Die philophischen schriften von Gottfried Wilheim Leibniz, vol. I
C. I. Gerhardt (ed)
pp 380-5

Date: 2 September 1686

Translated from the French

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[G I p380]

Extract from my letter to Mr Foucher, 1686

     Your parcel has reached me at last. I thank you very much for it, and I did not stop reading until I had finished it. I read your thoughts on this wisdom of the ancients with a great deal of pleasure. I have known for a long time that they are more able than our moderns think, and it would be hoped that people be more familiar with them.
     Lipsius1 and Schoppe2 have tried to resurrect the philosophy of the Stoics; Gassendi3 has worked on Epicurus; Scheffer4 has collected what he could of the philosophy of Pythagoras; Ficino5 and Patrizi6 have followed Plato, but badly in my opinion, since they have thrown themselves into hyperbolic thoughts and abandoned what was simpler and at the same time more solid. Ficino talks everywhere only of ideas, of souls of the world, of mystical numbers, and similar things, instead of seeking the exact definitions Plato tries to give of concepts. I would like someone to draw from the ancients what is most appropriate for our century's use, and what is most in accordance with our century's taste, [G I, p381] without distinction of sect, and I wish you had the time to do it, just as you have the faculty, inasmuch as you could reconcile and sometimes even correct the ancients, by joining a number of fine thoughts of your own.
     I have read Mr Morland's book on the raising of water.7 His cyclo-elliptic motion is nothing special, in my opinion; it proceeds more uniformly, but in return for more difficulty than the cranks he so much disapproves of, and which we find very effective in our mines, where, by their means, pumps located 500 toise8 or more from the wheel are made to work. Since I left Paris, all I have seen from Mr Ozanam is his book on practical geometry, his trigonometry and his new gnomonics.9 I await what he will give us on Diophante, a matter on which he could give us something good. I have found that he has not acted particularly well towards me, as he inserted in the Geometry my quadrature of the circle (namely that, with the diameter being 1, the circle is 1 - 1/3 + 1/5 - 1/7 + 1/9 etc.) together with my demonstration, without naming me, and speaking with an air as if this demonstration was his.
     I very much beseech you, Sir, to give my regards to Mr Huet10 and to Mr Lantin,11 both of whom I hold in the highest regard. I was told a long time ago of the history of pleasure and pain that Mr Lantin planned to write.12 It is an important project. Mr Justel13 had also toiled on a significant work on the conveniences of life, but I fear that he remains behind schedule, as I gather from the letter I received from him recently.
     The philosophy of the Academics, which is the knowledge of the weaknesses of our reason, has good beginnings, and as we are always at the beginning as regards religion, it is doubtless suitable for the better subjugation of reason to authority, which you have shown very well in one of your discourses. But we must try to advance with regard to human knowledge, and even if this were only by establishing many things on a few suppositions, that would nonetheless be useful, for at least we would know that it only remains for us to prove these few suppositions in order to reach a full demonstration, and in the meantime we would at least have hypothetical truths and would extract ourselves from the confusion of disputes. This is the method of geometers. For example, Archimedes supposes only these few things: that the straight line is the shortest; that of two lines, each of which is everywhere [G I, p382] concave on the same side, the enclosed line is shorter than the enclosing line, and with those he robustly completes his demonstrations. This is what I have to remark on the occasion of page 7 of your response to Father Robert of Gabez.14
     So, if we supposed, for example, the principle of contradiction, namely that in every true proposition the concept of the predicate is contained in the concept of the subject, and some other axioms of this nature, and if from these we could prove many things as demonstratively as geometers do, would you not think that this would be important? But this method would have to be begun one day, in order to start the process of finishing off disputes. It would always be a matter of gaining ground.
     It is likewise certain that we have to suppose some truths, or give up all hope of making demonstrations, for proofs could not go on to infinity. We should not ask for anything that is impossible, otherwise we would show that we were not serious in searching for the truth. So I will always boldly suppose that two contradictories could not be true, and that what implies contradiction could not be the case, and consequently, that necessary propositions (that is, those whose contrary implies contradiction) have not been established by a free decree, or else it is to misuse words. Nothing clearer could be provided to prove these things. You yourself suppose them in writing and in reasoning, otherwise you could constantly defend the exact opposite of what you say. And that is said concerning the second supposition.
     I think you are right, Sir, to maintain in the third supposition, in responding to Father Robert, that there has to be some natural relation between certain traces in the brain and what are called pure intellections. Otherwise, one could not teach one's opinions to other people. And although words are arbitrary, there have to be some non-arbitrary marks in order to teach the meaning of these words.
     It also seems to me that you are right (in the 3rd supposition, page 24) to doubt that bodies can act on minds, and vice versa. On this matter I have a pleasing opinion, which seems necessary to me and which is quite different from the opinion of the author of the Recherche.15 I believe that every individual substance expresses the whole universe in its own way, and that its next state is a consequence (although often free) of its previous state, as if there were only God and it in the world. But as all substances [G I, p383] are a continual production of the sovereign being, and express the same universe or the same phenomena, they agree with each other exactly, and that leads us to say that the one acts on the other, because one expresses more distinctly than the other the cause or reason of the changes, somewhat as we attribute motion to a ship rather than to the sea as a whole, and rightly so. I also draw this consequence, that if bodies are substances, they could not consist in extension alone. But that changes nothing in the explanations of particular phenomena of nature, which ought always to be explained mathematically and mechanically, provided that it is understood that the principles of mechanics do not depend on extension alone. So I am neither in favour of the common hypothesis of the real influence of one created substance on another, nor the hypothesis of occasional causes, as if God produced thoughts in the soul on the occasion of motions of the body and so changed the course the soul would have otherwise taken by means of a totally unnecessary kind of perpetual miracle. But I maintain a concomitance or agreement between what happens in the different substances, as God created the soul from the outset so that all of that happens to it or arises from its own depths without it needing to accommodate itself to the body thereafter, any more than the body needs to accommodate itself to the soul. With each following its own laws, and one acting freely, the other without choice, both agree with each other in the same phenomena. All of this does not greatly disagree with what you said in your response to Father Robert on p26, that man is the actual object of his own sensation. It can be added, however, that God is so too, as he alone acts on us immediately, in accordance with our continual dependence. So it can be said that God alone, or what is in him, is our immediate object, which is outside of us, if this term 'object' is fitting for him.
     As for the sixth supposition, it is not necessary that what we conceive of things outside of us be perfectly similar to them, but that it express them, just as an ellipse expresses a circle seen sideways on, so that a point of the ellipse corresponds to each point of the circle, and vice versa, according to a certain law of relation. For as I have already said, each individual substance expresses the universe in its own way, somewhat as the same town is expressed in different ways according to different points of view. Every effect expresses its cause, and the cause of each substance is the resolution that God took to create them; but this resolution envelops relations [G I, p384] to the whole universe, as God had the whole in mind when making a resolution about each part, for the wiser one is the more one has interconnected designs.
     As for the question of whether there is extension outside of us, or whether it is only a phenomenon like colour, you are right to think that it is not very easy to answer. The concept of extension is not as clear as is imagined. We would have to determine the following: whether space is something real, whether matter contains something more than extension, and whether and how matter is itself a substance, and it would take some time to express my thoughts on these issues; nevertheless, I hold that these things can be decided.
     As for the first assertion, and what you said about it to Father Robert, I hold that to judge is not an act of will, strictly speaking, but that the will can contribute a great deal to the judgement. For when one wants to think about something, one can suspend judgement, and when one wants to give one's attention to certain arguments, one can obtain persuasion.
     The general rule that many people lay down as a principle of the sciences, quicquid clare distincteque percipio est verum,16 is without doubt very faulty, as you have rightly recognized. For we would have to have signs of what is clear and distinct. Otherwise, it is to authorize the visions of people who flatter themselves, and who cite their ideas to us at every moment.
     When there is a dispute about whether something is a substance or a way of being, we have to define what substance is. I don't find this definition anywhere, and I have been obliged to work on it myself.
     I come to your Examination of the great principle of Cartesians and of Father Robert, which I have already touched on, namely that our ideas or concepts are always true. And as I have already said, I am someway off from admitting that, since we often combine concepts which are incompatible, so that the composite contains contradiction. I have examined this principle more distinctly in a remark on true or false ideas I placed in the journal of Leipzig.17 And I hold that to be certain that what I conclude from some definition is true, I have to know that this concept is possible. For if it implies contradiction, conflicting things can be simultaneously concluded from it. This is why I call real definition the definition that shows that the thing defined is possible, and the definition which does not do so is only nominal in my view. For example, if one [G I, p385] defined the circle as a shape, each segment of which receives the same angle throughout (that is, that the angles in one and the same segment, from straight lines drawn from two extremities to any point whatever, are the same), it is one of those properties I call paradoxes, and it can be doubted from the outset whether they are possible, for it can be doubted whether such a shape is found in the nature of things. But when it is said that the circle is a shape described by a straight line which is moved in a plane, so that one extremity remains at rest, the cause or reality of the circle is known. This is why our ideas involve a judgement. It is only in this that the demonstration of God's existence, invented by Anselm and revived by Descartes, is faulty. Quidquid ex definitione Entis perfectissimi sequitur, id ei attribui potest. Atqui ex definitione entis perfectissimi seu maximi sequitur existentia, nam Existentia est ex numero perfectionum seu, ut loquitur Anselmus, majus est existere quam non existere. Ergo Ens perfectissimum existit. Respondeo: Ita sane sequitur, modo ponatur id esse possibile.18 And it is the privilege of the sovereign being to need only its essence or its possibility in order to exist. But to complete the demonstration in a rigorous way, this possibility has to be proved, for it is not always permissible to go to the superlative; for example, the concept of the highest velocity implies contradiction.
     So, Sir, I have allowed myself to get carried away by the pleasure I found in following you through the whole of your response to Father Robert of Gabez, and in telling you informally what occurred to me in recalling a few of my old meditations, of which I make you the judge.


1. Justin Lipsius (1547-1606): Physiologiae Stoicorum libri tres [Three books on the physiology of the Stoics] (Antwerp, 1604).
2. Caspar Schoppe (1576-1649).
3. Pierre Gassendi (1592-1655).
4. Johann Scheffer (1621-1679): De natura et constitutione philosophiae Italicae seu pythagoricae [On the nature and constitution of Italian Philosophy, or a book on the Pythagorians] (Upsala, 1664).
5. Marsilio Ficino (1433-1499).
6. Francesco Patrizi (1529-1597).
7. Samuel Morland, Elevation des Eaux, par toute sorte de machines, reduite a la mesure, au poids, et a la balance [Raising of waters by any kind of machines, reduced to measure, weight and balance] (Paris, 1685).
8. A toise is a unit of measurement, and until 1799 was taken to be 1.949 metres in length (approx. 6 and a half feet). After 1799, it became 2 metres in length.
9. Jacques Ozanam, Geometrie pratique (Paris, 1684); Jacques Ozanam, Traité de gnomonique, ou de la construction des cadrans sur toute sourte de plans (Paris, 1683).
10. Pierre Daniel Huet (1630-1721).
11. Jean Baptiste Lantin (1620-1695).
12. Leibniz is referring to Lantin's missing manuscript Traité de la joie et de la douleur [Treatise on joy and pain].
13. Henri Justel (1620-1693).
14. The 'Father Robert' is Robert Desgabets (1610-1678). Leibniz is referring to Foucher's Nouvelle Dissertation sur la Recherche de la verité, contenant la Reponse à la Critique de la Critique de la Recherche de la verité. Où l'on découvre les erreurs des dogmatistes, tant anciens que nouveaux. Avec une discution particuliere du grand principe des Cartesiens [New dissertation on the Search after Truth, containing the response to the critique of the critique of the Search after Truth, in which the errors of the dogmatists, both ancient and new, are revealed, together with a particular discussion on the great principle of the Cartesians] (Paris, 1679). This work was a response to Desgabets' Critique de la Critique de la Recherche de la Verité [Critique of the Critique of the Search after Truth] (Paris, 1675), which was itself a response to Foucher's Critique de la Recherche de la Verité où l'on examine en même-tems une partie des principes de Mr Descartes [Critique of the Search after Truth, in which a part of Mr Descartes' principles are examined at the same time] (Paris, 1675).
15. Malebranche. Leibniz is referring to Malebranche's De la recherche de la verité [The Search after Truth] (Paris, 1674-5).
16. 'whatever I perceive clearly and distinctly is true'.
17. Leibniz is referring to his 'Meditationes de cognitione, veritate, et ideis', published in the Acta Eruditorum, November 1684, pp537-542.
18. 'Whatever follows from the definition of the most perfect Being can be attributed to it. And existence follows from the definition of the most perfect or greatest being, since existence is numbered among the perfections or, as Anselm says, it is greater to exist than not to exist. Therefore, the most perfect Being exists. My response is that this indeed follows only if the most perfect being is assumed to be possible.'

© Lloyd Strickland 2007