as well. Therefore everything boils down to the analysis of contingents and necessaries, or rather to the two relations the world has with God. And unless it is said that the relation of creatures to the will of God is as necessary as the one they have to the divine understanding, it will remain certain that there is a difference between necessaries and contingents great enough that one group, namely the essences, exists from all eternity, and the other, namely the existences, exists within time, or, which is the same thing, that they have a beginning.
     If it were said that essences precede existences merely by a priority of order alone, it would follow that everything would be equally necessary, and there would be no room for doubt that the world is eternal. Nevertheless it seems to me that the idea of eternity involves a complete lack of change; it is something absolute. We also [G III p586] see that the wisest theologians have this idea of the eternity of God. The notion of eternity is therefore very different from that of time, which is a true attribute of beings whose nature subsists in a continuous change. To conceive a time without a beginning is the same as conceiving a mountain without a valley.6
     I have nothing to say on the subject of English Mathematicians, except that I believe they were wrong in the proceedings they initiated against you, Sir, over the invention of the differential calculus. It is my opinion that Mr Newton is delighted about this. He is showing one of your letters which, it is claimed, is decisive in his favour. I suspect that your extreme modesty will have caused this misunderstanding. It would now be highly desirable if you finally gave to the public your Dynamic Science, which is certainly the key to the most sublime geometry, just as it is to the most certain philosophy.
     A doctor called Micheloti who lives in this city, and who is very mathematically minded and a friend of Mr Herman and the gentlemen Bernouilli, has asked me to assure you of his esteem and veneration. He asked Mr Herman to give you a letter, in which he demonstrates his sentiments; but having not seen the appearance of any response on your part, he fears that some accident has befallen it which has deprived him of having the honour of receiving some expression of your benevolence.
     The response from Count Riccato to the gentlemen Bernoulli is very good. He protests from the start that it will be the last one on his part. We will see if Mr Nicolas Bernoulli will want to continue this dispute, which certainly will not bring him, or his Uncle, any honour. There is in the response in question a passage subtly addressed against the latter, which will cut him to the quick, without him being able to complain, because the argument is drawn from the actual dissertation of the nephew. 7

     From Venice, August 1715.


1. See Leibniz's letter to Bourguet of 5 August 1715: G III, 580.
2. In his previous letter, Leibniz had asked "I would like to learn Mr Vallisnieri's view about why, in the copulation of certain kinds of animals, a single egg is normally fertilised, and why twins are rather rare among them." G III, 580.
3. In his previous letter, Leibniz had written: "I would not wish to speak as decisively as you do, Sir, when saying that Mr Leeuwenhoek's view is a fable of extravagant proportions." Leibniz to Bourguet, 5 August 1715: G III, 579.
4. David Derodon (c. 1600-1664). Bourguet is probably referring to Derodon's La lumiere de la raison opposee aux tenebres de l'impiete ou athees (Geneva, 1665).
5. Bourguet is here referring to 3 hypotheses described by Leibniz in his letter of 5 August 1715, an English translation of which is to be found in SLT 198.
6. Leibniz wrote between the lines of the letter here: "Every time has a beginning, but it can follow another time. Strictly speaking, there is no infinite time or infinite line, or any infinity generally."
7. HHere Leibniz wrote the following on Bourguet's letter: "If there was a desire to put a stop to the dispute, he should not have included this passage."

© Lloyd Strickland 2004. Revised 2016.