the name in the place of the thing; then the name says more than the definitions; thus to give a good definition of sub stances, we must study natural history.
Th. You see then, sir, that the name gold, for example, signifies not only that which he who pronounces it knows of it, — for example, something yellow, very heavy, — but also what he does not know, and which another may know, i.e. a body endowed with an internal constitution from which pro ceed color and weight, and from which spring still other prop erties admitted to be better known by experts.
§ 25. Ph. It were now to be wished that those practised in physical researches would set down the simple ideas in which they observe that the individuals of each species constantly agree. But the composition of a dictionary of this kind which would contain, so to speak, a natural history, would re quire too many persons, too much time, trouble, and sagacity for such a work ever to be hoped for. It would be well, how ever, to accompany words with small copper-plate engravings of things known by their external form. Such a dictionary would be of much service to posterity and would spare future critics much trouble. Small figures as of the celery-plant (apium), of a Bouquetin (ibex, a kind of wild goat), would be more valuable than long descriptions of this plant or of this animal. And in order to know what the Latins called striyiles and sistrum, tunica and pallium, figures in the margin would be incomparably more valuable than the pretended synonym.es, currycomb, cymbal, dress, cloak, mantle, which show but little of them. For the rest I shall not stop upon the seventh remedy of the abuse of words which is to employ constantly the same term in the same sense, or to give notice when you change it. For we have spoken sufficiently of this subject.
Tli. Rev. Father Grimaldi,1 President of the Mathematical 1 Claudius Philip Grimaldi, with whom Leibnitz became acquainted during his stay in Rome in 1689, and with whom he corresponded, receiving from him after his return to Pekin much interesting information. Cf. Guhrauer, G. W. Freiherr v. Leibtiiz, 2, 05 sq.; Kuno Fischer, Gesch. d. n. Philos., Vol. 2, p. 201, 3d ed., Heidelberg, 1889; Dutens, Lribniz. op. <>m., 4, Pt. I. 81, 88 sq., 88; 6, 106, 128, 227, Gerhardt, Leibniz, philos. Schrift. 3, 166, 174. Schaarschmidt states that such dictionaries as Leibnitz here mentions on the authority of Grimaldi exist in fact among the Chinese, and have been brought to Europe, that the Bonn University library possesses a couple of parts of one such dictionary, and that it must be regarded as an alphabetically arranged orbis pictus. — TR.
CH. xi] ON HUMAN UNDERSTANDING 395 Society at Pekin, tells me that the Chinese have illustrated dictionaries. There is a small nomenclator printed at Nurem berg in which there are such figures for each word which are good enough. Such an illustrated universal dictionary were to be desired, and would not be very difficult to make. As for the description of species, it is properly natural history, and we are working at it by degrees. Were it not for the wars (which have troubled Europe since the first foundation of the Societies or Royal Academies) it would be farther advanced, and already in a condition to profit from our labors; but the great for the most part do not recognize its importance, nor what good they deprive themselves of by neglecting the ad vancement of solid knowledge; and besides they are ordinarily too much indisposed by the pleasures of peace or by the cares of war to weigh things which do not strike them at once.
ESSAY ON UNDERSTANDING BOOK IV. — OF KNOWLEDGE CHAPTER I OF KNOWLEDGE IN GENERAL § 1. Ph. Hitherto we have spoken of ideas and of ivords which represent them; let us come now to the knoidedge, which the ideas furnish, for it rests only upon our ideas. § 2. Knowledge is simply the perception of the connection and agreement, or of the opposition and disagreement, which we find between- two of our ideas. Whether we imagine, con jecture, or believe, it is always that. We perceive, for exam ple, by this means, that white is not black, and that the angles of a triangle and their equality to two right angles have a necessary connection.
Tli. Knowledge has a still more general signification, so that we find it also in ideas or terms, before we reach proposi tions or truths. And it may be said that he who has atten tively looked at more pictures of plants and animals, more diagrams of machines, more descriptions or representations of houses or fortresses, who has read more ingenious romances, heard more curious narratives, this one, I say, will have more knowledge than another, even though there should not be a word of truth in all that which was portrayed or related to him; for the custom he has of representing in his mind many express and actual conceptions or ideas, renders him more fit to conceive what is placed before him; and it is certain that he will be better instructed and more capable than another who has neither seen nor read nor heard anything, provided 398 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv that in these stories and representations he takes nothing as true which is not so and that these impressions do not prevent him elsewhere from distinguishing the real from the imagi nary, or the existent from the possible. This is why certain logicians of the period of the Reformation who were in some measure of the party of the Ramists,1 were not wrong in say ing that the topics or orders of invention (argumenta, as they call them) serve as much for the explication or very detailed description of an incomplex theme, i.e. of a thing or idea, as for the proof of a complex theme, i.e. of a thesis, proposition, or truth. And indeed a thesis may be explained, in order that its sense and force may be well known, without raising the question of its truth or proof, as is seen in sermons and homi lies explaining certain passages of Holy Scripture, or in instruction or lectures upon certain texts of civil or canon law whose truth is presupposed. We can even say that there are some themes which are means between an idea and a proposi tion. These are the questions, some of which demand only yes or no; and they are the nearest to propositions. But there are some also which demand the how, the circumstances, etc., where there is more to be supplied in order to make proposi tions. It is true, it may be said, that in descriptions2 (even of things purely ideal) there is a tacit affirmation of possibility. But it is also true that, as we may undertake the explanation and proof of a falsehood, a method which sometimes serves as its best refutation, the art of description may fall upon the impossible also. Something like this is found in the novelle of the Count of Scandiano followed by Ariosto,3 and in the 1 The Ramists were disciples of Peter Ramns (rf. infra p. 408, note 1). Sehaarschmidt states that Leibnitz probably has in mind chiefly J. H. Alstod, whom he has previously (ff. ante. pp. 311, note 2, 362) cited, and whom lie greatly prized and studied, in whose Systema Ingicse harmonicum, Her- borniae, 1614, p. 69, the arr/vmentum is divided into araumentum simpler (which Leibnitz calls theme inrnmpler.e) and into nrtjumerttum complexitm. The former, according to Alsted, is a "terminus extra omnem dispositionem dirigens materiam " (Leibnitz says: " une chose on idee"), the latter is a " definitio et distributio " (Leibnitz says: " une these, proposition on verite ").
2 I.e. in the sense of nominal definitions, which allow the really impossible.
3 Leibnitz here refers to Matteo Maria Boiardo, c. 1434-1494, Count of Scandiano, and the author of Orlando Innamorato, which a recent writer calls " the most chivalrous poem of the Renaissance," and " a masterpiece of CH. i] ON HUMAN UNDERSTANDING 399 "Amadis of Gaul"1 or other old romances, in the fairy-stories which were again in fashion some years since, in the "True History " 2 of Lucian and in the " Voyages " of Cyrano de Bergerac; 3 to say nothing of the grotesque figures of the painters. So we know stories with the rhetoricians belong in the number of progymnasmata or preliminary exercises. But taking knowledge in a narrower sense, i.e. as knowledge of inventive genius," and which furnished Ludovico Ariosto, 1474-1533, with the theme of his Orlando Furioso. For an account of the two writers and their works, ff. J. A. Symonds, Renaissance in Italy, Pt. IV., Italian Literature, Vol. 1, pp. 45t> 6-7., Vol. 2, pp. 1 sq. New York, H. Holt & Co., 1885.
Through a misunderstanding of Leibnitz's reference to the Count of Scan- diano, Schaarschmidt, in his note to the passage, has wrongly identified him with Tito Giovanni Ganzarini, 1518-1582, Professor of Literature at Modeua, called il Scandianese, from his birthplace, Scandiano. Ariosto published his Orlando Furioso in 151(i, two years before Ganzarini was born, and could scarcely be said to have "followed " an author who was only fifteen years old when the poet himself died. — TR.
1 The Amadis de Gaula, the best of all the old romances of chivalry, was originally written, it is supposed, about 13!X), by Vasco de Lobeira, a Portu guese knight attached to the court of John I. of Portugal, and who died in 1403. The oldest text now extant is in Spanish prose, a version from the Portuguese original, now lost, made by Garcia Ordonez de Montalvo, between 1492 and 1504. Editions of the Spanish version are numerous, the earliest accessible being that of 1519; and there are translations in English, French, German, Italian, and other languages. The best and at present the only readable edition in English is the abridged translation (with a Preface giving an account, not, however, without error, of the work), made from the Spanish, by Robert Southey, London, 1803, 4 vols., 12mo, new ed., London, 1872, 3 vols., l(!mo. f'f. also, V. de Lobeira, Amadis de Gaula, Barcelona, 1847-8, 4 vols., 16mo; George Ticknor, Hist, of Spanish Lit., 3d ed., Boston, 18G3, Vol. 1, pp. 198-207; L. Brannfels, Kritischer Versuch iiber Amadis, Leipzig, 187G. It may be added that the writer of the article, "Amadis of Gaul," in the Encyclop. Brit., 9th ed., argues for the Anglo-Norman origin of the romance, on the ground that all its ideas and materials, its design and machinery, belong to the Anglo-Norman romance-cycle in vogue before Lobeira was born. — TR.
2 The '.UijfloCs ioropc'as Ad-yos ( Verse Ilistorisd) of Lucian is one of the witty satirist's cleverest works, written in easy and elegant Greek, and exhibiting great fertility of invention. It was purposely composed, says Lucian, as a satire on the poets and logographers who have written so many marvellous tales, and contains tilings which neither he nor any one else has ever seen, which not only do not, but cannot, exist, and descriptions of experiences and adventures which are absurd and impossible, chief among which is a voyage to the moon. Lucian himself says that the only true statement in his History is that it contains nothing but lies from beginning to end. It has without doubt supplied hints to, or served as a model for, writers like Rabelais, Swift, and Cyrano de Bergerac. — Tit.
3 Cf. ante, p. 228, note 2. Amid many imaginative extravagances, these Voyages contain a pretty exact knowledge of the philosophy of Descartes. — TR.
400 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv truth, as you, sir, do here, I say it is quite true that truth is always grounded in the agreement or disagreement of ideas, but it is not true in general that our knowledge of truth is a perception of this agreement or disagreement. For when we know truth only empirically, from having experienced it, without knowing the connection of things and the reason there is in what we have experienced, we have no perception of this agreement or disagreement, unless we mean that we feel it in a confused way without being conscious of it. But your examples, it seems, show that you always demand a knowl edge in which one is conscious of connection or opposition, and this is what cannot be granted you. Further, we can treat a complex theme not alone by seeking the proofs of its truth, but also in explicating and otherwise illustrating it, according to the topical order, as I have already observed. Finally, I have a further remark to make upon our definition: viz. that it appears only suited to categorical truths, in which there are tivo ideas, the subject and the predicate; but there is besides a knowledge of hypothetical truths or what may be reduced thereto (as disjunctives and others) in which there is connection between the antecedent and the consequent propo sition; thus more than two ideas may enter therein.
§ 3. Ph. [Let us limit ourselves here to the knowledge of truth and then apply what will be said of the connection of ideas to the connection of propositions, in order to include in one whole the categorical and hypothetical truths.] ISTow I believe that this agreement or disagreement may be reduced to four kinds: (1) Identity or diversity, (2) Relation, (3) Co existence or necessary connection, (4) Real existence. § 4. For the mind perceives immediately that one idea is not an other, that white is not black; § 5. then it perceives their relation by comparing them with each other; for example, that two triangles whose bases are equal and which are found between two parallels are equal. § G. Next there is coexist ence (or rather connection), as fixedness always accompanies the other ideas of gold. § 7. Finally there is real exist ence beyond the mind, as when it is said: God is.
Th. I believe it may be said that the connection is nothing else than the agreement or the relation taken generally. And I have remarked above that every relation is either of comen. i] ON HUMAN UNDERSTANDING 401 parison or concurrence. That of comparison gives diversity and identity, either complete or partial; whereby are consti tuted the concepts of the same or the diverse, the like or unlike. Concurrence contains what you call coexistence, i.e. connection of existence. But when we say that a thing exists or that it has real existence, this existence itself is the predicate, i.e. it has a notion joined with the idea in question, and there is connection between these two notions. The existence of the object of an idea may also be conceived, as the concurrence of this object with the Ego. Thus I believe it may be said that there is only comparison or concurrence; but that the com parison which marks identity or diversity, and the concurrence of the thing with the Ego, are the relations which deserve to be distinguished among others.1 More exact and more pro found researches might perhaps be made; but I content myself here with making remarks.
§ 8. Ph. There is actual knowledge, which is the present perception of the relation of ideas; and there is habitual knowledge, when the mind has so evidently perceived the agreement or disagreement of ideas, and so placed it in its memory, that every time it comes to reflect upon the proposi tion, it is at once certain of the truth it contains without the least doubt. For being capable of thinking clearly and dis tinctly of but one thing at once, men would all be very igno rant if they knew only the actual object of their thoughts; and he who knew most would know but one truth.
Th. It is true that our science, the most demonstrative in deed, being very often obliged to acquire its existence by a long chain of inferences, must involve the memory of a past demonstration which is no longer distinctly in view, when the conclusion is made; otherwise it would always be repeating this demonstration. And even while it lasts it cannot be understood as a complete whole at once; for all its parts can not be present in the mind at the same time; thus always re calling the preceding part to mind, we should never advance to the last which achieves the conclusion. This is the reason also 1 Leibnitz reduces Locke's four kimls of agreement or disagreement to two, and thus generalizes the relation and considers the existence as the concur rence of the object with the Ego. This concurrence Leibnitz explains by his doctrine of pre-established harmony. — Til. 2D 402 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv that without writing it would be difficult properly to establish the sciences, the memory not being sufficiently reliable. But having put in writing a long demonstration, like, for example, those of Apollonius/ and having gone over again all its parts, as if they were examining a chain, link by link, men can assure themselves regarding their reasonings; for which pur pose proofs are also of use, and the result at last justifies the whole. But we see by this that as all belief consists in the memory of past life, of proofs or reasons, it is not within our power or choice to believe or disbelieve, since memory is not a thing depending on our will.
§ 9. Ph. It is true that our habitual knowledge is of two sorts or degrees. Sometimes, truths laid up as it were in the memory no sooner present themselves to the mind, than it sees the relation between the ideas entering therein; but, some times, the mind contents itself with the memory of the convic tion, without retaining the proofs, and often, indeed, without the power to recall them if it wished. It may be thought that this is rather to believe one's memory than really to know the truth in question, and this formerly appeared to me to be a mean between opinion and knowledge, a kind of assurance superior to simple belief based upon the testimony of another. But upon due reflection I find that this knowledge contains perfect certainty. I remember, i.e. I know (memory being only the reviving of something past), that I was once certain of the truth of this proposition, that the three angles of a tri angle are equal to two right angles. Now, the immutability of the same relations between the same immutable things is at present the mediate idea which shows me that, if they wvere once equal, they will be so still. It is upon this ground that in mathematics particular demonstrations furnish general knowledge; otherwise a geometer's knowledge would not ex tend beyond this particular figure which he had drawn while demonstrating it.
Th. The mediate idea of which you, sir, speak, presupposes the fidelity of our memory; but it sometimes happens that our memory deceives us, and that we have not made every neces sary effort, although we now believe we have. This is clearly seen in the examination of accounts. Sometimes there are CH. ij ON HUMAN UNDERSTANDING 403 examiners officially appointed, as at our mines in the Harz, and to make the receivers of the particular mines more atten tive, they have imposed a money, penalty upon every error in calculation; nevertheless they find them in spite of this pen alty. But the more care we employ, the more reliance we can place upon past reasonings. I have devised a method of keep ing accqunts, by which he who collects the sums of the col umns leaves upon the paper traces of the progress of his reasoning, so that he does not reason in vain. He can always revise and correct the last errors without affecting the first: the examination, also, which another desires to make costs, in this way, almost no trouble, because he can examine the very same traces at a glance. There are, besides, means of verifying the accounts of each article, by a very convenient kind of proof, without increasing to any considerable extent the labor of the computation. And all this easily shows that men may have rigorous demonstrations on paper, and have an infinite number of them. But unless we remember that we have been abso lutely accurate, we cannot have this certainty in the mind. And this accuracy consists in an orderly procedure, the observ ance of which in each part is an assurance as regards the whole; as in the examination of a chain by links, in which inspecting each to see if it is strong, and measuring with the hand so as not to skip any, assurance is obtained of the good quality of the chain. And by this means we have all the certitude of which human things are capable. But I do not agree that in mathematics particular demonstrations upon the figure which is drawn furnish this general certitude, as you seem to take it. For you must know that it is not the figures which furnish the proof with geometers, although the style of the exposition may make you think so. The force of the dem onstration is independent of the figure drawn, which is drawn only to facilitate the knowledge of our meaning, and to fix the attention; it is the universal propositions, i.e. the definitions, axioms, and theorems already demonstrated, which make the reasoning, and which would sustain it though the figure were not there. Hence it is that a learned geometer, like Scheube- lius,1 has given Euclid's figures without the letters which might 1 Johaim Scheybl — Latin, Schcnbolius — 1494-1570, was, according to Jocher, Allyemcines Gelchrten-Lcxicun, Leipzig, 1750-51, Vol. 4, p. 257, a professor 404 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv bind them to the demonstration he has put with them; and another, like Herlinus,1 has reduced the same demonstrations to syllogisms and prosyllogisms.
CHAPTER II QF THE DEGREES OF OUR KNOWLEDGE § 1. Ph. Knowledge is then intuitive when the mind per ceives the agreement of two ideas immediately by themselves without the intervention of any other. In this case, the mind takes no pains to prove or examine the truth. As the eye sees the light, the mind sees that white is not black, that a circle is not a triangle, that three is two and one. This knowl edge is the clearest and most certain of which human weak ness is capable; it acts in an irresistible manner without allowing the mind to hesitate. It is knowledge that the idea is in the mind as perceived. Whoever asks for greater certi tude, knows not what he asks.
Th. Primitive truths, which are known by intuition, are of two kinds, like the derivative. They are truths of reason or truths of fact. Truths of reason are necessary, and those of fact are contingent. The primitive truths of reason are those which I call by the general name of identical, because they seem only to repeat the same thing without giving us any information. They are affirmative or negative. The affirma tive are such as the following: Each thing is what it is, and in of mathematics in the University at Tiibingen. His Eudidis sex libriprimi de geometricis principiis gr. et lat. cum commentario appeared at Basle, 1590.
1 Christian Herlinus, whom Leibnitz also mentions toward the end of his Meditationes de, Gog., Ve.rU., ct Ideis, as co-editor with Conrad Dasypodius (15.°>2-1()00, professor of mathematics in Strassburg University, and Canon of St. Thomas' Church) of Euclid, appears to be otherwise unknown. Their joint work, of which Herlinus did the first and fifth books, and Dasypodius the other four, appeared under the title Analysis r/eometrise sex libroram Eudidis, etc., Strassburg, 15(!f!, fol. It is, says Michand, ft/or/. Unirerselle, Vol. 10, p. 500, a pedantic work in which the demonstrations of the Greek geometer are reduced to syllogistic form, so that a proposition of fifteen or twenty lines is spun out into several pages, and is often more involved or at least more difficult to follow. — TR.
en. n] ON HUMAN UNDERSTANDING 405 as many examples as you please, A is A, B is B. I shall be what I shall be. I have written what I have written. And nothing in verse as in prose, is to be nothing or a trifle. The equilateral rectangle is a rectangle.1 The rational animal is al ways an animal. And in the hypothetical: If the regular figure of four sides is an equilateral rectangle, this figure is a rectangle. Copulatives, disjunctives, and other propositions are also sus ceptible of this identicism, and I reckon indeed among the affirmatives: non-A is non-A. And this hypothetical: if A is non-B, it follows that A is non-B. Again, if non-A is BC, it follows that non-A is BC. If a figure having no obtuse angle may be a regular triangle, a figure having no obtuse angle may be regular. I come now to the identical negatives which belong either to the principle of contradiction or to the disparates. The principle of contradiction is in general: a proposition is either true or false: this contains two true statements, one that the true and the false are not compatible in one and the same proposition, or that a 2^'oposition cannot be true and false at once; the other that the opposition or the negation of the true and the false are not compatible, or that there is no mean be tween the true and the false, or rather: it is impossible for a proposition to be neither true nor false. JSTow all this is also true in all imaginable propositions in particular, as ivhat is A cannot be non-A. Again,2 AB cannot be non-A. An equilat eral rectangle cannot be non-rectangle. Again, it is true that every man is an animal, then it is false that any man is found who is not an animal. We may vary these statements in many ways, and apply them to copulatives, disjunctives, and others. As for the disparates, they are the propositions which state that the object of one idea is not the object of another idea; as, that heat is not the same thing as color; again, man and animal are not the same, although every man is an animal. All this may be asserted independently of all proof or of re duction to opposition, or to the principle of contradiction, 1 Erdmann and Jacques omit: " Est un rectangle. L'animal raisonnable est toujonrs un animal. Et dans les hypothetiques: Si la figure reguliere de quatre costes est un rectangle equilateral." — TB.
2 Erdmann and Jacques omit: "Item AB ne sauroit estre non-A. Un rectangle equilateral ne sauroit estre non-rectangle. Item il est vray quo tout liomme est un animal, done il est faux," and instead of the last four words, read: " Item il est vray," etc. — Tu.
406 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv when these ideas are sufficiently understood not to require here analysis; otherwise they are liable to be misunderstood: for in saying, the triangle and the trilateral are not the same, we should be mistaken, since upon proper consideration we find that three sides arid three angles always go together. In say ing, the quadrilateral rectangle and the rectangle are not the same, we should also be mistaken. For it is found that the four- sided figure alone can have all the angles right angles. But we may also say in the abstract that the triangle is not the tri lateral, or that the formal causes of the triangle and of the tri lateral are not the same, as the philosophers express it. They are different relations of one and the same thing.