August 1st, 1687.

I have learned with much pleasure that his Serene Highness, Count Ernst, has seen and found you in good health. I hope with all my heart that I shall have such news frequently, and that the body will feel as little the effects of age as has the mind, whose energy still manifests itself. I have myself appreciated this energy, and I confess that I know no one from whom I look for a judgment upon my meditations more stable, more penetrating, and also more sincere than from you.

I do not wish to trouble you, but the material of the later letters being of an importance second only to that of religion and having great affinities with it, I confess that I should like to be able to enjoy once more your enlightenment and at least to learn your opinion in regard to my last explanations; for if you find in them an appearance of reason, I shall be confirmed, but if you find anything to say against them I shall advance more cautiously and shall be obliged to examine some day the whole subject anew.

In place of M. Catelan it was the Rev. Father Malebranche who replied a short time ago in The News of the Republic of Letters to the objection which I had put forward. He seems to realize that certain of the laws of nature or principles of motion which he advanced would be difficult to maintain; but he thought this was because he had based them on the assumption of absolute hardness which is not found in nature, while I think that if absolute hardness could be found in nature these laws would still be untenable. It is a defect in the reasoning of Descartes and his followers not to have considered that everything that is said of motion, of inequality, and of elasticity, should also be true if things are supposed to be infinitely small. In this case motion (infinitely small) becomes rest, inequality (infinitely small) becomes equality, and elasticity (infinitely prompt) is nothing else than extreme hardness; somewhat as everything which geometers demonstrate regarding an ellipse proves true of a parabola, when conceived as an ellipse with its second focus infinitely distant. It is a remarkable thing to see that almost all Descartes' laws of motion conflict with this principle, which I hold to be quite as infallible in physics as it is in geometry, because the author of things acts as a perfect geometer. If I make any reply to Father Malebranche it will be principally in order to point out the above mentioned principle, which is of great utility and which has not as yet been generally considered, so far as I know.

But I am detaining you too long and this matter is not worthy of your attention, I am, etc.,

XX: Arnauld to Leibniz

August 28th, 1687.

I must begin by making excuses for replying so late to your letter of April 3d. Since then I have had various illnesses and various occupations and beside it is a little hard for me to apply myself to such abstract things; I therefore ask for your consideration if I give rather briefly my opinion about the new points in your last letter.

1. I have no clear idea what you mean by the word express when you say that "our soul expresses more distinctly, other things being equal, that which pertains to its own body, since it expresses even all the universe in a certain sense." For if by this

expression you mean a certain thought or a certain knowledge, I cannot agree that my soul has more thought and knowledge regarding the movement of the lymph in the lymphatic ducts than regarding the movement of the satellites of Saturn; if what you call expression is neither thought nor knowledge, I do not know what it is. Therefore it cannot be of service in solving the difficulty which I raised; namely, how my soul can have a feeling of pain when I am pricked during my sleep; since for this it would have to know that some one were pricking me, while in fact it obtains this knowledge only by the pain which it feels.

2. In regard to the following reasoning in the philosophy of occasional causes: "my hand moves as soon as I wish it; now it is not my soul which is the real cause of this motion, neither is it the body, therefore it is God"; you say that this supposes that a body cannot move itself. Your thought, however, is that it can, and you hold that whatever there is of reality, in the state which is called motion, proceeds quite as much from the corporeal substance itself, as the thought and the will proceeds from the mind.

This is what seems to me very hard to understand, that a body which has no motion can give itself motion. And if this is admitted, one of the proofs for the being of God is destroyed; namely, the necessity for a first mover.

Moreover, if a body could give motion to itself, it would not result in my hand's moving itself every time that I wished it; for, being without knowledge, how would it know when I wished it to move itself.

3. I have more to say in regard to the indivisible and indestructible substantial forms which you think should be admitted in the case of all animals and perhaps even in the case of plants, because otherwise matter (which you consider as neither composed of atoms nor of mathematical points, but to be divisible to infinity) would not be a unum per se but only an

aggregatum per accidens.

(1). I replied to you that perhaps it is an essential of matter, which is the most imperfect of all beings, not to have any true and proper unity, just as St. Augustine thought, that is, to be plura entia and not properly unum ens; and that this is no more incomprehensible than is the infinite divisibility of matter, which you admit.

But you replied that this cannot be so, because there can be no

plura entia where there is no unum ens.

But how can you employ this argument, which M. Cordemoy perhaps might have thought true, but which, according to you, must be necessarily false, since, excepting animated beings, which do not form one hundred thousand thousandth part, all the rest must, in your opinion, be without substantial forms, merely