Th. The bad use of maxims should not cause their general use to be censured; all truths are liable to this disadvantage, that, by uniting them with falsehoods, false or even contradic tory conclusions may be drawn. And in this example there is but little need of these identical axioms to which is im puted the cause of the error and contradiction. This would be seen if the argument of those who concluded from their definitions, that space is body, or that space is not body, were reduced to form. There is, indeed, something exces sive in this inference: body is extended and solid, then exten sion, i.e. the extended is not body, and extension is not a corporeal thing; for I have already remarked that there are superfluous expressions of ideas, or those which do not mul tiply things, as if some one said, by triquetrum I mean a trilateral triangle, and concluded therefrom that every trilat eral is not a triangle. Thus a Cartesian might say that the idea of a solid extension is of this same nature, i.e. that it is superfluous; as in reality, taking extension as something sub stantial, every extension will be solid, or rather every exten sion will be corporeal. As for the vacuum, a Cartesian will be right in concluding from his idea or form of idea that there is none, supposing his idea to be valid; but another will not be 484 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv right in concluding at once from his form that there may be a vacuum, as in reality, although I am not for the Cartesian view, I nevertheless think there is no vacuum,1 and I find that in this example a worse use is made of ideas than of maxims.
§ 15. Ph. It seems at least that from such use as you would make of maxims in verbal propositions they cannot give us the least knowledge of substances existing outside us.
Th. I am altogether of another opinion. For example, this maxim that nature proceeds by the shortest paths, or at least by the most definite, suffices alone to give a reason for nearly the whole of optics, catoptric and dioptric, i.e. of what takes place outside us in the action of light, as I have formerly shown2 and Molyiieux has strongly approved in his Dioptric, which is a very excellent book.3 Pit. It is maintained, however, that when use is made of identical principles to prove propositions in which there are words signifying complex ideas as man or virtue, their use is extremely dangerous, and invites men to regard or receive falsehood as manifest truth. And this is because men think that when the same terms are retained the propositions re volve about the same things, although the ideas which these terms signify are different; so that men taking the words for the things, as they usually do, these maxims commonly serve to prove contradictory propositions.
Th. How unjust to blame the poor maxims for that which should be imputed to the bad nse of terms and to their equiv ocations. By the same reasoning you will blame the syllo gisms because they conclude badly when the terms are equiv ocal. But the syllogism is innocent, because in reality there are then four terms contrary to the rules of the syllogism. By the same reasoning you would also blame the calculations of arithmeticians, or of algebraists, because by putting Xfor V or by taking a for b by inadvertence, they draw therefrom false and contradictory conclusions.
1 Cf. ante, p. 16, and New Essays, Bk. II., chap. 4, ante, pp. 125-127; also Descartes, Princip. Philos., II., §§ 1(5 sq., Veitch's trans., pp. 241 sq.— TR.
2 Leibnitz probably refers to his article Unicum opticse catoptricse et di- optricse principium, published in the " Acta Erud. Lips.," June, 1G82, pp. 185- 1!K), and found in Dutens, 3, 145-150.— TR.
8 Cf. ante, p. 138, note 1. Molyneux's Dioptrica nova was for a long time the chief work on Optics. — TH.
en. vn] ON HUMAN UNDERSTANDING 485 § 19. Ph. I should think at least that maxims are of little use when we have clear and distinct ideas; and others will have it indeed that then they are absolutely of no use, and maintain that any one who in these instances cannot discern truth and falsehood without these kinds of maxims, will not be able to do so by their agency; and our author (§§ 16, 17) shows indeed that they are of 110 use in deciding whether such a one is a man or not.
Tli. If the truths are very simple and evident, and closely approaching the identicals and the definitions, there is but little need of expressly employing maxims to draw from them these truths, for the mind virtually employs them and makes its conclusion all at once without intermediate ideas. But without axioms and theorems already known, mathema ticians would have much trouble in advancing; for in long processes of reasoning (consequences'), it is well to stop from time to time, and to set up, as it were, military columns in the midst of the road, which will serve furthermore to indi cate it to others. Otherwise these long roads will be too inconvenient, and will appear even confused and obscure, while we are unable to discern anything, or to point out what place we are in. It is like going to sea without a compass in a dark night, seeing neither bottom, shore, nor stars; it is like travelling in vast moors in which there are neither trees nor hills nor streams; it is like a linked chain destined for the measurement of lengths, in which there are some hundreds of links, perfectly alike, without a distinction of a bead, or of coarser grains or of larger links or other divisions which might indicate the feet, fathoms, perches, etc. The mind which loves unity in multiplicity then joins together some of the consequences to form from them mediate conclusions, and this is the use of maxims and theorems. By this means there is more pleasure, more light, more memory, more application and less repetition. If some analyst in calculating should choose not to assume these two geometrical maxims, that the sqTiare on the hypothenuse is equal to the two squares of the sides about the right angle, and that the corresponding sides of similar triangles are proportional, thinking that, because we have the demonstration of these two theorems by the con nection of the ideas they contain, he can pass them by easily 486 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv by putting the ideas themselves in their place, he will find himself far removed from his reckoning. But that you may not think, sir, that the proper use of these maxims is confined to the limits of the mathematical sciences alone, you will find that its use is not less in jurisprudence, and one of the prin cipal means of rendering it easier, and of looking at its vast ocean as upon a geographical map, is to reduce a multitude of particular decisions to more general principles. For exam ple, you will find that a multitude of laws, of Digests, of actions or exceptions, of those which are called in factum,1 depend on this maxim, ne quis alterius damno fiat locupletior,* let no one profit by the injury which might happen to an other, a principle which should, however, be expressed with a little more precision. It is true that there is a great distinc tion to be made between the rules of law. I speak of good ones, and not of certain brocards (brocardica)9 introduced by the doctors which are vague and obscure; although these rules also might often become good and useful, if reformed, while with their infinite distinctions (cum siiis fallentiis) they serve only to confuse. Now good rules are either aphorisms or maxims, and under maxims I include both axioms and theo rems. If these are aphorisms which are formed by induction and observation, and not by reason a priori and which clever people have made after a review of established law, this text of the jurisconsult Paulus in the title of the Digests, which speaks of the rules of law, has place: non ex regula jus sumi, 1 Cf. Dif/cst., Lib. XLIV., Tit. VII., 25, Ulpianus, lib. singul. Regularum: "§ 1. — In factum actio dicitur, qualis est (exempli gratia) actio quae datur patrono adversus libertum, a quo contra edictum pra^toris in jus vocatus 2 For a similar expression, cf. Dif/cst., Lib. L., Tit. XVII., 206, Pomponius, lib. 9, ex variis Lectionibus: "Jure natural aequum est, neminem cum alterius detrimento et injuria fieri locupletiorem "; Digest., Lib. XII., Tit. VI., 14; also Lib. XXIII., Tit. III., (i, Pomponius, lib. 14 ad Sabinum, § 2: "...quia bono et sequo non conveniat, aut lucrari aliquem cum damno alterius, aut damnum sentire per alterius luorum "; Lib. XIV., Tit. III., 17, § 4, ad fin. — TR.
3 Cf. Letter 11, to Kestner, Jan. 30, 1711, § 2 (Dutens, 4, Pt. III., 2G4, also Kortholt, Leibnit. epist. ad diversos, Lips. 1734-1742, 3, 251): " Brocardica qua? vocant, vel sunt ipsa solida juris principia, vel regular, quasdam topicse: priora neoossaria sunt: posteriores utiles forent, si satis examinata^, explica- treque habcrentur: pertinent enim fere ad facti qua;stionem. artemque conji- cieudi, ad quam refero etiam interpretandi artificium." C'f. also Leibnitz's Nora methndus dixcendse docendseque jurisprudentix, Pt. II., § 25, Dutens, 4, CH. vn] ON HUMAN UNDERSTANDING 487 sed ex jure quod est regulam fieri,1 i.e. we draw rules from a law already known, in order the better to remember them, but we do not establish the law upon these rules. But there are fundamental maxims constituting the law itself and forming actions, exceptions, replications, etc., which, when they are taught by pure reason, and do not arise from the arbitrary power of the state, constitute natural law; and such is the rule of which I have just spoken, which forbids tortious profit. There are also rules whose exceptions are rare, and which consequently pass as universal. Such is the rule of the Institutes of the Emperor Justinian in § 2 of the title Actions, which declares that when the question concerns corporeal things, the actor does not possess, except in a single case which the emperor states is indicated in the Digests; but he leaves us to search for it. It is true that some read instead of sane uno casu, sane non uno;2 and from one case you can sometimes make many. Among the physicians the late Mr. ]>arner,3 who, in giving us his Prodromus, made us hope for anew Sennertus,4or system of medicine accommodated 1 Of. Dir/cst., Lib. L., Tit. XVII., 1. Paulus [lib. 16 ad Plautium]: " Regula est, quse rera, quae est, breviter enarrat. Non ut ex regula jus sutnatur, sed ex jure, quod est, regula fiat." Gerbardt's text omits tbe name Paulus, and his footnote states that there is a gap in tbe Ms. — TR.
2 Of. Sandars, Inst. of Justinian, Lib. IV., Tit. VI., De actionibus, § 2, ad fin. (p. 431, 8th ed., London, 1888): "Quod genus actionis in controversiis rerum corporulium proditum non est, nam in his is agit qui non possidet: ei vero qui possidet, non est actio prodita per quam neget rem actoris esse. Sane uno casu, qui possidet, nihilominus actoris partes obtinet, sicut in latioribus Digestorum libris opportunius apparebit." The reading "sane uno casu" is adopted and followed by the modern editors. The references to the Digests are, according to Saudars, Lib. VIII., 5, 2, Lib. XXXIX., 1, 15, ed. Mommsen, Berlin: Weidmann, 1870, pp. 267, 378. — TR.
3 Jacob Earner, 1641-1686, a German physician, was professor of chemistry at Padua, and of philosophy and medicine at Leipzig, and the author or com piler of a large number of works which give a sufficiently faithful account of the medicine and especially the chemistry of his time, wholly occupied as it was in the chimerical search for the philosopher's stone. His Prodromus Sen- nerti novi, Augnstfe Vindelicornm, 1674, 4to, was published as the prospectus of a proposed, but never completed, work, which, like that of Sennert, should cover the history of medicine from the earliest times to his own day. — TR.
4 Daniel Seimert, 1572-1637, a celebrated German physician, was professor of medicine in the University of Wittemberg from 1602-1637, and introduced into its curriculum the teaching of chemistry, in spite of strong and continued opposition from those who thought it useless. He disputed the doctrine of the soul held by the Schoolmen, and by maintaining the immateriality of the souls of animals raised against himself many adversaries, among whom was Honora- 488 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv to the new discoveries or views, advances the opinion that the method which physicians ordinarily observe in their systems of practice is to explain the art of healing by treating of one disease after another following the order of the parts of the body human or other, without having given universal precepts of practice common to many diseases and symptoms, and that this involves them, in an infinite number of repetitions; so that we might suppress, in his view, three-quarters of Senner- tus, and abridge the science infinitely by universal propositions, and especially by those with which agrees the KaOoXov irpwrov of Aristotle,1 i.e. which are reciprocal, or approach thereto. I think there is reason in advising this method, especially as regards the precepts wherein medicine is ratiocinative; but in proportion as it is empirical, it is not so easy nor so certain to form universal propositions. Further, there are usually complications in particular diseases, which form, as it were, an imitation of substances, so that a disease is like a plant or an animal, which demands a history by itself, i.e. they are modes or forms of being with which agrees what we have said of bodies or substantial things, a quartan 2 fever being as diffi cult to examine thoroughly as gold or quicksilver. Thus it is well, without detriment to the universal precepts, to seek in the tus Fabri, who accused him of blasphemy and impiety, because he had not seen the bearing of his reasonings. Sennert protested that he had never main tained the immortality of the souls of animals, but it was a strict consequence of his principle.
In his Institutiones medicse et de origine animarum in brutis, Wittemberg, 1611, 4to, Sennert endeavored to unite for the first time the principles of Galen (cf. ante, p. 407, note 1) with those of Paracelsus, 1493-154:1. His Opera omnia, ed. novissima, Lugduni, 1676, 6 vols., fol. Sprengel says he was "the most celebrated of all the conciliators of the seventeenth century," "a man who united to immense erudition and to a perfect knowledge of the ancients great credulity, a taste little refined, and a weak judgment." — TB.
1 Aristotle limited scientific consideration to that which is universally or for the most part valid. His Ka06\ov np^rov is the universal in its original and proper sense, as the essential attribute of individual things in which alone it has any realization, and whose essence consists in just this realization of the universal in them. This universal is conceived of as the cause, and as such becomes the middle term in the syllogism, and constitutes the absolutely essen tial element in logical demonstration, in the absence of which the reasoning has no validity. Cf. Wallace, Outlines of the Philos. of Aristotle, 3d ed., §§ 23, 32-34, pp. 47, 64; Zeller, Philos. d. Griech. II. 2 [Vol. 4], 304 sq., 3d ed.; Prantl, Gesch. d. Lor/ik, 1, 104 sq., 119 sq.; Wiudelband, A Hist, of Philos., trans, by J. H. Tufts, Ph.D., 133-143. New York: Macmillan & Co., 1893. — Tu.
'2 I.e. a fever running in periods of four days. — Tn.
cii. VH] ON HUMAN UNDERSTANDING 489 different kinds of diseases methods of healing, and remedies which satisfy many symptoms and complications of causes, and especially to gather together those which experience has approved. This Sennertus has not sufficiently done, for com petent judges have remarked that the compositions of the receipts he proposes are often made more ex ingenio by estimate than authorized by experience, as would be neces sary if one would be more certain of his case. 1 think then that the better course would be to unite these two ways, and not to complain of repetitions in a matter so delicate and so important as is medicine, wherein I find that we lack what we have in too large measure in my view in jurisprudence, i.e. books of particular cases, and repertories of observations already made. For I think that a thousandth part of the books of the jurisconsults would suffice us, but that we would have none too many in the matter of medicine, if we had thou sands more of well-detailed observations. The fact is, juris prudence is wholly based upon reasons in regard to which nothing is expressly indicated by laws or by customs. For we can always derive it either from law or, in default of this, from natural right by means of the reason. The laws of each country are finished and determined, or may become so; while in medicine, the principles of experience, i.e. the ob servations, cannot be too greatly multiplied in order to give more opportunity to the reason to decipher what nature only half allows us to know. For the rest, I do not know any one who employs the axioms in the way that the clever author of whom you speak does (§§ 16, 17), as if any one, in order to demonstrate to a child that a negro is a man, availed himself of the principle what is, is, by saying: a negro has a rational soul; now the rational soul and man is the same thing, and consequently if having a rational soul he were not a man, it would be false that what is, is, or rather one and the same thing would be or would not be at the same time. For with out employing these maxims, which are not in season here, and do not enter directly into the reasoning, as they also do not advance it in any respect, everybody will be content to reason thus: a negro has a rational soul, whoever has a rational soul is a man, therefore the negro is a man. And if any one assuming that there is no rational soul if it does not 490 LEIBNITZ'S CRITIQUE OF LOCKE [HK. iv appear to us, concluded that infants just born and imbeciles do not belong to the human species (as, in fact, the author states that he has conversed with very reasonable persons who made this denial), I do not think that the bad use of the maxim, that it is impossible for a thing to be and not to be, would delude them, nor that they think of it even in drawing this conclusion. The source of their error would be an exten sion of the principle of our author, which denies that there is anything in the soul of which it is not conscious, while these gentlemen would proceed as far as to deny the soul itself, when others did not perceive it.
CHAPTER VIII OF TRIFLING PROPOSITIONS Ph. I believe, indeed, that reasonable persons have not been disinclined to employ identical axioms in the way of which we have just spoken. § 2. It also seems that these purely identical maxims are only trifling propositions or nugato- rice, as the schools indeed call them. I should not be content to say that they seem thus, did not your surprising example of the demonstration of conversion by the agency of the identi cals1 make me proceed, bridle in hand, thenceforth, when contempt for anything is the question. But I shall tell you that what you allege in their favor proclaims them wholly trifling; viz.: (§ 3) you recognize at first sight that they con tain 110 instruction unless to show a man sometimes the ab surdity in which he is involved.
Th. Do you count that as nothing, sir, and do you not recog nize that to reduce a proposition to absurdity is to demonstrate its contradictory? I indeed believe that you will instruct no man by telling him that he must not deny and affirm the same thing at the same time, but you instruct him by showing him by the force of the consequence, that he does this without thinking of it. It is difficult, in my opinion, always to pass 1 Cf. New Essays, Bk. IV., chap. 2, mite, p. 409. — TB.
CH. vin] ON HUMAN UNDERSTANDING 491 from these apagogical demonstrations, i.e. demonstrations which reduce to absurdity, and to prove everything by the ostensives,1 as they are called; and geometers, who are very curious on this point, have tried it sufficiently. Proclus speaks of it from time to time, when he sees that certain ancient geome ters, coming after Euclid, have found a demonstration more direct (as they think) than his. But the silence of this an cient commentator sufficiently shows that they did not always accomplish it.
§ 3. Ph. You Avill at least admit, sir, that a million proposi tions may be formed at little expense, but also of very little use; for is it not trifling to remark, for example, that the oyster is the oyster, and that it is false to deny it, or to say that the oyster is not the oyster? As to which our author agreeably says that a man who would make this oyster some times the subject, sometimes the attribute, or the predicatum, would justly be like a monkey who should amuse himself by throwing one oyster from one hand to the. other, which pro ceeding could altogether as well satisfy the hunger of the monkey as these propositions are capable of satisfying the understanding of man.
Th. I find that this author, as full of intelligence as gifted with judgment, has every reason in the world for speaking against those who would so use them. But you certainly see how the identicals must be employed to render them useful; viz.: by showing by force of consequences and definitions that other truths which you wish to establish reduce to them.
§ 4. Ph. I know it and I see clearly that they may be applied with much stronger reason to propositions which appear trifling and on many occasions are so, wherein a part of the complex idea is affirmed of the object of this idea, as in the statement: lead is a metal. In the mind of a man who is acquainted with the meaning of these terms and who knows that lead signifies a very heavy fusible and malleable body, there is this use alone, that in saying metal, you indicate to him at once many simple ideas instead of enumerating them one by one. § 5. The same is true when part of the defini- 1 I.e. direct demonstrations, a term used as the opposite of the indirect or apar/ofiical demonstrations, which show the truth of a thing by proving the absurdity of denying it. — TR.
492 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv tion is affirmed of the thing defined; as in the statement: all gold is fusible, supposing you have defined gold as a yellow, heavy, fusible, and malleable body. Again, to say that the triangle has three sides, that man is an animal, that a palfrey (palefroy, an old French word) is an animal which neighs, serves to define the words, but not to teach anything besides the definition. But we learn something from the statement that man has a notion of God and that opium plunges him into sleep.
Th. Besides what I have said of the identicals which are wholly so, we shall find that these semi-identicals have also a particular use. For example, a wise man is always a man; that gives us the knowledge that he is not infallible, that he is mortal, etc. Some one in danger needs a pistol-ball, and lacks the lead to found it in the form he has; a friend says to him: remember that the silver you have in your purse is fusible; this friend will not teach him a quality of the silver, but will make him think of a use he may make of it, in order to have pistol-balls in this pressing need. A large part of moral truths and of the most beautiful sentences of authors is of this nature: they very often teach us nothing, but they make us think at the right time of what we know. That iambic senarius of the Latin tragedy, — Cuivis potest accidere, quod cuiquam potest,1 which might be expressed thus, although less prettily: that which may happen to one, may happen to everybody, only makes us remember the human condition, quod niliil humani a nobis alienum putare debemus.2 This rule of the jurisconsults: qui jure suo utitur, nemini facit injuriam 3 (he who uses his 1 Publilius Syrus, in Seneca, DC Tranquillitate, chap. 11. — TR.
2 Cf. Terence, Ileauton. 1. 1. 23-25: " Homo sum; humani nihil a me alie num puto." — TR.
3 Schaarschmidt states that this rule of the jurisconsults comes from the "Rer/ulse et prsecepta juris," which were customarily appended to the older editions of the Instilutiones. The exact phrase does not occur in the Corpus Juris Civilis; but cf. Digest, Lib. XXXIX., Tit. II., 24, ad fin., where Trehatius says: " non teneri me damni infecti: neque enim existimari, operis mei vitio damnum tibi dari in ea re, in qua jure meo nsus sum "; ib. 26: " Proculus ait, cum quis jure quid in suo faceret," etc.; Digest, Lib. L., Tit. XVII., 55, where Gaius says: " Nullus videtur dolo facere, qui suo jure utitur"; ib. 129, where Paulus says: " Nihil dolo creditor facit, qui suum recipit." — TR.
CH. vni] ON HUMAN UNDERSTANDING 493 own right, injures no one) appears trifling. Bnt it is very useful on certain occasions and makes one justly think of what is necessary. If, for instance, any one raised his house as far as he is allowed by the statutes and usages, and by so doing deprived his neighbor of some view, he would pay this neighbor at once, according to this rule of law, if he ventured to complain. For the rest, propositions of fact, or experiences, like that which states that opium is a narcotic, carry us farther than the truths of pure reason, which can never make us go beyond that which is in our distinct ideas.1 As for this propo sition, that every man has a notion of God, it is from the reason, since notion signifies idea. For the idea of God, ac cording to my view, is innate in all men: but if this notion signifies an idea in which you actually think it, it is a propo sition of fact which depends on the history of the human race. § 7. Finally, to say that a triangle has three sides is not so identical as it seems, for a little attention is required to see that a polygon must have as many angles as sides; it would also have an additional side, if the polygon were not supposed to be closed.
§ 9. Ph. It seems that the general propositions concerning substances are for the most part trifling, if they are certain. He who knows the meanings of the words: substance, man, animal, form, soul, vegetative, sensitive, rational, will form from them many indubitable but useless propositions, partic ularly about the soul, of which we often speak without know ing what it really is. Every one may see an infinite number of propositions, reasonings, and conclusions of this nature in the books of metaphysics, scholastic theology, and a certain kind of physics, the reading of which will teach him nothing more of God, spirits, and bodies than he knew before having run through these books.
Th. It is true, that abstracts of metaphysics and such other books of this character as are commonly seen, teach only words. To say, for example, that metaphysics is the science of being in general, which explains the principles and affec tions emanating from it; that the principles of being are 1 Truths of fact furnish occasion for inductive conclusions which enlarge our knowledge; while truths of reason can only be explicated, or made clearer as to their already existing content. — TR.
494 LEIBNITZ'S CRITIQUE OF LOCKE [>K. iv