It is very remarkable how Catelan has so entirely missed my meaning, as you suspected he had; he advances three propositions and says that I find contradictions in them, while, in fact, I find none there, and employ these very propositions to prove the absurdity of the Cartesian principle. This is the result of dealing with men who take up things only superficially. If it can happen in a question of mathematics what should we not expect in metaphysics and in ethics. It is for this reason that I consider myself fortunate in having found in you a critic as exact as he is fair. I wish you long life, as well for the interests of the public as for my own.

I am, etc.

Part of a letter sent at the same time to Arnauld

Here is the reply to your last objection, it has become a little long because I wish to explain myself explicitly and to leave none of your doubts untouched. Several times I inserted your own words which contributed toward increasing its size. As I took all those positions a long time ago and have foreseen, if I might dare to say, most of the objections, they cost me hardly any meditation, and all I needed to do was to pour out my thoughts upon paper and to re- read them afterwards. I say this, M., so that you may not think me too deeply engrossed in such matters at the expense of other necessary business; you drew me on to go so far, when you made objections and questions which I wished to satisfy, as much in order to profit by your enlightenment as to make you recognize my wish to disguise nothing.

At the present time I am very busy with a history of the noble house of Brunswick. I have looked over several archives this summer and I am to make a journey in Southern Germany to seek certain documents; this does not prevent my desiring to learn your opinion regarding my explanations when your leisure will permit it and also regarding my reply to Catelan which I send herewith; I do this because it is short and, in my opinion, demonstrative, provided that it is read with the least attention. If Catelan does not do better than hitherto, I cannot expect any enlightenment from him on this subject. I wish you might be able to give a moment of serious attention to it, and you would, perhaps, be surprised to see that something which is so easy to overthrow has been accepted as an incontrovertible principle because it is clear that the velocities which bodies acquire in descending are as the square roots of the heights from which they have fallen: now, if we leave out of question external resistances a body can return exactly to the height from which it has descended, therefore-

Another draft of the above

I herewith send you my reply to Catelan which will, perhaps, be inserted in The News of the Republic of Letters; we are at the beginning again, and I made a mistake in replying to his first answer. I should simply have said that he did not touch my objection, and should have indicated these points to which a reply was necessary, as I have now done- I have added in my reply a mechanical problem, which can be solved by geometry, but a good deal of skill must be used and I will see if M. Catelan will dare tackle it. It seems to me that he is not very able, and I am surprised to see that among so many Cartesians there are so few who imitate Descartes in trying to advance further.

XXIV: Leibniz to Count Ernst von Hessen-Rheinfels

I beg your Highness to ask M. Arnauld as well as yourself if there is really so great an evil in saying that everything (whether a species or whether an individual or person), has a certain perfect concept which involves all that can be truly said regarding it, and, according to this concept, God, who conceives of everything perfectly, conceives of the said thing? And to ask further if M. A. thinks in good faith that a man who holds such a position could not be accepted into the Catholic church, even when he sincerely rejects the supposed fatalistic consequence; and Your Highness may ask how that agrees with what M. A. formerly wrote, namely, that no trouble was made for a man in the Church on account of these kinds of opinions, and if it is not to repulse men by a useless and untimely strictness, to condemn so easily all kinds of opinions which have nothing to do with the faith?

Can it be denied that everything, whether genus, species or individual has a complete concept according to which God conceives of it (he who conceives of everything perfectly), a concept which involves or embraces all that can be said of the thing? And can it be denied that God is able to have such an individual conception of Adam or of Alexander that it shall embrace all the attributes, affections, accidents and, in general, all the predicates of this subject? And finally since St. Thomas could maintain that every separate intelligence differed in kind from every other, what evil will there be in saying the same of every person and in conceiving individuals as final species, provided that the species shall not be understood physically but metaphysically or mathematically; for, in physics when a thing engenders something similar to it, they are said to be of the same kind, but in metaphysics or in geometry we say that things differ in kind when they have any difference in the concept which suffices to describe them, so that two ellipses in one of which the major and minor axes are in the ratio of two to one and in the other in the ratio of three to one, differ in kind. Two ellipses which differ only in magnitude or proportionately, and where, in their description, there is no difference of ratio in the axes, have no specific difference or difference in kind, for it must be remembered that complete beings cannot differ merely because of differences in size.

XXV: Leibniz to Arnauld