THE PHILOSOPHICAL WORKS OF LEIBNITZ. COMPRISING The Monadology, New System of Nature, Principles of Nature and of Grace, Letters to Clarke, Refutation of Spinoza, and his other important philosophical opuscules, together with the Abridgment of the Theodicy and extracts from the New Essays on Human Understanding. TRANSLATED FROM THE ORIGINAL LATIN AND FRENCH. WITH NOTES BY Instructor in Mental and Moral Philosophy, Yale University NEW HAVEN. TUTTLE, MOREHOUSE & TAYLOR, PUBLISHERS. 1890. PHOTOCOPIED BY PRESERVATION SERVICES -1 1QQ7 COPYRIGHT, 1890, BY TUTTLE, MOREHOUSE & TAYLOR. 654845 . INTRODUCTION. THIS translation of the more important philosophical works of Leibnitz furnishes much needed assistance to all teachers of philosophy and its history, in this country or in England. Until recently no collection, at once complete and trustworthy, of the writings of this great and versatile thinker has ever been made. The magnificent edition of Gerhardt has now rendered it possible for the -anslator to select, from all the recorded philosophical utterances of Leibnitz (including his voluminous and elaborate letters), those portions which will give the most satisfactory survey of his system of thinking. The selections of the present volume appear judicious ; they are sufficient to afford a tolerably comprehensive and circumstantial account of this system. It is not, however, to teachers of philosophy alone that I commend this volume. The interests and scholarship of Leibnitz were unexampled as respects range and variety. He was eminent in mathematics, physical science, languages, history, theology, philosophy, and belles-lettres. Even his more definitely philosophical writings are framed in accordance with this varied eminence. They therefore contain much which appeals to any person who is inclined at all to approach the problems of philosophy, from whatever point of view. Their style is free from certain characteristics which lovers of good literature often find repulsive in works of more definitely pedagogical, or systematic and technical, character. Indeed, the principal tenets of Leibnitz are all to be discovered, at least in their inchoate form, in his interesting and instructive letters to various notable persons of his day. It has not been possible for me to compare any considerable portion of this translation with the original. But my confidence in Mr. Duncan s compe tence and accuracy of scholarship is so great that I have no doubt of its excellence. It gives me great pleasure, therefore, to welcome, and to aid in introduc ing this book. It certainly fills and, I believe, it well fills an important gap in our philosophical literature. GEORGE TRUMBULL LADD. Yale University, December, 1890. PREFACE This translation has been made with the hope of rendering the specula tions of one of the greatest of modern thinkers more accessible to ordinary students. Whatever estimate may be taken of the intrinsic merits of these speculations, their influence has been too marked to allow the student of philosophy to ignore them. He will here find all that is necessary to enable him to gain a comprehensive insight into Leibnitz s own system and to understand the objections found by him to the philosophy of his great predecessors, Descartes, Malebranche, Spinoza, Locke. All the important philosophical opuscules are given entire ; also the abridgment of the Theodicee and extracts from the Nouveaux Essais. A few notes and references have been added to help the student. The translations have been made directly from the original Latin and French by_niy_wife and myself,__the only exception being the Letters to Clarke, which are repu b- lished from Clarke s own translation. In making the translations Erdmann s Leibnitii Opera Philosophica (Berlin, 1840), Janet s Oeuvres Philosophiques de Leibniz (Paris, 1866), Gerhardt s Die philosophischen Schriften von O. W. Leibniz (Berlin, 1875-1890), and Foucher de Careil s Refutation Inedite de Spinoza par Leibniz (Paris, 1854), have been used. G. M. D. Yale University, Nov. 30, 1890. TABLE OF CONTENTS. Page I On the Philosophy of Descartes, 1679-1680, . . 1 II Notes on Spinoza s Ethics, c.^l6_7g . 11 III Thoughts on Knowledge, Truth and Ideas, 1684, ... 27 IV On a General Principle useful in the Explanation of the Laws of Nature, 1687, ....... 33 V Statement of personal views on Metaphysics and Physics, 1690, . 37 VI Does the Essence of Body consist in extension? 1691, . . 41 VII Animadversions on Descartes Principles of Philosophy, books 1 and 2, 1692, ........ 46 VIII Reply of Leibnitz to the Extract of the Letter of Foucher, canon of Dijon, published in the Journal des Savans of March 16, 1693, 64 IX On the Philosophy of Descartes, 1693, . . . . 66 X On the reform of Metaphysics and of the Notion of Substance, 1694, .68 XI A New System of Nature, and of the Interaction of Substances, as well as of the Union which exists between the Soul and the Body, 1695, ........ 71 XII The Reply of Foucher to Leibnitz concerning his New System, 1695, . . . . . . . . .81 XIII Explanation of the New System, 1695, . 85 XIV Second Explanation of the New System, 1696, ... 90 XV Third Explanation of the New System, 1696, ... 92 XVI Observations on Locke s Essay on Human Understanding, 1696, 94 XVII On the Ultimate Origin of Things, 1697, . . 100 XVIII On Certain Consequences of the Philosophy of Descartes, \i"97, 107 XIX On Nature in Itself, 1698, . . . . . .112 XX Ethical Definitions, 1697-1698, ..... 127 XXI On the Cartesian Demonstration of the Existence of God, 1700- 1701, . . 132 XXII Considerations on the Doctrine of a Universal Spirit, 1702, . 139 XXIII On the Supersensible in Knowledge and on the Immaterial in Nature, 1702, ....... 149 XXIV Explanation of Points in his Philosophy, 1704, . . .159 XXV On the Principle of Life, 1705, ..... 163 XXVI Necessity and Contingency, 1707, ..... 170 XXVII Refutation of Spinoza, c^J708. .... 175 XXVIII Remarks on the Doctrine of Malebranche, 1708, . . 185 XXIX On the Active Force of the Body, the Soul, and the Souls of Brutes, 1710, ....... 190 XXX Abridgment of the Theodicy, 1710, . . . . .194 XXXI On Wisdom the Art of Reasoning, etc., 1711, . . 205 XXXII The Principles of Nature and of Grace, 1714, . . .209 XXXIII The Monadology, 1714, ..... 218 XXXIV On the Doctrine of Malebranche, 1715, . . . .233 XXXV Five Letters to Samuel Clarke, 1716, ... 238 XXXVI Extracts from the Nouveaux Essais, 1704, . . . 287 Notes. 363 "One day I happened to say that the Cartesian philosophy in so far as it was true was but the ante-chamber of the true philosophy. A gentleman of the company who frequented the Court, who was a man of some reading and who even took part in discussion on the sciences, pushed the figure to an allegory and perhaps a little too far ; for he asked me thereupon, if I did not believe that it might be said that the ancients had shown us the stairs, that the modern school had come as far as into the ante-chamber, and that he should wish me the honor of introducing us into the cabinet of nature ? This tirade of parallels made us all laugh, and I said to him You see, sir, that your comparison has pleased the company ; but you have forgotten that there is the audience chamber between the ante-chamber and the cabinet, and that it will be enough if we obtain audience without pretending to penetrate into the interior. " Leibnitz, Letter to a friend on Cartesianism, 1695. LEIBNITZ. I. ON THE PHILOSOPHY OF DESCARTES. 1679-1680. [From the French.] As to the Philosophy of Descartes, of which you ask my opinion, I do not hesitate to say absolutely that it leads to atheism. It is true that there are some things very suspicious to me who have considered it attentively : for example, these two passages, that final cause ought not to be considered in physics, and that matter takes successively all the forms of which it is capable. There is an admirable passage in the Phaedo of Plato which justly blames Anaxagoras for the very thing which displeases me hi Descartes. For myself, I believe that the laws of mechanics which serve as a basis for the whole system depend on final causes ; that is to say, on the will of God determined to make what is most per fect, and that matter does not take all possible forms but only the most perfect ; otherwise it would be necessary to say that there will be a time when all will be evil in turn, which is far removed from the perfection of the author of things. As for the rest, if Descartes had been less given to imaginary hypotheses and if he had been more attached to experiments, I think that his physics would have been worthy of being followed. For it must be admitted that he had great penetration. As for his geometry and analysis they are far from being as perfect as those pretend who are given but to the investigation of minor problems. There are several errors in his metaphysics, and he has not known the true source of truths nor that general analysis of notions which Jung, in my opinion, has better understood than he. Nevertheless, I confess that the reading of Descartes is very useful and very instructive, and that I like incomparably more to have to do with a Cartesian than with a man from some other school. Finally, I consider this philosophy as the ante-chamber of the true philos ophy. Extract from, a letter to Philipp, 1679. I esteem Descartes almost as highly as it is possible to esteem a man, and although there are among his opinions some which appear to me false and even dangerous, I do not hesitate to say that we owe almost as much to Galileo and to him in matters of philosophy as to all antiquity. I remember at present but one of the two dangerous propositions of which you wish me to indicate the place, viz : Principiorum, Philosophicorurn Part. 3, Articulo 47, his verbis : " Atque omnino parum refert, quid hoc pacto supponatur, quia postea justa leges naturae est mutandurn. Et vix: aiiquid supponi potest ex quo non idem effectus, quanquam fortasse operosius, deduci possit. Cum enim illarum ope materia formas omnes quarum est capax successive assumat, si formas istas ordine consideremus, tandem ad illam quae est hujus mundi pote- rimus devenire, adeo ut hie nihil erroris ex falsa hypothesi sit timendum." I do not think that it is possible to form a more dan gerous proposition than this. For if matter receive successively all possible forms it would follow that nothing so absurd, so strange and contrary to what we call justice, could be imagined, which has not occurred or would not some day occur. These are exactly the opinions which Spinoza has more clearly explained, namely, that justice, beauty, order belong only to things in relation to us, but that the perfection of God consists in a fullness of action such that nothing can be possible or conceivable which he does not actually produce. This is also the opinion of Hobbes who maintains that all that is possible is past, or present, or future, and that there will be no room for relying on providence if God produces all and makes no choice among possible beings. Descartes took care not to speak so plainly, but he could not help revealing his opinions in passing, with such address that he would not be understood save by those who examine profoundly these kinds of subjects. This, in my opinion, is the nptoroK ^eDdoc, the foundation of atheistic philosophy, which does not cease to say things beautiful in appear ance of God. But the true philosophy ought to give us an entirely different notion of the perfection of God which could serve us both in physics and in morals ; and I, for my part, hold that far from excluding filial causes from the consideration of physics, as Descartes pretends, Part 1, Article 28, it is rather by them that all should be determined, since the efficient cause of things is intelli gent, having a will and consequently tending toward the Good, that which is still far from the opinion of Descartes who holds that goodness, truth and justice are so simply because God by a free act of his will has established them, which is very strange. For if things are not good or bad, save by an effect of the will of God, the good will not be a motive of his will since it is subsequent to the will. And his will would be a certain absolute decree, with out reason ; here are his own words, Resp. ad object, sext. n. 8 : " Attendenti ad Dei immensitatem manifestum est, nihil omnino esse posse quod ad ipso non pendeat, non modo nihil subsistens, sed etiam nullum ordinem, nullam legam, nullamve rationem veri et boni, alioqui enim, ut paulo ante dicebatur, non fuisset plane indifferens ad ea creanda quae creavit [he was then indifferent as regards the things which we call just and unjust, and if it had pleased him to create a world in which the good had been forever unhappy and the wicked (that is to say, those who seek only to destroy the others) happy, that would be just. Thus we cannot determine anything as to the justice of God, and it may be that he has made things in a way which we call unjust, since there is no notion of justice as respects him, and if it turns out that we are unhappy in spite of our piety, or that the soul perishes with the body, this will also be just. He continues] : Nam si quae ratio boni ejus per ordinationem antecessisset, ilia ipsum determinasset ad it quod optimum est faciendum [without doubt, and this is the basis of providence and of all our hopes ; namely, that there is something good and just in itself, and that God, being Wisdom itself, does not fail to choose the best]. Sed contra quod se deter- minavit ad ea jam sunt facienda, idcirco, ut habetur in Genesi, sunt valde bona [this is cross reasoning. If things are not good by any idea or notion of goodness in themselves, but because God wills them, God, in Genesis, had but to consider them when they were made and to be satisfied with his work, saying that all was good ; it would have sufficed for him to say, I will it, or to have remembered that he willed them, if there is no formal difference between the two things, to be willed by God, and to be good. But it is apparent that the author of Genesis was of another opinion, introducing a God who would not be content with having made them unless he found further that he had made them well.] hoc est ratio eorum bonitatis ex eo pendet, quod voluerit ipsa sic facere." This is as distinct an expression as one could desire. But after this it is useless to speak of the goodness and justice of God, and providence will be but a chimera. It is evident that even the will of God will be but a fiction employed to dazzle those who do not sufficiently strive to fathom these things. For what kind of a will (good God !) is that which has not the Good as object or motive ? What is more this God will not even have understanding. For if truth itself depends only on the will of God and not on the nature of things, and the understanding being necessarily BEFORE the will (I spea_k de prioritate naturae, non temporis\ the understanding of God will be before the truth of things and consequently will not have truth for its object. Such an understanding is undoubtedly nothing but a chimera, and consequently it will be necessary to conceive God, after the manner of Spinoza, as a being who has neither understanding nor will, but who produces quite indiffer ently good or bad, and who is indifferent respecting things and consequently inclined by no reason toward one rather than the other. Thus, he will either do nothing or he will do all. But to say that such a God has made things, or to say that they have been pro duced by a blind necessity, the one, it seems to me, is as good as the other. I have been sorry myself to find these things in Descartes, but I have seen no means of excusing them. I wish he could clear himself from these, as well as from some other imputations with which Morus and Parker have charged him. For to wish to explain everything mechanically in physics is not a crime nor impiety, since God has made all things according to the laws of mathematics ; that is, according to the eternal truths which are the object of wisdom. There are still many other things in the works of Descartes which I consider erroneous and by which I judge that he has not penetrated so far in advance as is imagined. For example, in geometry, I do not really believe that he has made any paralogism (as you inform me that some one has said to you) ; he was a suffi ciently skillful man to avoid that, and you see by this that I judge him equitably ; but he has erred through too much presumption, holding all for impossible at which he saw no means of arriving ; for example, he believed it was impossible to find x a proportion between a curved line and a straight line. Here are his own words : Lib. 2, Geom., articulo 9 fin. editionis Schotenianae de anno, 1659, p. 39 : cum, ratio quae inter rectas et curvas existit, non eoynita sit nee etiam db hominibus ut arbitror cognosci queat. In which, estimating the powers of all posterity by his own, he was very much mistaken. For a little while after his death a method was found of giving an infinity of curved lines to which could be geometrically assigned equal straight lines. He would have perceived it himself if he had considered sufficiently the dex terity of Archimedes. He is persuaded that, all problems may be reduced to equations (quo rnodo per methodum qua utor, inquit, p. 96, lib. 3, Geom., id omne quod sub Geometricam contempla- tionein cadit, ad unum idemque genus problematum redueatur, quod est ut quaeratur valor radicum alicujua aequationis). This is wholly false, as Huygens, Hudde and others who thoroughly understand Descartes geometry, have frankly avowed to me. This is why there is need of much before algebra can do all that is promised for her. I do not speak lightly and there are few people who have examined the matter with as much care as I. The physics of Descartes has a great defect ; this is that his rules of motion or laws of nature, which should serve as its foundation, are for the most part false. There is demonstration of this. His great principle also that the same quantity of motion is preserved in the world is an error. What I say here is acknowledged by the ablest men of France and England. Judge from this, sir, whether there is reason for taking the opin ions of Descartes for oracles. But this does not hinder me from con sidering him an admirable man, and for saying between ourselves that if he still lived perhaps he alone would advance farther in physics than a great number of others, although very able men. That befalls me here which ordinarily befalls moderate men. The Peripa tetics regard me as a Cartesian, and the Cartesians are surprised that I do not yield to all their pretended lights. For when I speak to prepossessed men of the school who treat Descartes with scorn, I extol the brilliancy of his qualities ; but when I have to do with a too zealous Cartesian I find myself obliged to change my note in order to modify a little the too high opinion which they have of their 6 master. The greatest men of the time in these matters are not Car tesians, or if they have been in their youth they have gotten over it, and I notice among the people who make a profession of philos ophy and of mathematics, that those who are properly Cartesians ordinarily remain among the mediocre and invent nothing of importance, being but commentators of their master, although for the rest they may be more able than the man of the school. Letter to Philipp, Jan., 1680. [The following is an extract from a letter of about the same date as the preceding and on the same subject, written to an unknown correspondent.] Sir, since you desire very much that I express freely my thoughts on Cartesianism, I shall not conceal aught of what I think of it, and which I can say in few words ; and I shall advance noth ing without giving or being able to give a reason for it. In the first place, all those who give themselves over absolutely to the opinions of any author are in a slavery and render themselves sus pected of error, for to say that Descartes is the only author who is exempt from considerable error, is a proposition which could be true but is not likely to be so. In fact, such attachment belongs only to small minds who have not the force or the leisure to medi tate themselves, or will not give themselves the trouble to do so. This is why the three illustrious academies of our times, the Royal Society of England, which was established first, and then the Academic Royale des Sciences, at Paris, and the Academia del Cimento, at Florence, have loudly protested that they wish to be known neither as Aristotelians, nor Cartesians, nor Epicureans, nor followers of any author whatever. I have also recognized by experience that those who are wholly Cartesians are not adepts in inventing, they are but interpreters or commentators of their master, as the philosophers of the school were of Aristotle ; and of the many beautiful discoveries which have been made since Descartes, I know of not one which comes from a true Cartesian. I know these gentlemen a little and I defy them to name one comino- from them. This is an evidence that O Descartes did not know the true method or that he has not trans mitted it to them. Descartes himself had a sufficiently limited mind. Of all men he excelled in speculations, but in them he found nothing useful for life which is evident to the senses and which serves in the practice of the arts. All his meditations were either too abstract, like his metaphysics and his geometry, or too imaginary, like his prin ciples of natural philosophy. The only thing of use which he be lieved he had given was his telescope, made according to the hyper bolic line, with which he promised to make us see animals, or parts as small as animals, in the moon. Unfortunately he was never able to find workmen capable of executing his design, and since then it has even been demonstrated that the advantage of the hyperbolic line is not so great as he believed, it is true that Descartes was a great genius and that the sciences are under great obligations to him, but not in the way the Cartesians believe. I must therefore enter a little into details and give examples of what he has taken from others, of what he has himself done, and of what he has left to be done. From this it will be seen whether I speak without knowledge of the subject. In the first place, his ETHICS is a com pound of the opinions of the Stoics and of the Epicureans, something not very difficult, for Seneca had already reconciled them very well. He wishes us to follow reason, or the nature of things as the Stoics said, with which everybody will agree. He adds that we ought not to be disturbed by the things which are not in our power. This is exactly the dogma of the Portico which established the greatness and liberty of their sage, so praised for the strength of mind which he had in resolving to do without the things which do not depend upon us and to endure them when they come in spite of us. It is for this reason that I am wont to call this ethics the art of patience. The Sovereign Good, accord ing to the Stoics and according to Aristotle himself, was to act in accordance with virtue or prudence, and the pleasure resulting therefrom together with the resolution mentioned above is prop erly that tranquility of the soul, or indolence, which the Stoics and Epicureans sought and equally recommended under different names. One has only to examine the incomparable Manual of Epictetus and the Epicurus of Laertius to acknowledge that Descartes has not advanced the practice of morals. But it seems to me that this art of patience in which he makes the art of living consist, is yet not the whole. A patience without hope does not endure and does not console, and it is here that Plato, in my opinion, surpasses the others, for by good arguments he makes us hope for a better life and approaches nearest to Christianity. It is sufficient to read the excellent dialogue on the Immortality of the Soul or the Death of Socrates, which Theophile has translated into French, to conceive a high idea of it. I think that Pythagoras did the same, and that his metempsychosis was merely to accom modate himself to the range of common people, but that among his disciples he reasoned quite differently. Also Ocellus Lucanus, who was one of them, and from whom we have a small but excellent fragment on the universe, says not a word of it. It will be said that Descartes establishes very well the EXISTENCE OF GOD and the immortality of the soul. But I fear that we are deceived by fine words, for the God. or Perfect Being, of Descartes is not a God such as we imagine him and such as we desire ; that is to say, just and wise, doing everything for the good of creatures as far as is possible, but rather he is similar to the God of Spinoza, namely, the principle of things, and a certain sovereign power or primitive nature which sets everything in action and does everything which is feasible. The God of Descartes has neither will nor under standing, since according to Descartes he has not the Good as the object of the will nor the True as object of the understanding. Also he does not wish that his God should act according to some end, and for this reason he rejects from philosophy the search after final causes, under the adroit pretext that we are not capable of knowing the ends of God. Plato, on the contrary, has very well shown that God being the author of things and provided he acts according to wisdom, true physics is to know the ends and the uses of things, for science is the knowledge of reasons, and the reasons of what has been made by an understanding are the final causes or the designs of him who made them, and these appear from the use and the function which they have. This is why the consideration of the use of parts is so useful in anatomy. This is why a God such as that of Descartes leaves us no other consolation than that of patience par force. He says in some passages that matter passes successively through all possible forms ; that is to say, that his God does everything which is feasible and passes, following a necessary and fated order, through all possible combinations ; but for this the mere necessity of matter sufficed, or rather his God is nothing but this necessity, or this principle of necessity, acting in matter as it can. It must not, therefore, be believed that this God has any more care of intelligent creatures than of the others. Each one will be happy or unhappy, according as it will find itself involved in great torrents or whirlpools ; and he is right in recommending to us patience without hope (in place of felicity). But some one of the better class of Cartesians, deluded by the fine discourses of his master, will say to me that he nevertheless establishes very well the IMMORTALITY OF THE SOUL and consequently a better life. When I hear these things I am astonished at the ease with which the world is deceived, if one can merely play adroitly with agreeable words, although their meaning is corrupted ; for just as hypocrites abuse piety, heretics the scriptures, and the seditious the word lib erty, so the Cartesians have abused those grand words, the existence of God and the immortality of the soul. It is necessary, therefore, to unravel this mystery and to show them that the immortality of the soul, following Descartes, is worth no more than his God. I well believe that I shall not please some, for people do not enjoy being awakened when their minds are occupied with an agreeable dream. But what is to be done ? Descartes teaches that false thoughts should be uprooted before true ones are introduced ; his example ought to be followed, and I shall think that I am ren dering a service to the public if I can disabuse them of such dangerous doctrines. I say then that the immortality of the soul, as it is established by Descartes, is of no use and can in no way console us. For grant that the soul is a substance and that no sub stance perishes ; this being so the soul will not perish, but in reality also nothing perishes in nature. But like matter the soul too will change in form, and as the matter composing a man has at other times formed plants and other animals, so this soul may be immor tal in reality but it will pass through a thousand changes and not remember at all what it has been. But this immortality without memory is altogether useless, viewed ethically, for it destroys all reward, all recompense, and all punishment. Of what use would it be to you, sir, to become king of China on condition of forgetting what you have been. Would it not be the same thing as if God at the same time that he destroyed you created a king in China I This is why, in order to satisfy the hope of the human race, it must be proved that the God who governs all is wise and just, and that he will leave nothing without recompense and without punish ment. These are the great foundations of ethics ; but the doctrine 10 of a God who does not act for the Good, and of a soul which is immortal without memory, serves only to deceive the simple and to pervert the spiritually minded. I could, however, show mistakes in the pretended demonstration of Descartes, for there are still many things to be proved in order to complete it. But I think that at present it is useless to amuse one s self thus, since these demonstrations would be of almost no use, as I have just shown, even if they were good. II. NOTES ON SPINOZA S Ethics. [From the Latin.] PART I. CONCERNING GOD. DEFINITION 1. Self-Caused is that the essence of which involves existence. DEFINITION 2. That a thing is finite, which can be limited by another thing of the same kind, is obscure. For what is thought limited by thought ? Or what other greater than it is given ? He says that a body is limited because another greater than it can be conceived. Add to this what is said below, Prop. 8. DEFINITION 3. Substance is that which is in itself and is con ceived through itself. This also is obscure. For what is it to be in itself ? Then we must ask. Are to be in itself and to be con ceived through itself conjoined cumulatively or disjunctively . That is, whether this means : Substance is that which is in itself, also substance is that which is conceived through itself ; or, indeed, whether it means : Substance is that in which both these concur ; namely, that it both is in itself and is conceived through itself. Or it will be necessary for him to demonstrate that what has the one, has also the other, when rather, on the contrary, it seems that there are some things which are in themselves although they are not conceived through themselves. And so men usually conceive substances. He adds : Substance is that, the conception of which does not require the conception of another thing. But there is also a difficulty in this, for in the following definition he says, An attribute is that which the intellect perceives of substance as con stituting its essence. Therefore the concept of attribute is neces sary for the formation of the concept of substance. If you say that the attribute is not the thing itself, but require indeed that substance shall not need the conception of another thing, I reply : You must explain what is called thing, that we may understand the definition and how the attribute is not the thing. DEFINITION 4. That an attribute is that which the intellect per ceives of substance as constituting its essence, is also obscure. For 12 we ask whether by attribute he understands every reciprocal predi cate ; or every essential predicate whether reciprocal or not ; or, finally, every first or undemonstrable essential predicate. Vide Definition 5. DEFINITION 5. A mode is that which is in another and is con ceived through another. It seems, therefore, to differ from attribute in this, that attribute is indeed something in substance, yet is conceived through itself. And this explanation added, the obscurity of Definition 4, is removed. DEFINITION 6. God, he says, I define as a being absolutely infinite, or a substance consisting in infinite attributes, of which each expresses eternal and infinite essence. He ought to show that these two definitions are equivalents, otherwise he cannot sub stitute the one in place of the other. But they will be equivalents when he shall have shown that there are many attributes or predi cates in the nature of things, which are conceived through them selves ; likewise, when he shall have shown that many predicates can co-exist. Moreover, every definition (although it may be true arid clear), is imperfect, which, although understood, allows of doubt as to the possibility of the thing defined. This, moreover, is such a definition, for thus far it may be doubted whether being- does not imply having infinite attributes. Or for this reason, because it may be questioned whether the same simple essence can be expressed by many diverse attributes. There are, indeed, many definitions of compound things but only a single one of a simple thing, nor does it seem that its essence can be expressed except in a single way. DEFINITION T. A free thing is that which exists and is deter mined to action by the necessity of its own nature ; a constrained thing is that which is determined to existence and to action by another. DEFINITION 8. By eternity I understand existence itself so far as it is conceived to follow from the essence of a thing. These definitions [i. e., 7 and 8], I approve. As to the AXIOMS, I note these things : The first is obscure as long as it is not established what to be in itself is. The second and seventh require no comment. The sixth seems incongruous, for every idea agrees with its ideate, nor do I see what a false idea can be. The third, fourth and fifth can, I think, be demonstrated. 13 PROPOSITION 1. Substance is by nature prior to its modifica tions ; that is, modes, for in Def . 5 he said that by modifications of substance he understands modes. Still he did not explain what to be by nature prior is, and thus this proposition cannot be demon strated from what precedes. Moreover, by nature prior to another seems to mean that through which another is conceived. Besides I confess that there is some difficulty in this, for it seems that not only can posterior things be conceived through the prior, but also prior things through the posterior. Nevertheless, prior by nature may be defined in this way, as that which can be conceived without another thing being conceived ; as also, on the other hand, the other, second thing, cannot be conceived except the first itself be conceived. But if I may say what the matter is, prior by nature is a little too broad ; for example, the property of ten, that it is 64-4, is by nature posterior to this, that it is 6 + 3 + 1 (because the latter is nearer to the first of all : ten is 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) and nevertheless it can be con ceived without this ; nay, what is more, it can be demonstrated without it. I add another example : The property in a triangle, that the three internal angles are equal to two right angles is by nature posterior to this : that two internal angles are equal to the external angle of the third, and nevertheless the former can be con ceived without the latter ; nay, even, although not equally easily, it can be demonstrated without it. PROPOSITION 2. Two substances whose attributes are diverse have nothing in common. If by attributes he means predicates which are conceived through themselves, I concede the proposi tion, it being posited, however, that there are two substances, A and B, and that c is an attribute of substance A, d an attribute of substance B ; or if c, e are all the attributes of substance A, like wise d, f are all the attributes of substance B. It is not so if these two substances have some diverse attributes, some common attri butes, as if the attributes of A itself were c, d and of B itself were d^f. But if he denies that this can happen, the impossibility must be demonstrated. He will, perchance, in case of objection, dem onstrate the proposition itself in this way : Because d and c equally express the same essence (since ex hypothesi they are attributes of the same substance, A), and for the same reason also d and f (since also ex hypothesi they are attributes of the same substance, B) ; 14 therefore c and f express the same essence. Whence it follows that A and B are the same substance, which is contrary to the hypothesis ; therefore it is absurd to say that two diverse substances have anything in common. I reply, that I do not concede that there could be two attributes which can be conceived through themselves, and nevertheless express the same thing. For when ever this happens then these two attributes, expressing the same thing in a diverse way, can moreover be resolved, or at least one or the other of them. This I can easily demonstrate. PROPOSITION 3. Things which have nothing in common cannot be the one the cause of the other, by Axioms 5 and 4. PROPOSITION 4. Two or more distinct things are distinguished one from the other, either by the difference of the attributes of the substances or by the difference of their modifications. He demon strates this thus : Everything which exists, exists either in itself or in something else, by Axiom 1 ; that is, by Defs. 3 and 5, nothing is granted in addition to the understanding, except substances and their modifications. [Here I am surprised that he forgets attri butes for, Def. 5, by modification of substance he understands only modes ; it follows, therefore, either that he spoke ambiguously, or that attributes are not numbered by him among the things existing outside of the understanding, but only substances and modes. Still he could have proved the proposition more easily if only he had added, that things which can be conceived through attributes or modifications are necessarily known and therefore distinguished.] PROPOSITION 5. There cannot be given in the nature of things two or more substances having the same nature or attribute. [I note here what seems to be obscure in this, viz : in the nature of things. Does he mean, in the universe of existing things, or in the region of ideas or possible essences. Then it is not clear whether he wishes to say that many essences are not given having the same common attribute, or whether he wishes to say many individuals are not given having the same essence. I wonder indeed why he here employs the words nature and attribute as equivalents, unless he understands by attribute that which contains the whole nature. Which being posited, I do not see how there can be given many attributes of the same substance which may be conceived through themselves.] Demonstration : If they are dis tinguished, they are distinguished either by their modifications or 15 bj their attributes ; if by their modifications, then since substance is by nature prior to its modifications, by Prop. 1, their modifica tions being put aside, they must still be distinguished, therefore, by their attributes ; if by their attributes, then two substances are not given possessing the same attribute. I reply that a paralogism seems to lurk here. For two substances can be distinguished by attributes, and yet have some common attribute, provided they also have in addition some which are peculiar. For example, A and B ; c d de the attribute of the one being c d, of the other, d e. I remark that Prop. 1 is only useful for this. But it might have been omitted because it suffices that substance can be conceived without modifi cations whether it be by nature prior or not. PROPOSITION 6. One substance cannot be produced by another substance, for two substances, by Prop. 5, do not possess the same attribute, therefore they have nothing in common, by Prop. 2 ; therefore, it cannot be that one is the cause of the other, by Axiom 5. The same in other words and more briefly : Because what is con ceived through itself cannot be conceived through another as cause, by Axiom 4. But I reply, that I grant the demonstration, if sub stance is understood as a thing which is conceived through itself ; it is otherwise if it is understood as a thing which is in itself, as men commonly understand it, unless it be shown that it be in itself and to be conceived through itself are the same thing. PROPOSITION 7. Existence belongs to the nature of substance. Substance cannot be produced by anything else, Prop. 6. There fore it is the cause of itself ; that is, by Def. 1, its essence involves existence. He is not unjustly censured because sometimes he employs cause of itself as a definite something to which he ascribes a peculiar signification, Def. 1 ; sometimes he uses it in the common and vulgar meaning. Nevertheless, the remedy is easy, if he converts this Def. 1 into an Axiom and says : Whatever is not by another, is by itself or of its own essence. But here other diffi culties still exist : the reasoning, namely, is valid only when it is posited that substance can exist. For it is then necessary that, since it cannot be produced by another, it exists by itself, and thus necessarily exist ; but it must be demonstrated that it is a possible substance ; that is, that it can be conceived. It seems that it can be demonstrated from the fact that if nothing can be conceived 16 through itself nothing also can be conceived through another, and hence nothing at all can be conceived. But that it may be shown distinctly, we must consider that if a is posited as conceived through >, there is in the conception of a itself the conception of J itself. And again, if is conceived through c, there is in the con ception of b the conception of c itself, and thus the conception of c itself will be in the conception of a itself, and so on to the last. But if any one reply that the last is not given, I answer, neither is the first, which I thus show. Because in the conception of that which is conceived through another there is nothing except what belongs to the other, so step by step through many there will either be nothing at all in it or nothing except what is conceived through it itself ; which demonstration, I think, is wholly new but infalli ble. By this means we can demonstrate that what is conceived through itself can be conceived. But nevertheless, thus far it can be doubted whether it be possible in the way in which it is here assumed to be possible, certainly not for that which can be con ceived, but for that of which some cause can be conceived, to be resolved into the first. For those things which can be conceived by us, nevertheless cannot therefore all be produced, on account of others which are preferable and with which they are incompatible. Therefore, being which is conceived through itself must be proved to be in actual existence by the additional evidence that because those things exist which are conceived through another, therefore that also through which they are conceived, exists. You see what very different reasoning is needed for accurately proving that a thing exists through itself. However, perhaps there is no need of this extreme caution. PROPOSITION 8. Every substance is necessarily infinite, since otherwise it would be limited by another of the same nature, by Def . 2, and two substances would be given with the same attribute, contrary to Prop. 5. This proposition must be understood thus : A thing which is conceived through itself is infinite in its own kind, and thus is to be admitted. But the demonstration labors not only with obscurity as respects this is limited, but also with uncertainty, by reason of Prop. 5. In the scholium he has excellent reasoning to prove that the thing which is conceived through itself is one, of course after its kind, since many individuals, are posited as existing, therefore there ought to be a reason in nature why 17 there are so many, not more. The reason which accounts for there being so many accounts for this one and that one ; hence also for this other one. But this reason is not found in one of these rather than in another. Therefore it is outside of all. One objection might be made, if it were said that the number of these is bound less or none, or that it exceeds every number. But it can be disposed of, if we assume only some of these and ask why these exist, or if we posit more having something in common, for exam ple existing in the same place, why they exist in this place. PROPOSITION 9. The more reality or being a thing has the greater the number of its attributes. [He ought to have explained what is meant by reality or being, for these terms are liable to various significations.] Demonstration : It is clear from Def. 4. Thus the author. It seems to me not to be clear from it. For one thing may have more of reality than another, as what is itself greater in its own kind, or has a greater part of some attribute ; for example, a circle has more extension than the inscribed square. And still it may be doubted whether there are many attributes of the same substance, in the way in which the author employs attri butes. I confess, however, that if this be admitted and if it is posited that attributes are compatible, substance is more perfect according as it has more attributes. PROPOSITION 10. Each particular attribute of the one substance must be conceived through itself, by Defs. 4 and 3. But hence it follows, as I have several times urged, that there is but a single attribute of one substance, if it expresses the whole essence. PROPOSITION 11. God, or substance, consisting of infinite attri butes, of which each expresses eternal and infinite essence, necessarily exists. He offers three demonstrations of this. First, because he is substance ; therefore, by Prop. 7, he exists. But in this he supposes both that substance necessarily exists, which, up to Prop. 7, was not sufficiently demonstrated, and that God is a possi ble substance, which is not equally easy to demonstrate. Second. There must be a reason as well why a thing is as why it is not. But there can be no reason why God does not exist, not in his own nature for it does not involve a contradiction ; not in another, for that other will either have the same nature and attribute, and hence will be God, or will not have them and hence will have nothing in common with God, and thus it can neither posit nor prevent his 2 18 existence. I reply, 1st, that it is not yet proved that the nature of God does not involve a contradiction, although the author says it is absurd to assert, without proof, that it does, 2d. There might be something having the same nature with God in some things, not in all. Third. Finite beings exist (by experience) ; therefore if the infinite does not exist there will be beings more powerful than the infinite being. It may be answered, if it implies anything, infinite being will have no power at all. I need say nothing of the impro priety of calling the potentiality of existence a power. PROPOSITIONS 12 AND 13. No attribute of substance can be conceived, from which it would follow that substance can be divided ; or substance taken absolutely is indivisible. For it will be destroyed by division and the parts will not be infinite and hence not substances. Many substances of the same nature would be given. I grant it of a thing existing through itself. Hence the corollary follows that no substance, and therefore no corporeal sub stance is divisible. PROPOSITION 14. Besides God, no substance can be granted or conceived. Because all attributes belong to God, nor are several substances having the same attribute given ; therefore, no sub stance besides God is given. All these suppose the definition of substance, namely, being which is conceived through itself, and many others noted above which are not to be admitted. [It does not yet seem certain to me that bodies are substances. It is other wise with minds.] COROLLARY 1. God is one. COROLLARY 2. Extension or thought are either attributes of God, or, by Axiom . . ., modifications of attributes of God. [This is speaking confusedly ; besides he has not yet shown that extension and thought are attributes or conceived through themselves.] PROPOSITION 15. Whatever is, is in God, and without God nothing can be, or be conceived. For since there is no substance except God, Prop. 14, so all other things will be modifications of God, or modes, since besides substances and modes nothing is given. [Again he omits attributes.] PROPOSITION 16. From the necessity of the divine nature must follow an infinite number of things in infinite ways ; that is, all things which can fall within the sphere of infinite intellect, by Def. 6. 19 COROLLARY 1. Hence it follows that God is the efficient cause of all things which fall under his intellect. COROLLARY 2. God is a cause through himself, not indeed per accidens. COROLLARY 3. God is the absolutely first cause. PROPOSITION 17. God acts solely by the laws of his own nature, and is not constrained by any one, since there is nothing outside of himself. COROLLARY 1. Hence it follows, 1st, that there can be no cause which, either extrinsically or intrinsically, besides the perfection of his own nature, moves God to act. COROLLARY 2. God only is a free cause. In the SCHOLIUM he further explains that God created everything which is in his intellect (although, nevertheless, it seems that he has created only those which he wished). He says also that the intellect of God differs from our intellect in essence, and that, except equivocally, the name intellect cannot be attributed to both, just as the Dog, the heavenly constellation, and a dog, a barking animal, differ. The thing caused differs from its cause in that which it has from the cause. A man differs from man as respects the existence which he has from that man ; he differs from God as respects the essence which he has from God. PROPOSITION 18. God is the immanent, not the transient cause of all things. From this it follows that God only is substance ; other things are its modes. PROPOSITION 19. God, or all his attributes are eternal. For his essence involves existence, and his attributes involve his essence. In addition, the author cites and approves the way in which he demonstrated this in Prop. 19 of his "Principles of Descartes." PROPOSITION 20. The essence of God and his existence are one and the same thing. He proves all this from the fact that the attributes of God because eternal (by Prop. 19), express existence (by the definition of eternity). But they also express essence, by the definition of attribute. Therefore essence and existence are the same thing in God. I answer that this does not follow, but only that they are expressed by the same. I note, moreover, that this proposition supposes the preceding, but if in place of the pre ceding proposition its demonstration be employed in the demon stration of this, a senseless circumlocution will be apparent. Thus : 20 I prove that the essence and existence of God are one and the same thing, because the attributes of God express both existence and essence. They express essence by the definition of attribute, they express existence because they are eternal ; they are, moreover, eternal because they involve existence, for they express the essence of God which involves existence. What need is there, therefore, of mentioning the eternity of the attributes and Prop. 19, when the point merely is to prove that the existence and essence of God are one and the same thing, since the essence of God involves existence. The rest is pompously introduced that it may be fash ioned into a sort of demonstration. Reasonings of this sort are exceedingly common with those who do not possess the true art of demonstration. COROLLARY 1. Hence it follows that God s existence, like his essence, is an eternal truth. I do not see how this proposition fol lows from the preceding ; on the contrary, it is far truer and clearer than the preceding. For it is immediately apparent when it is posited that the essence of God involves existence, although it may not be admitted that they are one and the same. COROLLARY 2. God and all his attributes are immutable. This the author proposes and proves obscurely and confusedly. PROPOSITION 21. All things which follow from the absolute nature of any attribute of God must always exist and be infinite ; or, in other words, are eternal and infinite through the said attri bute. He demonstrates this obscurely and quite at length, although it is easy. PROPOSITION 22. Whatsoever follows from any attribute of God, in so far as it is modified by a modification which exists nec essarily and as infinite through the said attribute, must also exist necessarily and as infinite. He says the demonstration proceeds as in the preceding. Therefore, also obscurely. I could wish that he had given an example of such a modification. PROPOSITION 23. Every mode, which exists both necessarily and as infinite, must necessarily follow either from the absolute nature of some attribute of God, or from some attribute modified by a modification which exists necessarily, and as infinite. That is, such a mode follows from the absolute nature of some attribute either immediately or mediately through another such mode. 21 PROPOSITION 24. The essence of things produced by God does not involve existence ; otherwise, by Def. 1, they would be the cause of themselves, which is contrary to the hypothesis. This from elsewhere is manifest ; but this demonstration is a paralogism. For cause of itself, by his Def. 1, has not retained its common meaning, but has received a peculiar one. Therefore the author cannot substitute the common meaning of the word for the pecul iar one assumed by him at his will, unless he shows that they are equivalent. [Leibnitz has remarked on the margin of the manu script : From this proposition it follows, contrary to Spinoza him self, that things are not necessary. For that is not necessary whose essence does not involve existence. Gerhardt.\ PROPOSITION 25. God is the efficient cause not only of the existence of things but also of their essence. Otherwise the essence of things could be conceived without God, by Axiom 4. But this proof is of no moment. For even if we concede that the essence of things cannot be conceived without God, from Prop. 15, it does not therefore follow that God is the cause of the essence of things. For the fourth axiom does not say this : That without which a thing cannot he conceived is its cause (which would indeed be false, for a circle cannot be conceived without a center, a line with out a point, but the center is not the cause of the circle nor the point the cause of the line), but it says only this : Knowledge of the effect involves knowledge of the cause, which is quite different. For this axiom is not convertible; not to mention that to involve is one thing, not able to he conceived without it is another. Knowl edge of a parabola involves in it knowledge of a focus, nevertheless it can be conceived without it. COROLLARY. Individual things are nothing but modifications of the attributes of God, or modes by whicli the attributes of God are expressed in a fixed and definite manner. This, he says, is evident from Def. 5 and Prop. 15, but it does not appear in what way the corollary is connected with this Prop. 25. Certainly Spinoza is not a great master of demonstration. This corollary is sufficiently evident from what was said above ; but it is true if it is understood in a right sense, not indeed that things are such modes, but modes of conceiving particular things are determinate modes of conceiv ing divine attributes. PROPOSITION 28. Every individual thing, or everything which is finite and has a conditioned existence, cannot exist or be condi tioned to act, unless it be conditioned for existence and action by a cause other than itself, which also is finite, and has a conditioned existence ; and likewise this by another, and so on ad ifijmitwii. Because nothing conditioned, finite and existing in a certain time, can follow from the absolute essence of God. From this opinion strictly taken many absurd consequences follow. For indeed things will not follow in this way from the nature of God. For the conditioning thing itself is again conditioned by another, and so on ad infinitum. In no way, therefore, are things determined by God. God only contributes of himself certain absolute and gen eral things. It would be more correct to say, that one particular thing is not determined by another in a progression ad infinitum, for otherwise, indeed, they always remain indeterminate, however far you progress; but rather all particular things are determined by God. Nor are posterior things the full cause of prior things, but rather God creates posterior things so that they are connected with the prior, according to rules of wisdom. If we say that prior things are the efficient causes of the posterior, the posterior will in turn be in a way the .final causes of the prior, according to the view of those who claim that God operates according to ends. PROPOSITION 29. Nothing in the nature of things is contingent, but all things are conditioned to exist and operate in a particular manner by the necessity of the divine nature. The demonstration is obscure and abrupt, deduced from preceding propositions abrupt, obscure and doubtful. It depends upon the definition of contin gent, which he has nowhere given. I, with others, employ contingent for that the essence of which does not involve existence. In this meaning, particular things are contingent, according to Spinoza himself, by Prop. 24. But if you employ contingent according to the custom of certain scholastics, a custom unknown to Aristotle and to other men and to the usage of life, for that which happens, so that a reason can in no way be given why it should occur thus rather than otherwise ; the cause of which also, all the requisites as well within as without it having been posited, was equally disposed toward acting or not acting ; I think that such a contingent implies that all things are by their nature, according to the hypothesis of the divine nature and the condition of things, 23 certain and determinate, although unknown to us, and do not have their determination in themselves but through the supposition or hypothesis of things external to them. PROPOSITION 30. Intellect, in action (actu) finite, or in action infinite, must comprehend the attributes of God and the modifica tions of God, and nothing else. This proposition, which is suffi ciently clear from the preceding and in a right sense true, our author according to his custom proves by others which are obscure, doubtful and remote ; namely, that a true idea must agree with its ideate, that is, as known per se (so he says, although I do not see how r what is known per se is any the more true) ; that what is contained in the intellect objectively must necessarily be granted in nature; that but one substance is given, namely, God. Never theless, these propositions are obscure, doubtful and far-fetched. The genius of the author seems to have been greatly distorted. He rarely proceeds by a clear and natural road ; he always goes by an abrupt and circuitous one. And most of his demonstrations rather surprise (surpr&rMwnf) the mind than enlighten it. PROPOSITION 31. The intellect in action, whether finite or infinite, as will, desire, love, etc., should be referred to passive nature (natura naturata], not to active nature (natura naturans). He understands by active nature, God and his absolute attributes ; by passive nature, his modes. But the intellect is nothing else than a certain mode of thought. Hence elsewhere he says that God properly does not know or will. I do not assent to this. PROPOSITION 32. Will cannot be called a free cause, but only a necessary cause, because, forsooth, that is free which is determined by itself. The will, moreover, is a mode of thought and so is mod ified by another. PROPOSITION 33. Things could have been produced by God in no other manner or order than that in which they have been pro duced. For they follow from the immutable nature of God. This proposition is true or false according as it is explained. On the hypothesis of a divine will choosing the best or operating most perfectly, certainly nothing but these could have been produced ; but according to the nature of things regarded in themselves, things might have been produced otherwise. Just as we say that the angels confirmed [in holiness] cannot sin, in spite of their liberty ; they can if they will but they do not will. They may be able, 24 absolutely speaking, to will it, but in this existing state of affairs they are not able to will it. The author rightly acknowledges in the scholium that a thing is rendered impossible in two ways, either because it implies it in itself or because no external cause is given suitable for producing it. In the second scholium he denies that God does all things with the Good in view (sub ratione boni}. He certainly has denied to him will, and he thinks that those differing from him subject God to fate, although nevertheless he himself confesses that God does all things by reason of the Perfect (sub ratione perfecti}. PROPOSITION 34. God s power is his very essence, because it follows from the nature of essence that he is the cause of himself and of other things. PROPOSITION 35. Whatever exists in the power of God exists necessarily ; that is, follows from his essence. PROPOSITION 36. Nothing exists from whose nature some effect does not follow, because it expresses the nature of God in a certain and determined mode ; that is, by Prop. 34, the power of God [it does not follow, but it is nevertheless true]. He adds an APPENDIX against those who think that God acts with an end in view, mingling true with false. For although it may be true that all things do not happen for the sake of man, nevertheless it does not follow that God acts without will or with out knowledge of good. In the copy of Spinoza s Opera Postkuma, now contained in the royal library at Hanover, Leibnitz has written the following notes : PART SECOND OF THE " ETHICS." On Def . 4, " By an adequate idea, I mean an idea which, in so far as it is considered in itself, without relation to the object has all the properties or intrinsic marks of a true idea," Leibnitz writes : He had therefore to explain what a true idea is, for Part I, Axiom 1, it is employed only as agreement with its ideate. At the end of the Proof of Prop. 1, "Thought is an attribute of God or God is a thinking thing," Leibnitz adds : In the same way he will prove that God fears and hopes. If you reply that they are modes of thought, it can perhaps be said that thought is a mode of another attribute. 25 On Prop. 6, " The modes of any given attribute are caused by God, in so far as he is considered through the attribute of which they are modes, and not in so far as he is considered through any other attribute." Leibnitz remarks : I doubt it, because it seems that something besides is required for modifying any attribute. The reason is the same with that which concludes that not all exist ; on the contrary, that certain distinct ones exist. On Prop. 12, " Whatever comes to pass in the object of the idea, which constitutes the human mind, must be perceived by the human mind, or there will necessarily be an idea iri the human mind of this occurrence. That is, if the object of the idea constitut ing the human mind be a body, nothing can take place in that body without being perceived by the mind," is written : Ideas do not act. The mind acts. The whole world is indeed the object of each mind. The whole world in a certain way is perceived by any mind whatever. The world is one, and nevertheless minds are diverse. Therefore the mind is made not through the idea of the body, but because GOD in various ways intuites the world as I do a city. To Prop. 13, " The object of the idea constituting the human mind is the body; in other words, a certain mode of extension which actually exists, and nothing else," Leibnitz adds: Hence it follows that some mind is momentarily, at least, in the same man. At the end of the Proof to Prop. 15, " The idea which consti tutes the actual being of the human mind, is not simple, but compounded of a great number of ideas," he remarks : Therefore, also, the human mind is an aggregate of many minds. On Prop. 20, " The idea or knowledge of the human mind, is also in God, following in God in the same manner, and being referred to God in the same manner, as the idea or knowledge of the human body," he writes : Therefore the idea of the idea is given. Hence it would follow that the thing would go on in injvnitum, if indeed the human mind is an idea. On the words of the Scholium to Prop. 21, " That is, mind and body are one and the same individual, conceived now under the attribute of thought, now under the attribute of extension," he remarks : Therefore, in fact, mind and body do not differ any more than a city regarded in different ways differs from itself. It fol lows that extension does not in fact differ from thought, drona. 26 At the end of this scholium Leibnitz adds : Hence it follows that to understand the idea of the body, or the mind, there is no need of another idea. On Prop. 23, " The mind does not know itself, except in so far as it perceives- the ideas of the modifications of the body," he writes : If the mind perceives itself in any way whatsoever, it fol lows that there is no idea of the mind in God, other than from the mind itself, for it perceives itself in so far as it expresses God per ceiving the mind. On the words in the proof of this proposition, " The human mind does not know the human body itself," he remarks : On the con trary, just as God .or the mind knows the body through the ideas of the modifications of the body, so they know the mind through the ideas of the modifications of the mind. PART THIRD OF THE " ETHICS." On Def. 3, " By emotion I mean the modifications of the body by which the active power of the body itself is increased or dimin ished, aided or constrained, and also the ideas of these modifica tions," he remarks : Emotion is understood also when we do not think of the body. To Propy. 23, "When we love a thing similar to ourselves we endeavor, as far as we can, to bring about that it should love us in return," he writes : The reason why we endeavor to do good to it is to bring about that we may be loved. But this can and ought to be proved otherwise, for any one can will to do good although he does not seek and think to be loved in return. On Def. 2 of the Emotions, " Joy is the transition of a man from less to greater perfection," he remarks : I can increase the perfection of the body, so that I am not aware that I am becoming more beautiful and that my limbs are growing to greater strength. It may be replied that this transition is insensible, and so also is the joy. On Parts I Y and V of the Ethics no remarks are found. III. THOUGHTS ON KNOWLEDGE, TRCTH AND IDEAS. [From the Latin. Acta Eruditorum Lipsiensium, Nov., 1684.] SINCE eminent men are to-day raising discussions concerning true and false ideas, and since this subject, which even Descartes has not always satisfactorily explained, is of the greatest importance for the knowledge of truth, I propose to explain in a few words, what, in my opinion, may be said with certainty regarding the distinctions and the criteria of our ideas and of our knowledge. Thus knowledge is either obscure or clc-ar, and clear knowledge is farther either, confused or distinct, and distinct knowledge is either inadequate or adequate, or again, symbolical or intuitive ; and if it is at the same time symbolical and intuitive, it is perfect in every respect. A notion is obscure when it is not sufficient to enable us to recognize the thing represented ; as for example, where I should have some vague idea of a flower or of an animal which 1 should have already seen but not sufficiently to be able to recognize it if offered to my sight, nor to distinguish it from some neighboring animal ; or where I should consider some term badly defined in the schools, such as the entelechy of Aristotle, or cause in so far as it is common to matter, to form, to efficient cause, or to end, and other expressions of which we have no lixed definition ; this renders the proposition of which such a notion forms part equally obscure. Knowledge then is clear when it is sufficient to enable me to recognize the thing represented, and it is farther either con futed or distinct / confused, when I cannot enumerate separatelv the marks necessary to distinguish one thing from others, notwith standing that the object has in reality such marks, as well as data requisite to the analysis of the notion. It is thus that we recog nize clearly enough, colors, odors, flavors and other particular objects of the senses, and that we distinguish the one from the other by the simple testimony of the senses and not by enunci- able signs. This is why we cannot explain to a blind person what red is, nor can we make other people recognize qualities of this 28 kind except by placing them in direct communication with them, that is, by making them see, smell and taste, or at least by recalling to them a certain sensation which they have already experienced ; and nevertheless it is certain that the notions of these qualities are composite and may be analyzed, because they have their causes. Just so we often see painters or other artists who judge very correctly that a work is good or defective, without being able to account for their judgment, and who reply to those who ask their opinion, that that of which they disapprove, lacks somethings, / know not what. But a distinct notion resembles that which the assayers have of gold, by the aid of distinctive signs and of means of comparison sufficient to distinguish the object from all other similar bodies. Such are the means of which we make use for notions common to several senses, such as those of number, of magnitude and of figure, as well as for many affections of the mind, such as hope and fear : in a word, for all the objects of which we have a nominal definition, which is nothing else than an enumeration of sufficient distinctive marks. We have however a distinct knowledge of an indefinable thing when it is primitive, or when it is only the mark of itself that is, when it is irreducible and is only understood through itself, and consequently does not possess the requisite marks. As for composite notions where each of the component marks is sometimes clearly known, although in a confused way, as gravity, color, aqua fortis, which form a part of those [the marks] of gold, it follows that such a knowledge of gold is distinct without always being adequate. But when all the elements of a distinct notion are themselves also known distinctly, or when its analysis is complete, the idea is adequate. I do not know that men can give a perfect example of this, although the knowledge of numbers approaches it very nearly. It very often happens, nevertheless, especially in a long analysis, that we do not perceive the whole nature of the object at one time, but substitute in place of the things, signs, the explanation of which, in any present thought, we are accustomed for the sake of abbreviation to omit, knowing or believing that we can give it ; thus when I think a chiliogon, or polygon with a thousand equal sides, I do not always consider the nature of a side, of equality, and of the number thousand (or of the cube of ten) ; but these words, the sense of which presents itself to my mind in an obscure, or at least 29 imperfect manner, take the place to me of the ideas which I have of them, because my memory attests to me that I know the signifi cation of these words, and that their explanation is not now neces sary for any judgment. I am accustomed to call this thought Hind or again symbolical and we make use of it in algebra, in arithmetic and almost everywhere. And assuredly when a ques tion is very complex, we cannot embrace in thought at the same time all the elementary notions which compose it ; but when this can be done, or at least as far as this can be done, I call this thought intuitive. We can only have an intuitive knowledge of a distinct, primitive notion, as most often we have only a symbolical knowledge of composite ideas. From this it clearly follows that even of the things which we know distinctly, we only conceive the ideas in as far as they form the object of intuitive thought. Also it often happens that we imagine that we have in our minds the ideas of things, from suppos ing wrongly that we have already explained to ourselves the terms of which we make use. And it is not true, as some say, or at least it is very uncertain, that we cannot speak of anything, understand ing fully what we say, without having an idea of it. For often we vaguely understand each of these terms or we remember that we have. formerly understood them; but as we content ourselves with this blind thought and as we do not push far enough the analysis of notions, it happens that unwittingly we fall into the contradiction which the composite idea may imply. I have been led to examine this question more closely by an argument, long celebrated in the schools and renewed by Descartes, for proving the existence of God. It is as follows : All that follows from the idea or from the definition of a thing may be affirmed of the thing itself. From the idea of GOD (or the most perfect being, or one a greater than whom cannot be conceived), existence follows. (For the most perfect being involves all perfections, among which is also existence). Therefore existence may be affirmed of GOD. But it must be known how it comes about that if God be possible, it follows that he exists. For to conclude, we cannot safely use definitions before knowing whether they are real and do not involve any contradiction. The reason of this is, that if the ideas involve contradiction, opposite things may be concluded at the same time, which is absurd. I am accustomed, in order to render 30 this truth clear, to make use of the example of quickest motion, which involves an absurdity. Suppose then that a wheel turn with the quickest motion, who does not see that a spoke prolonged will move more rapidly at its extremity than at the center of the cir cumference ; therefore the motion is not the quickest, which is contrary to the hypothesis. However it seems at first view, as if we might have an idea of quickest motion, for we understand fully what we say, and yet we cannot have an idea of impossible things. So it does not suffice that we think the most perfect being, to assure us that we have the idea of such a being, and in the demon stration which we have just produced, the possibility of the most perfect being must be shown or supposed, if the conclusion be legitimately drawn. However it is very true both that we have an. idea of GOD, and that the most perfect being is possible, and even necessary; but the argument is not conclusive and has already been rejected by Thomas Aquinas. And it is thus that we find a difference between nominal defini tions, which only contain the marks of the thing which is to be distinguished from others, and real definitions which show clearly that the thing is possible. And in this way answer is made to Hobbes, who pretended that truths were arbitrary, because they depended on nominal definitions, not considering that the reality of the definition is independent of arbitrariness, and that no tions are not always reconcilable among themselves. Nominal definitions are only sufficient to a perfect science when it is well established otherwise that the thing defined is possible. It is very evident also what a true idea is, what a false ; the idea is true when the notion is possible ; it is false when the notion involves contra diction. Now we know the possibility of a thing either a priori or a posteriori. A priori, when we resolve the notion into its elements, or into other notions of known possibility, and when we know that it includes nothing which is incompatible ; and, to cite but one case, this takes place when we understand by what means a thing may be produced, a fact which makes causal definitions more useful than any others : a posteriori, when experience shows us the thing actually existing ; for that which exists in fact is necessarily possible. Every time that we have an adequate knowledge, we have also knowledge of the possibility a priori ; for if we push the analysis to the end and no contradiction appears, the notion is 31 necessarily possible. Now, is it possible that men should ever con struct a perfect analysis of notions, or that they should reduce their thoughts down to first possibilities, to irreducible notions, or what is the same thing, down to the absolute attributes of God ; that is, to the h rst causes and to the final reason of things ? I should not dare to actually decide this question. Most often we content our selves with learning from experience the reality of certain notions, from which afterwards we compose others, after the example of nature. Whence I think it may be understood that it is not always safe to appeal to ideas, and that many abuse this specious title for establishing certain imaginations of their own. For we have not always immediately the idea of the thing of which we are conscious of thinking, as we have shown above in the example of greatest swift ness. And I see that none the less to-day do men abuse this famous principle : Everything that I conceive clearly and distinctly of a thing is true or may l>e predicated of it. For often men, judging hastily, imagine things clear and distinct which are obscure and confused. The axiom is therefore useless unless the criteria of clearness and distinctness, which we have indicated be applied, and the truth of the ideas be well established. As for the rest, it is not necessary in the exposition of truth to reject as criteria the rules of ordinary logic of which geometricians make use and which consist in admitting nothing as certain which is not proved by exact expe rience or solid demonstration. Now a solid demonstration is one which observes the form prescribed by logic, without, however, always having need of syllogisms disposed in the regular order of the schools (like those of which Christianus Herlinus and Conradus Dasypodius made use for the demonstration of the first six books of Euclid) ; but at least in such a way that the reasoning is conclu sive by virtue of its form an example of such reasoning conceived in the regular form may be found in any legitimate calculus. Thus no necessary premise will be omitted, and all the previous premises must be either proved or at least admitted as hypotheses, in which case the conclusion is hypothetical. Those who will care fully observe these rules will easily guard themselves from deceptive ideas. It is in accordance with such principles that the great genius, Pascal, in an excellent dissertation on the Mathemat ical Genius (a fragment of which exists in the remarkable book of 32 the celebrated Antoine Arnauld, On the Art of Thinking Well), says that the geometrician must define all terms in the least obscure and prove all truths in the least doubtful. But I wish he had defined the limits beyond which a notion or an affirmation is no longer in the least obscure or doubtful. However, we may judge what there is in it by an attentive examination of the considerations which we have just mentioned, for now I wish to be brief. As to the question whether we see all things in God (an old opinion, too, which reasonably understood ought not to be altogether rejected), or whether we have ideas of our own, it must be understood that even if we see all things in God it is none the less necessary that we have also ideas of our own ; that is, not as it were certain little images, but affections or modifications of our mind, answering to that which we perceive in God. For since our thoughts are constantly being succeeded by others, a certain change is wrought in our mind ; as for the things not actually conceived by us, ideas of them are in our mind as the statue of Hercules in the rough marble. But with God, on the contrary, must neces sarily exist in actuality the idea not only of absolute and infinite extension, but also of each figure, which is nothing else than the modification of absolute extension. Moreover, when we perceive colors and odors we have no other perception but that of figures and motions, but so multiplex and delicate that our mind, in its present state, is incapable of distinctly considering each one and consequently it does not notice that the perception is only com posed of extremely small figures and motions. So when, after having mixed yellow powder with blue we perceive a green color, we do not perceive anything but the yellow and blue minutely mixed, although we do not notice it, or rather imagine that we per ceive some new entity. IV. EXTRACT FROM A LETTER TO BAYLE, CONCERNING A GENERAL PRINCIPLE USEFUL IN THE EXPLANATION OF THE LAWS OF NATURE. 168T. [From the French.] I HAVE seen the reply of Malebraiiche to the remark which I made concerning certain laws of nature which he had estab lished in the Search after Truth. He seems sufficiently disposed to abandon them himself, and this ingenuousness is highly praise worthy ; but as he gives reasons and restrictions, which would land us in the obscurity from which I think I have relieved this subject, and which clash with a certain principle of general order which I have observed, I hope that he will have the kindness to permit me to avail myself of the present opportunity to explain this principle, which is of great use in reasoning and which I think is not yet sufficiently employed nor sufficiently known in all its bearing. It takes its origin from the infinite j it is absolutely nec essary in geometry but it holds good also in physics, for this reason that the sovereign wisdom which is the source of all things acts as a perfect geometrician, and according to a harmony to which noth ing can be added. This is why this principle often serves as proof or test to show at first sight and from without, the error of a badly constructed opinion, even before coming to the discussion of the matter itself. It may be stated thus : When the difference of two cases may be diminished below any magnitude given in datis or in that which is posited, it must also be found diminished below any magnitude given in quaesitis or in that which results therefrom. Or to express it more familiarly, when the cases (or that which is given), continually approach each other and finally lose themselves one in the other, the results or events (or that which is required), must also do the same. This depends again on a more general principle, to wit: datis ordinatis etiam quaesita sunt ordinata. But in order to understand it examples are necessary. It is known that the case or the supposition of an illipse mav approach the case of a parabola as much as may be, so that 3 34 the difference of the illipse and of the parabola may become less than any given difference, provided that one of the foci of the illipse be sufficiently distant from the other, for then the radii com ing from this distant focus will differ from the parallel radii as little as may be, and consequently all the geometrical theorems which are true of the illipse in general can be applied to the parabola by considering the latter as an illipse, one of the foci of which is infinitely distant, or (to avoid this expression), as a figure which differs from some illipse less than any given difference. The same principle holds good in physics ; for example, rest may be considered as an infinitely small velocity, or as an infinite slow ness. This is why all that is true in respect to slowness or velocity in general, must be true also of rest thus understood ; so much so that. the rule of rest ought to be considered as a particular case of the rule of motion ; otherwise, if this does not hold, it will be a sure sign that the rules are badly contrived. So equality may be considered as an infinitely small inequality, and inequality may be made to approach equality as much as you please. It is among other faults of this consideration that Descartes, very able man as he was, failed in more than one way in his pretended laws of nature. For (not to repeat here what I said before of the other source of his error, when he took the quantity of movement for force), his first and his second rules, for example, do not agree ; the second says that two bodies, B and C, meeting in the same line with equal velocities, and B being as little as possible larger, C will be turned back with its first velocity, but B will continue its movement ; whereas according to the first rule, B and C being equal, both will turn back and retrograde with a velocity equal to that which had carried them thither. But the difference in the results of these two cases is not reasonable ; for the inequality of the two bodies may be as slight as you please, and the difference which is in the suppositions of these two cases, to wit : the differ ence between such an inequality and a perfect equality could be less than any given ; hence, by virtue of our principle, the differ ence between the results or outcomes ought also to be less than any given ; notwithstanding if the second rule were as true as the first the contrary would happen, for according to this second rule any increase, however small, of body B before equal to C, makes a difference grandissime in the effect, such that it changes absolute retrogression into absolute continuation, which is a great leap from one extremity to the other, whereas in this case body B ought to turn back a little less, and body C a little more than in the case of equality, from which this case can hardly be distinguished. There are many other like incongruities resulting from the Car tesian rules, which the attention of a reader applying our principle will easily remark, and the like case which I had found in the rules of the Search after Truth came from the same source. Malebranche in a way avows that there are inconsistencies, but he does not cease to believe that the laws of movement depending on the good pleasure of God, are regulated by his wisdom, and the geometricians would be also almost as much surprised to see these kinds of irregularities coming into nature as to see a parabola to which might be applied the properties of an illipse with an infin itely distant focus. Also such inconsistencies will never be encountered in nature, I think. The better it is known the more it is found to be geometrical. It is easy to judge from this that these inconsistencies do not properly come from that which Male branche asserts they do, to wit : from the false hypothesis of the perfect hardness of bodies, which I admit is not found in nature. For even if we should suppose in it this hardness, regarding it as infinitely quick elasticity, there would result from it nothing which could not be adjusted perfectly to the true laws of nature as regards elastic bodies in general, and never shall we encounter rules so little connected as these in which I have found something to censure. It is true that in composite things sometimes a little change may produce a great effect ; as for example, a spark falling into a great mass of gunpowder is capable of overturning a whole city ; but this is not contrary to our principle, and these cases may be accounted for by even general principles, but as respects ele ments or simple things, nothing similar could happen, otherwise nature would not be the effect of infinite wisdom. Whence it is seen (a little better than in what is commonly said of it), how true physics must be derived really from the source of the divine perfections. It is God who is the final reason of things and the knowledge of God is no less the principle of the sciences than his essence and his will are the principles of beings. The most reasonable philosophers agree in this, but there are very few of them who can make use of it to discover truths of importance. 36 Perhaps these little attempts will arouse some to go much farther. It is sanctifying philosophy to make its streams flow from the fountain of the attributes of God. Far from excluding final causes and the consideration of a being acting with wisdom, it is from thence that all must be derived in physics. This it is which Socrates in the Phaedo of Plato has already admirably remarked, when reasoning against Anaxagoras and other material philoso phers who, after having at first recognized an intelligent principle above matter, do not employ it at all when they come to philoso phize on the universe, and instead of showing that this intelligence does everything for the best, and that this is the reason of the things which it has found good to produce conformably to its ends, try to explain everything by the mere concourse of senseless parti cles, confounding the conditions and instruments with the true cause. It is (said Socrates), as if in order to explain why I am seated in prison awaiting the fatal stroke and am not on the way to the Boeotians or other peoples, whither, it is known, I might have escaped, it should be said that it is because I have bones, tendons and muscles which can be bent as is necessary in order to be seated. My faith (he says), these bones and these mus cles would not be here, and you would not see me in this posture if my mind had not judged that it is more worthy of Socrates to suffer what the laws of the country ordain. This passage in Plato deserves to be read entire, for these are very beautiful and solid reflections. Nevertheless I admit that particular effects of nature may and must be explained mechanically, without forgetting, how ever, their admirable designs and uses which Providence has known how to take care of, but the general principles of physics and even of mechanics themselves depend on the direction of a sovereign intelligence, and cannot be explained without taking it into consid eration. Thus it is that piety must be reconciled with reason, and that good people may be satisfied who fear the results of the mechanical or corpuscular philosophy, as if it would lead us from God and immaterial substances, whereas with the required correc tions and everything well understood, it ought to lead us to him. V. LETTER FROM LEIBNITZ TO AKNAULD IN WHICH HE STATES HIS PERSONAL VIEWS ON METAPHYSICS AND PHYSICS. 1690. [From the French.] SIR I am now on the point of returning home after a long journey, undertaken at the order of my prince for the purpose of historical researches, in which I found certificates, titles and indu bitable proofs sufficient to justify the common origin of the illus trious houses of Brunswick and Este, which Messrs. Justel, du Cange and others had good reasons for calling in question, because there were contradictions and falsities in the historians of Este in this respect, together with an utter confusion of times and persons. At present I think of returning and resuming my former course of life, and having written to you two years ago shortly before my departure, I take the same liberty to-day, to inform myself of your health, and to make known to you how the idea of your eminent merit is always present in my mind. When I was at Eome I saw the denunciation of a new heresy attributed to you, or to your friends, and afterwards I saw the letter of reverend Father Mabillon to one of my friends, in which there was the statement that the defense by the reverend Father Le Tellier of the mission aries against the practical morals of the Jesuits, had given to many people impressions favorable to these Fathers, but that he had heard that you had replied to it and that it was said that you had overthrown by geometrical reasoning the arguments of that Father. All of which leads me to think that you are still in condition to render service to the public, and I pray God that it may be so for a long time to come. It is true that this is to my interest, but it is a praiseworthy interest which may give me the means of learning, whether it be in common with all others who shall read your works, or personally, when your judgments shall instruct me if the little leisure you have may permit me again to hope sometimes for that advantage. As this voyage has in part served to relieve my mind from its ordinary occupations, I have had the satisfaction of conversing on 38 matters of science and erudition with several able men, and I have communicated my personal views, which you know, to some in order to profit by their doubts and difficulties ; and there have been some who, not satisfied with the common doctrines, have found an extraordinary satisfaction in some of my views. This lias led me to write them down that they may be the more easily communi cated, and perhaps I shall cause some copies to be printed some day without my name, merely to send them to my friends in order that I may have their judgment on them. I would like you to be able to examine them first, and for that reason I have made the following abstract : Body is an aggregate of substances, and not properly speaking one substance. It must be, consequently, that everywhere in body there are found indivisible substances, ingenerable and incorruptible, having something corresponding to souls. That all these substances have always been and always will be united to organic bodies diifer- ently transformable. That each of these substances contains in its nature legein continuationis seriei suarwm aperationum and all that has happened or will happen to it. That all its actions come from its own depths, except dependence on God. That each sub stance expresses the entire universe, but one more distinctly than an other, especially each as regards certain things and according to its own point of view. That the union of soul with body, and the operation also of one substance or another consists merely in that perfect mutual accord, expressly established by order of the first creation, in virtue of which each substance following its own laws agrees in what the others demand ; and the operations of the one follow or accompany thus the operation or change of the other. That intelligences or souls capable of reflection and of the kno\vl- edge of eternal truths and of God, have many privileges which exempt them from the vicissitudes of bodies. That for them moral laws must be added to physical. That all things are made princi pally for them. That they form together the republic of the universe, of which God is the monarch. That there is a perfect justice and police observed in this city of God, and that there is no wrong action without chastisement, nor good action without pro portioned recompense. That the more we come to know things, the more we will find them beautiful and conformed to that which a sage would desire. That we should always be content with the 39 order of the past, because it is conformed to the absolute will of God which is known by the event ; but that we must try to render the future as far as it depends on us, conformable to the presump tive will of God or to his commandments ; to beautify our Sparta and to labor to do good, without being depressed, however, when success fails, and this in the firm belief that God can x discover the times most suited for changes for the better. That those who are not satisfied with the order of things cannot boast of loving God as he should be loved. That justice is but the love of the sage. That love is a universal benevolence which the sage fulfils con formably to the measure of reason, to the end of obtaining lasting contentment, which consists in a continual advance to greater per fection, or at least in the variation of a like degree of perfection. As regards physics, it is necessary to understand the nature of force, a thing entirely different from motion, which is something more rel ative. That this force is to be measured by the quantity of effect. That there is an absolute force, a directive force and a respective force. That each of these forces continues in the same degree in the universe, or in each machine not in communication with others, and that the two latter forces, taken together, compose the first or absolute. But that the same quantity of movement is not pre served, since I show that otherwise the perpetual movement would be all found, and that the effect would be more powerful than its cause. It is now some time ago that I published in the Leipsic Ada an essay on physics, to find the physical cause of the movements of the stars. I lay down as basis that all movement of a solid in a liquid, taking place in a curved line or the velocity of which is continually changing, comes from the movement of the liquid itself; whence I draw the inference that the stars have con forming but fiuid orbits. I have demonstrated an important general proposition, viz : that every body that moves with a circu lation which is harmonious (i. e., such that the distances from the center being in arithmetical progression the velocities are in har monious progression, or reciprocal to the distances), and which furthermore has a paracentric movement, that is, of gravity or of levity as regards the same center (a certain law which this attrac tion or repulsion keeps), the said body has the areas necessarily as the times, just as Kepler observed among the planets. Then con- 40 sidering ex observationibus, that this movement is elliptic, I find that the laws of paracentric motion, which motion joined to har monious circulation describes ellipses, must be such that the gravitations are reciprocally as the squares of the distances ; i. e., as the illuminations ex sole. I shall say nothing to you of my calculus of increments or differ ences, by which I determine the tangents, without eliminating the irrational quantities and fractions even when the unknown quan tity is involved in them, and I subject quadratics and the transcendent problems to analysis. And I will not speak either of an entirely new analysis which belongs to geometry and is entirely different from algebra ; and still less of some other things on which I have not yet had time to prepare essays. All of which I should like to- be able to explain to you in few words, in order to have your opinion, which would be of greatest use to me, on them ; if you had as much leisure as I have deference for your judgment. But your time is too precious, and my letter is already sufficiently long. Therefore I close here, and am, sir, Your obedient and humble servant, LEIBNITZ. Venice, March 23, 1690. VI. LETTER ON THE QUESTION, WHETHER THE ESSENCE OF BODY CONSISTS IN EXTENSION. 1691. [From the French.] You ask, sir, the reasons which I have for believing that the idea of body or of matter is other than that of extension. It is true, as you say, that many able men are to-day of the opinion that the essence of body consists in length, breadth and depth. Never theless there are still others who cannot be accused of too much attachment to scholasticism, who are not content with this opinion. M. Nicole, in a certain place in his Essais, states that he is of this number and it seems to him that there is more of bias than of insight in those who do not appear repelled by the difficulties which are therein encountered. It would require a very full discourse to exp