In reference to the jus accrescendi — the law of increase — Sandars says, p. 198: " If any one instituted heir died before the testator, or refused to take his share of the inheritance, his share was, in fact, undisposed of. But as the testator was always supposed to have disposed of his whole estate, if he dis posed of any part, this share was divided among all those who entered on the inheritance in proportions corresponding to the share given them by the will. Their claim was called the 'jus accrescendi.' " — TR.
2 Leibnitz here refers to his thesis De conditionibus, which he defended under the presidency of Prof. Leonhard Bchwendendorfer, at Leipzig, in 1065. Guhrauer states (cf. Leibniz, eine Bior/raphie, Pt. I., pp. 36-37) that we do not know the treatise in its original form, but in the revision and rearrange ment of its material made by Leibnitz in 1672, in a collection of his juristic treatises under the title Specimina juris, and which is found in Duteus, Lcib- nit. op. om., 4, Pt. III., 92 sq. — TR.
3 The Dissertatio de Arte Cumbinatoria, cf. Gerhardt, 4, 27 sq., Erdmann. 6 sq., Dutens, 2, Pt. I., 341 sq., appeared at Leipzig in 1666. The pirated edi tion here referred to by Leibnitz was published at Frankfort, 1690, and re viewed by him in the " Acta Erud.," February, 1691. Cf. Guhrauer, Leibniz, eine Bio;/., Pt. I., pp. 37-38, and Anmerkungen z. erst. Buche, pp. 7, 8; CH. in] ON HUMAN UNDERSTANDING 435 of publishing such a piece in my mature years; for although it contains thoughts of some consequence, which I still ap prove, it also contains some which could become only a young student.]
§ 19. Ph. I find that diagrams are a great remedy for the uncertainty of words, but they cannot have place in moral ideas. Most moral ideas are more complex than the diagrams ordinarily considered in mathematics; thus the mind finds it difficult to retain the precise combinations of what enters into moral ideas, in a manner as perfect as is necessary in long de ductions. And if in arithmetic the different stages are not designated by marks whose precise meaning is known, and which last and remain in sight, it is well-nigh impossible to make extended computations. § 20. Definitions furnish some remedy provided they are constantly employed in ethics. And for the rest, it is not easy to foresee what methods may be suggested by algebra or by some other means of this nature to remove other difficulties.
Th. [The late Erhard Weigel,1 a mathematician of Jena in Thuringia, ingeniously invented diagrams to represent moral things; and when the late Samuel Puffendorf,2 his disciple, pub- 1 Erhard Weigel, 1025-1699, a distinguished German mathematician and astronomer, was professor of mathematics in Jena from 1053 on, where he was Leibnitz's first teacher in the subject, when he studied there in 1003, cf. Guhrauer Leibniz, eine Biographic, Pt. I., pp. 20, 82. The Diet of Ratisbon appointed him to organize a commission for the correction of the calendar. He also labored earnestly for the reform of the school system in Germany, travelling througli the country in 1690 for this purpose, cf. Guhrauer, op. cit., Pt. II., pp. 211-214, and the correspondence of Leibnitz and Placcius, from Feb. 12, 1096 on, Dutens, Leibnit. op. om., 0, 01 sq.
Weigel, who was a philosopher, moralist, and an original investigator of the law of nature (Naturrecht) as well as a mathematician, published many works, among them the Expose arithmetique de la morale, or, as the German title runs, Arithmetische Beschreibuny der Moralweisheit von Personen und Sachen, woraus das yemeine Wesen besteht, nach der pythayorischen Kreutz- zahl in lauter tetraktische Glieder einyetheilt, Jena, 1074, 4to, in which he attempted a mathematical exposition of moral philosophy, based upon the Pythagorean principle that the essence of things consists in numbers. Leibnitz thus speaks of this book in the Miscellanea, No. CLIII., Dutens, 6, 325: "M. Wcir/elius a fait un excellent livre en Allemand sur la morale cclairee par les nombres, et je ne crois pas que les Pythagoriciens'ayent rien dit de plus beau sur ce chapitre." For further remarks of Leibnitz on Weigel, cf. Guhrauer, Leibnitz's deutsche Schriftcn, 2, 473 sq. — TR.
- Samuel Pufendorf, 1632-1094, was one of the greatest German publicists and historians, and one of the founders of the science of public law. He studied at Jena under Weigel, with whom he formed an intimate friendship, 430 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv lished his " Elements of universal Jurisprudence " sufficiently conformed to the thoughts of Weigel, there was added thereto in the Jena edition the " Moral Sphere "of this mathematician. But these diagrams are a kind of allegory nearly like the table of Cebes,1 but less popular and serving the memory in the re tention and arrangement of its ideas rather than the judgment in the acquisition of demonstrative knowledge. They do not cease to have their use in arousing the mind. Geometrical diagrams appear simpler than moral things; but they are not so, because continuity includes the infinite from which it must be chosen. For example, to cut a triangle into four equal parts by two straight lines perpendicular to each other is a question apparently simple but really quite difficult. It is not the same in questions of morality since they are determinable and to whose teaching and influence he largely owes the orderly method and mathematical precision and dryness which characterize his style, and that independence of character which never yielded to the " ipsedixitism " of other writers, however high their position and authority. Among his works are: Elementa jurisprudentiss universalis, cum appe.ndice de Sphsera morali (of Weigel), Hag. Com., 1660, 12mo — also Jena, Ki(iO, " bei Meyer "; the ed. here meant by Leibnitz, according to Schaarschmidt, who states that in the 2d Jena ed., 1GG9, the Sphsera moralis occurs, p. 313 sq., — the book which obtained for him from the elector Charles Louis, to whom it was dedicated, the newly created chair of the law of nature and of nations at Heidelberg; De statu imperil yermanici, Geneva, 1607, — the book which first called forth Leibnitz's aversion and criticism, — small in bulk, but great in significance, in which he criticised the political organization of the empire, suggested a remedy for the evils therein, and revealed himself as a consummate statesman, subsequent events proving the justness of his conclusions; and the work on which his fame chiefly rests, De jure natures ct gentium, 1672, trans, into French, with notes, by Barbeyrac, Amsterdam, 1712, and into English by Basil Kennett, London, 1729, and resume of the same, De officio hominis et civis, 1675.
For Leibnitz's criticism of Pufendorf and bis work, — the severest, perhaps, he ever made on any one, and through which he is, to a considerable extent, responsible for the failure of posterity justly to estimate and acknowledge its debt to him, — c/. letter to Kestner, No. 7, § 2, Dutens, 4, Pt. III., 2(51; Monita qitsedam ad <S'. Puffendorfii principal, ibid., 275-283; letter to S. Kor- tholt, No. 3, Dutens, 5, 305; letters to Bierling, Gerhardt, Leibniz, philos. Schrift., 7, 487, 488, 490, 499, 506, 511, Dutens, 5, 355, 358, 361, 371, 386, 390 — Dutens gives Bierling's letters to Leibnitz also; letter to Bourguet, G. 3, 590, Erdmann, 734, b., Dutens, 2, Pt. I., 334. For a comparison of the views of Leibnitz and Pufendorf on the ultimate foundations of natural and public, law, c/. Monita qusedam above cited, and Guhrauer, Leibniz, eine Bio;/., Pt. I., 223 1 Cebes of Thebes, a disciple of Socrates, distinguished for his virtue and love of truth; c/. Plato, Fhxdo, 59 C, 60 C sq., 63 A. His iuv«f, Tabula, or ' picture,' is, according to Zeller, Philos. d. Griech., II., 1 [Vol. 3], 242, 4th ed., 1889, " certainly spurious." — Tit.
en. in] ON HUMAN UNDERSTANDING 437 by reason alone. For the rest it is not the place here to speak de proferendis scientiae demonstrandi pomoeriis, and to propose true means of extending the art of demonstration beyond its ancient boundaries which have been nearly the same up to the present time as those of mathematics. If God gives me the time necessary for it, I hope some day to publish an essay upon this subject, putting these means into effective use with out limiting myself to precepts.] l Ph. [If you carry out this plan, sir, and as it should be, you will infinitely oblige the Philalethes like myself, i.e. the class who sincerely desire to know the truth.] For truth is naturally agreeable to the mind, and there is nothing so deformed and so incompatible with the understanding as a lie. But men must not be expected to apply themselves much to these discoveries, so long as the desire and the esteem of riches or of power shall lead them to espouse opinions authorized by fashion, and to seek in consequence arguments either to make them pass as good or to varnish over and cover their deform ity. And while the different parties make all men whom they can get into their power receive their opinions without exam ining whether they are true or false, what new light can be hoped for in the sciences belonging to morals? This part of the human race which is under the yoke, ought to expect in most places in the world instead of that light, darkness as thick as that of Egypt, were not the candle of the Lord itself found present in the mind of men,2 a sacred light which all human power cannot wholly extinguish.
Th. [I do not despair that at some time and in a more tran quil country men will betake themselves more to reason than they have done. For in fact we must despair of nothing; and 1 Leibnitz's plan to extend and perfect the science of demonstration, or that part of logic which is concerned witli the methods of proof, and which in his view was conceived up to his own time too narrowly as virtually identical with the method of mathematics, is closely connected, but not identical, with his Universal Characteristic; cf. <tnte, pp. 292, note 1,:>75, note 1. Leibnitz, however, never carried his plan into execution, but left some preliminary essays or sketches which serve to indicate what he thought desirable in this direction, and what he purposed himself some day to provide. Cf. Prtceptes pour avancer les sciences, Erdmann, Leibnit. op. philos. 1(55-171, published in a more complete form in Gerhardt, Leibniz, philos. Schrift., 7, 157 sq.; and the fragment without title treating of the means of philosophical demonstra tion, O., 7, '2!>!»-:501. — Tu. 2 Cf. Proverbs '20:27. — TR.
438 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv I believe that great changes for evil and for good are reserved for the human race, but in the end more for good than for evil. Suppose we see some day a great prince, who, like the ancient kings of Assyria or of Egypt or like another Solomon, reigns a long time in a profound peace, and that this prince, loving virtue and truth and endowed with a great and solid mind, takes it into his head to make men happier and more accommodating among themselves and more powerful over natiire; what wonders will he not do in a few years? For it is certain that in this case more would be done in ten years than in a hundred or perhaps a thousand while letting things follow their ordinary course. Moreover, if the path were opened once for all, many people would enter therein as the geometers do, though this would be only for their pleas ure and to acquire fame. The public better civilized will some day turn more than it has hitherto done to the advance ment of medicine; natural histories of all countries will be published like almanacs or like the Mercures galans;1 no val uable observation will be left without being registered; those who will apply themselves thereto will be aided; the art of making such observations will be perfected, and further that of employing them to establish aphorisms. The time will come when the number of good physicians having become greater and the number of people of certain professions of which there will then be less need having become proportion ally less, the public will be in a condition to give more encouragement to natural research, and above all to the ad vance of medicine, and then this important science will be carried far beyond its present condition and will grow apace. I believe indeed that this business of the police should be the object of the greatest care of those who govern, after that of virtue, and that one of the greatest fruits of good morals or politics will be to produce a better (science of) medicine, 1 " Mercure galant," the title of different periodicals treating of politics, literature, and containing announcements, and news of various kinds; in par ticular, the title of a journal founded by De Vise in 1672, and continued, with several short periods of suspension, under various names and editors, till 1853. Leibnitz, in a letter to Sebastian Kortholt, Jan. 9, 1711, inquires whether a complete set can be obtained, and at what price: " Discere etiam velim, an totus Mercurius Gallant, ut sic dicam, vulgo Mercure Galant a Dei'ixseo nuper extincto a multis annis compositus, tolerabili pretio haberi possit, et quanti? " (cf. Dutens, Leibnit. op, om. 5, 315). — TR.
OH. in] ON HUMAN UNDERSTANDING 439 when men shall begin to be wiser than they are and the no bility shall learn the better to employ their wealth and their power for their own welfare.]
§ 21. Ph. As for the knowledge of real existence (which is the fourth kind of knoidedge) it must be said that we have an intuitive knowledge of our existence, a demonstrative knowledge of that of God, and a sensitive knowledge of other things. We shall speak of these fully in what follows.
Tli. [You could say nothing more justly.]
§ 22. Ph. Having now spoken of faiowledge, it appears ap propriate the better to discover the present condition of our mind that we should consider a little the dark side and take knowledge of our ignorance: for it is infinitely greater than our knowledge. The causes of this ignorance are as follows: (1) Want of ideas; (2) Inability to discover the connection between the ideas we have; (3) Neglect to trace and examine them with exactness. § 23. As for the want of ideas, we have as simple ideas only those coming to us from the senses [in ternal or external]. Thus as regards an infinite number of the creatures of the universe and their qualities we are like the blind as regards colors not indeed possessing the faculties necessary in order to their knowledge; and according to all appearances man holds the lowest rank among intellectual beings.
Th. [I do not know but that there are also some below us. Why should we degrade ourselves unnecessarily? Perhaps we hold a sufficiently honorable rank among rational animals; for superior genii may have bodies of another kind so that the name animal cannot agree with them. We cannot say whether our sun among the great number of other suns has more above than below it, and we are well placed in his sys tem: for the earth occupies the middle course between the planets, and its distance appears well chosen for a contem plative animal who should inhabit it. Besides we have in comparably more reason to praise than to complain of our lot, the majority of our evils rightly being imputed to our fault. Above all we should be very wrong to complain of the defects of our knowledge, since we avail ourselves so little of that which charitable nature presents to us.]
§ 24. Ph. It is, however, true that the extreme distance of 440 LEIBNITZ'S CRITIQUE OF LOCKE [BK. IT nearly all parts of the world which are exposed to our sight conceals them from our knowledge, and apparently the visible world is only a small part of this immense universe. We are confined in a small corner of space, i.e. in the system of our sun, and yet we do not know even what takes place in the other planets which as well as our ball revolve about it. § 25. This knowledge escapes us by reason of size and dis tance; but other bodies are concealed from us because of their minuteness; and these are the ones which it would most con cern us to know; for from their contexture we could infer the use and operation of those which are visible, and know why rhubarb purges, hemlock kills, and opium produces sleep. Thus § 26. whatever distance human industry may advance experimental philosophy upon physical things, I am compelled to believe that we can attain upon these matters a scientific knowledge.
Tli. [I fully believe that we shall never advance so far as will be desirable; but it seems to me that some considerable progress will be made in time in the explication of certain phenomena, because the large number of experiments which we are led to make may furnish us data more than sufficient, so that only the art of employing them will be lacking, (an art) the small beginnings of which I do not despair of seeing pushed forward, since the infinitesimal analysis1 has given us the means of uniting geometry with physics, and dynamics has furnished us with the general laws of nature.]
§ 27. Ph. Spirits are still further removed from our knowl edge; we cannot form any idea of their different orders, and yet the intellectual world is certainly grander and more beau tiful than the material world.
Tli. [These worlds are always perfectly parallel as regards efficient causes, but not as regards final. For in proportion as spirits rule in matter they produce therein wonderful arrange ments. This appears in the changes men have made, in order to embellish the earth, as little gods imitating the great archi tect of the universe, though only by employing bodies and 1 Sir Isaac Newton, 1(542-1727, in his Principia, was the first to apply in a systematic way the infinitesimal calculus to physics, after that Galileo, 15G4- 1G42, had paved the way for a theory of universal gravitation by his deter mination of the law of acceleration in falling bodies. — TR.
CH. in] ON HUMAN UNDERSTANDING 441 their laws. What may not be conjectured concerning this immense multitude of spirits which surpass us? And as spirits form all together a kind of state under God, whose gov ernment is perfect, we are far removed from comprehending the system of this intelligible world and from conceiving the punishments and rewards prepared for those who deserve them according to the most exact standard, and from imagin ing what eye has not seen, nor ear heard, nor has ever entered into the heart of man. But all this shows that we have all the distinct ideas necessary for knowing bodies and spirits, but not sufficient detail of facts, nor senses penetrating enough to distinguish confused ideas or sufficiently extended to per ceive them all.]
§ 28. Ph. As for the connection, the knowledge of which is wanting to us in the ideas which we have, 1 was going to say to you that the mechanical affections of bodies have no connection with the ideas of colors, sounds, smells, tastes, pleasure, and pain; and that their connection depends only upon the good pleasure and the arbitrary will of God. But I remember that you think there is a perfect correspondence, although this is not always an entire resemblance. But you recognize that the too great detail of small things entering therein hinders us from discerning that Avhich is concealed, though you hope still that we shall make much advance there in; and that thus you do not Avish to say with my illustrious author (§ 29), that it is labor lost to engage in such a search, from fear that this belief would injure the growth of science. I should have spoken also of the difficulty which has hitherto been found in explaining the connection between the soul and the body, since a thought cannot be conceived as producing a motion in the body, nor a motion as producing a thought in the mind. [But since I comprehend your hypothesis of pre- established harmony, this difficulty of which they despaired appears to me removed at once, and as it were, by magic.]
§ 30. There remains then the third cause of our ignorance, viz. that we do not follow the ideas we have or may have, and do not apply ourselves to finding intermediate ideas. Thus it is that we are ignorant of mathematical truths, al though there is no imperfection in our faculties, nor any incertitude in the tilings themselves. The bad use of words 442 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv has contributed the most to prevent us from finding the agree ment or disagreement of ideas; and the mathematicians who form their thoughts independently of names and accustom themselves to present to their minds the ideas themselves in stead of their sounds, have thereby escaped a great deal of embarrassment. If men had acted in their discoveries in the material world as they have been wont to do in regard to those having reference to the intellectual world, and if they had been wholly lost in a chaos of terms of an uncertain mean ing, they would have disputed endlessly about the zones, the tides, the building of vessels, and the routes; they would never have gone beyond the line, and the antipodes would still be as unknown as they were when to maintain them was declared a heresy.
Th. [This third cause of our ignorance is the only blamable one; and you see, sir, that the despair of further advance is therein contained. This discouragement does much injury; and persons of ability and importance have hindered the progress of medicine by the false persuasion that it is labor lost to work therein. When you see the Aristotelian philoso phers of past time speak of meteors, as the rainbow, for example, you will find that they believed they should not think alone of explaining distinctly this phenomenon; and the attempts of Maurolycus,1 and afterwards of Marc Antony de Dominis 2 appeared to them like the flight of Icarus. But the 1 Francesco Maurolico, 1494-1575, a celebrated Italian mathematician, whose father, a Greek, came originally from Constantinople, taught mathe matics at Palermo, Naples, Rome, and Messina. In his Treatise on Conies lie sought for the first time to deduce the properties of these curves from the corresponding curves in the circle of which they are the perspective. He first introduced secants into trigonometrical calculations, constructing and publish ing a table of them in his Theodosii sphxricorum, Messina, 1558, fol. He also investigated the structure of the eye, seeking therein the explanation of the phenomena of vision. He described exactly the course of the rays of light across the cornea and the crystalline lens, but stopped in utter astonishment when lie discovered that his theory led him to admit that the images of objects upon the retina are found inverted. The work of Maurolico, here referred to by Leibnitz, is his Problemata ad perspectivam et iridem pertinentia, appended to his Photismi [or Theoremata] delumine etumbraadperspectiramradiorum incidentmrn, Venice, 1575, 4to, new ed., with notes of Clavius, Lyons, 1(>13. — TR.
2 M. Ant. de Dominis, 156(5-1(524, a native of Dalmatia, was professor of eloquence, philosophy, and natural sciences at the University of Padua. Though archbishop of Spalatro, he was republican in his views of the consti tution and administration of the church and strongly opposed to the doctrine cir. in] ON HUMAN UNDERSTANDING 443 sequel has disabused the world of this. It is true that the bad use of terms has caused a good part of the confusion found in our knowledge, not only in ethics and metaphysics, or in what is called the intellectual world, but also in medi cine where this abuse of terms increases more and more. TVe cannot always aid ourselves with figures as in geometry: but algebra shows us that great discoveries may be made without recurring always to the ideas themselves of things. In ref erence to the pretended heresy about the antipodes I will say in passing that it is true that Boniface,1 Archbishop of May- ence, accused Virgil of Salzburg,2 in a letter, which he wrote of papal supremacy. While in England he published his views in his De republica ecclesiastica, London, 1617-1620, reprinted Frankfort, 1658, both eds., 3 vols., fol. For some specimen quotations from this book, cf. Larousse, Grande Diet. Univ. de XIXe Siecle, Vol. 6, p. 10(58, a. Returning to Italy, he and his book were condemned as heretical, in spite of his retraction of his errors, and he was imprisoned, and probably poisoned, in the Castle of St. Angelo, and his body exhumed and burned with great ceremony in the Campo de' Fiori in Rome in January, 1625.
In his De radiis visits et lucis in vitris perspectivis et iride, Venice, 1611, 4to, cited with high praise by Newton in his Optics, he presented to the world the first attempt at a theory of the rainbow. He successfully reflected rays of light through the interior of raindrops before making them come out again, but could not account for the angle at which the observer sees the ray of the bow. On his theory, cf. Venturi, Commentarii sopra la storia e le teorie dell' ottica, Bologna, 1814, Vol. 1, p. 149. Of the De radiis visus et lucis, chap. 9 and chap. 13, "Vera iridis tola r/eneratio explicatur," are printed in Libri, Histoire des Sciences math, en Italic depuis la Renaissance jusqu'a la Jin du XVIIo siecle, 1838-1841, 4 vols., 8vo, Vol. 4, p. 436 sq. Leibnitz thus speaks of him in the Miscellanea Leibnitiana, ed. Feller, No. CXV., p. 198 (cf. also Dutens, Leibnit. op. om., 6, 319): " Elegantissime materiam tractavit de- monstrationibusque mathematicis confirmavit. Iridis etiam et nonnullorum aliorum ejusmodi meteorum causam ab Aristotele assignatam recte ex- pendit." — TR.
1 Boniface (Wiufrid, the Anglo-Saxon Benedictine monk, named Bonifa- cius by Pope Gregory II.), 680-755, the apostle to the Germans, became arch bishop of Mayence (Mainz) in 748. On his life and labors, cf. Neander, Hist, of the Christ. Reliy. and Church, 3, 46 sq.; Smith and Wace, Diet, of Christ. Biog., Vol. 1, p. 324. His Opera quse extant omnia, ed. J. A. Giles, Londini, 1844, 2 vols., 8vo; also in Migne, Patrol, s. Lat., Vol. 89, Paris, 1863. His letters were edited, with notes, by the Jesuit Nic. Serarius, 1555-1609, Mayence, 1605 and 1629, 4to; and by Wiirdtwein, Moguntise, 1789, fol.— TR.
2 St. Fergil, best known by the Latinized form of his name, — Virgilius, — was an Irish priest from Aghavoe, Queen's Co., who came to Bavaria, became at first abbot of St. Peter's monastery in Salzburg, and finally, on the martyr dom of Boniface, 755, and the death of John, bishop of Salzburg, was appointed and consecrated bishop, June 13, 766 or 767. One of his last acts as bishop was to visit his entire diocese and to pay a long deferred visit to Cariuthia. He 444 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv to the Pope against him on this subject, and that the Pope replied thereto in a way which showed that he employed the term quite in the sense of Boniface; but it does not appear that this accusation has had any results. Virgil has always held his own. The two antagonists pass for saints, and the savants of Bavaria who regard Virgil as an apostle of Carin- thia and the neighboring countries, have justified their mem ory of him.]
CHAPTER IV OF THE REALITY OF OUU KNOWLEDGE § 1. Ph. Some one who has not understood the importance of having good ideas, and of understanding their agreement or disagreement, will think that in reasoning upon them so carefully we have been building castles in the air, and that there will be in our entire system only the ideal and imaginary. An extravagant man, whose imagination is heated, will have the advantage of possessing ideas more vivid and in greater num ber, thus he would also have more knowledge. There will be as much certitude in the visions of an enthusiast as in the