images. I agree with you that he has limited himself to these axioms, but it was better for him to limit himself to a small number of truths of this nature which appeared to him the simplest and to deduce from them the others which another less exact would also have taken as certain without demonstra tion, than to leave many of them undemonstrated, and what is worse, to allow people the liberty of extending their laxity according to their fancy. You see then, sir, that what you and your friends have said regarding the connection of ideas as the true source of truths needs explication. If you are willing to content yourself with the confused sight of this connection, you weaken the exactness of demonstrations, and Euclid has done incomparably better in reducing all to defini tions and to a small number of axioms. Yet if you wish this connection of ideas to be distinctly seen and expressed, you will be obliged to recur to definitions and identical axioms, as I claim; and sometimes you will be obliged to content yourself with some axioms less primitive, as Euclid and Archimedes have done, when you find difficulty in attaining a 524 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv perfect analysis, and you will do better in that way than to neglect or defer some fortunate discoveries which you can already make by their means: as in fact I have already said to you at another time, sir, that I believe we should not have a geometry (I mean a demonstrative science), if the ancients had not been willing to advance until they had demonstrated the axioms they were obliged to employ.
§ 7. Ph. I begin to understand what a distinctly known con nection of ideas is, and I see clearly that in this sense axioms are necessary. I see clearly also how necessary it is that the method we follow in our researches, when the question is that of the examination of ideas, be regulated by the example of the mathematicians who from certain very clear and easy beginnings (which are nothing else than the axioms and defi nitions) proceed by small degrees and a continual chain of reasoning to the discovery and demonstration of truths that appear at first beyond human capacity. The art of finding proofs, and these admirable methods they have invented for separating and putting in order mediate ideas is what has produced such wonderful and unexpected discoveries. But whether with time a similar method may not be found out useful in respect to other ideas as well as those belonging to magnitude is a question I will not determine. At least, if other ideas were examined according to the ordinary method of the mathematicians, they would lead our thoughts farther than we are perhaps led to imagine. § 8. And this might be done particularly in the case of morality, as I have more than once said.
Th. I believe you are right, sir, and I have been disposed for a long time to make it my business to accomplish your predictions.
§ 9. Ph. In regard to the knowledge of bodies we are com pelled to take a directly contrary path; for having no ideas of their real essences, we are obliged to recur to experience. § 10. But I do not deny that a man accustomed to making rational and regular experiments is capable of forming juster conjectures regarding their still unknown properties than another not so accustomed, but it is judgment and opinion, not knowledge and certainty. This makes me think that physics is incapable of becoming a science in our hands. But experien. xn] ON HUMAN UNDERSTANDING 525 ments and historical observations may be of use to us as regards the health of our bodies and the conveniences of life.
Tli. I admit that physics as a whole will never be a per fect science among us, but we shall not cease to be able to have some physical science, and indeed we have already some specimens of it. For example, magnetology may pass for such a science, for, making a few suppositions based upon experience, we can demonstrate from them by a certain infer ence a number of phenomena which really occur as we see that reason declares. We ought not to hope to give a reason for all experiments, as indeed the geometers have not yet proved all their axioms; but just as they are satisfied to deduce a large number of theorems from a small number of principles of the reason, so is it sufficient that the physicists by means of certain principles of experience give a reason for a multi tude of phenomena and can indeed prove them in practice.
§ 11. Ph. Since then our faculties are not fitted to make us discern the internal fabric of bodies, we must consider that it is enough that they discover to us the existence of God, and a sufficiently extended knowledge of ourselves to instruct us in our duties and in our greatest interests, particularly as related to eternity. And I think I am right in inferring therefrom that morality is the proper science and the important business of mankind in general, as, on the other hand, the different arts tvhich are conversant about different parts of nature are the lot of par ticular men. It may be said, for example, that ignorance of the use of iron is a reason in the countries of America, where nature has spread abroad abundantly all kinds of goods, for the lack of the greatest part of the conveniences of life. Thus very far from despising the science of nature, § 12. I hold, that if this study is directed, as it ought to be, it may be of greater use to the human race than all that has been done up to this time; and he who invented printing, who discovered the use of the compass, and who made known the virtue of quinquina, has contributed more to the propagation of knowl edge and to the advancement of the iiseful conveniences of life, and has saved more people from the grave, than the founders of colleges and hospitals and other monuments of the most exemplary charity, which have been built at great expense.
526 LEIBNITZ'S CRITIQUE OF LOCKE [r,K. iv Th. You could say nothing, sir, more to my liking. True morality or piety, very far from favoring the inactivity of cer tain idle quietists, must impel us to cultivate the arts. And as I said not long since, a better police would be able to bring us some day a much better medical science than that we have at present. We cannot preach this doctrine enough, next to the care for virtue.
§ 13. Ph. Although I recommend experiments, I do not despise probable hypotheses. They may lead us to new dis coveries, and are, at least, a great aid to the memory. But our mind has a great tendency to go too fast and to be satis fied with certain superficial appearances, for lack of taking the necessary time and trouble to apply them to a multitude of phenomena.
Th. The art of discovering the causes of phenomena, or true hypotheses, is like the art of deciphering, in which an ingenious conjecture often greatly shortens the road. Lord Bacon began to put the art of experimenting into precepts, and Chevalier Boyle 1 had a great talent for practising it. But if the art of employing experiments and of drawing con sequences therefrom is not joined with it, we shall never with the utmost cost attain to what a man of great penetration might discover at first sight. Descartes, assuredly such a man, has made a similar remark in one of his letters 2 regarding the method of the Chancellor of England; and Spinoza (whom I do not hesitate to quote when he says a good thing) in one of his letters 3 to the late Mr. Oldenburg, Secretary of the Eoyal Society of England, printed among the posthumous works of this subtle Jew, makes a similar reflection upon a work of Boyle, who, to speak the truth, stops a little too much to draw from a great number of fine experiments no other con- 2 The remark here referred to by Leibnitz as occurring in one of Descartes' letters has not as yet been found in any of those now extant; and, as mention is made of Bacon in Spinoza's remark cited immediately after, it is possible that Leibnitz confounded the two authors, a thing which might readily happen, especially as Leibnitz was often out of the reach of books when composing his works, as probably in this case, cf. ante, p. 8, note 1. — TR.
3 Cf. Spinoza, Opera, ed. Van Vloten and Land, 2, 19: " Sed interim nescio, cur clarissimus vir hoc" (i.e. universal mechanism) " adeo sollicite conetur colligere ex hoc suo experimento; cum jam hoc a Verulamio, et postea a Cartesio satis superque demonstratuin sit." — TR.
CH. xn] ON HUMAN UNDERSTANDING 527 elusion than this which he might take as a principle, viz.: that everything in nature takes place mechanically, a principle which can be rendered certain by reason alone, and never by experiments, whatever their number.
§14. Ph. After having established clear and distinct ideas with fixed names, the great means of extending our knowl edge is the art of rinding mediate ideas which can show us the connection or incompatibility of the extreme ideas. The max ims at least are of no avail in furnishing them. Suppose a man has not an exact idea of a right angle, he will vainly tor ment himself in demonstrating something about the right- angled triangle: and whatever maxims he employs, he will have difficulty in attaining by their aid the proof that the first squares of the sides enclosing the right angle are equal to the square on the hypothenuse. A man might, ruminate upon these axioms a long time without ever seeing more clearly into mathematics.
Tli. It is of no avail to ruminate upon the axioms without having something to which to apply them. Axioms often serve to connect ideas, as, for example, this maxim, that similar extensions of the second and third dimensions are in reason double and triple the corresponding extensions of the first dimension, is of very great use; and the quadrature, for ex ample, of the lune of Hippocrates l springs from it at once in the case of the circles by uniting therewith the application of these two figures the one to the other, when their given posi tion furnishes the opportunity for so doing, as their known comparison promises light thereupon.
1 Hippocrates of Chios, c. 440 B.C., a contemporary of Hippocrates of Cos, the physician (cf. ante, p. 476, note 2), was a celebrated Greek geometer, whose most noted achievement was the discovery of the quadrature of the lune, or the crescent-shaped plane figure produced by drawing two perpendicular radii in a circle and describing upon the line joining their extremities a semicircle. This lune is famous as the first curvilinear space whose area was exactly de termined, and its area is exactly equal to that of the triangle formed by the two radii and the line joining their extremities. For the demonstration of this, cf. Larousse, Grande Diet. Univ. de XIXe Siecle, Vol. 10, p. 791, a, b. On Hippocrates and his services to mathematics, cf. Allman, Greek Geom. from Thales to Euclid, (54 sq.; Gow, A Short Hist, of Greek Math., 1(>4 sq.; H. Suter, Gesch. d. math. Wissenschaften, 2d ed., Vol. 1, pp..'W-IJG, Ziirich, 528 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv CHAPTER XIII OTHER CONSIDERATIONS CONCERNING OUR KNOWLEDGE § 1. Ph. It will be perhaps further appropriate to add, that our knowledge has a close relation to our sight in this, as well as in other things, that it is neither wholly necessary nor wholly voluntary. We cannot fail to see when our eyes are open to the light, but we can turn them towards certain objects, § 2. and consider them with more or less application. Thus when the faculty is once applied, it does not depend upon the will to determine the knowledge; no more than a man can prevent himself from seeing what he sees. But he must employ his faculties, as it is necessary in order to inform himself.
Th. We have spoken before of this point, and established the fact that it does not depend upon man to have this or that opinion in the present state, but it depends upon him to pre pare himself to have it or not to have it eventually, and that thus opinions are voluntary only in an indirect manner.
CHAPTER XIV OF JUDGMENT § 1. Ph. Man would be found without direction in the greater part of the arts of his life, if he had nothing to con duct him from the point where certain knowledge fails him. § 2. He must often be contented with a simple twilight of prob ability. § 3. The faculty of using this is judgment. One is contented with it often of necessity, but often through want of diligence, patience, and skill. § 4. It is called assent or dissent, and is employed when anything is presumed, i.e. when it is taken as true before it is proved. When this is done con formably to the reality of things, it is a right judgment.
Tli. Others call judgment the act which is performed every time a statement is made after some knowledge of a cause; and there will be some also who will distinguish judgment CHS. xin-xv] ON HUMAN UNDERSTANDING 529 from opinion, as not of necessity being so uncertain. But I do not wish to criticise any one regarding the use of words, and it is allowed you, sir, to take judgment as a probable opinion. As for presumption, which is a term of the juris consults, good use with them distinguishes it from conjecture. It is something more, something which must pass for truth provisionally until there is proof of the contrary, while a sign, a conjecture, must often be weighed against another con jecture. Thus it is that he who admits having borrowed money from another, is presumed to pay the debt, unless he shows that he had done so already, or that the debt ceases by some other principle. Presumption is not then in this sense taking before proof, which is not allowed, but taking in advance but with foundation, while awaiting a contrary proof.
CHAPTER XV OF PROBABILITY § 1. Ph. If demonstration shows the connection of ideas, probability is nothing else than the appearance of this connec tion based upon proofs in which immutable connection is not seen. § 2. There are several degrees of assent from assurance down to conjecture, doubt, distrust. § 3. When there is cer tainty, there is intuition in all parts of the reasoning which show its connection; but what makes me believe is some thing extraneous. § 4. Now probability is grounded in its conformity with what we know, or in the testimony of those who know.
Th. I prefer to maintain that it is always grounded in like lihood (vraisemblance) or in conformity with the truth; and the testimony of another is also a thing which the truth has been wont to have for itself as regards the facts that are within reach. It may be said then that the similarity of the probable and the truth is taken either from the thing itself, or from some extraneous thing. The rhetoricians employ two kinds of arguments: the artificial, drawn from things by rea soning, and the non- artificial, based only upon the express testimony either of man or perhaps also of the thing itself.
530 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv But there are mixed arguments also, for testimony may itself furnish a fact which serves to form an artificial argument.
§ 5. Ph. It is for lack of similarity to truth that we do not readily believe that which has nothing like that which we know. Thus when an ambassador told the king of Siam that with us the water was so hardened in winter that an elephant might walk thereon without breaking through, the king said to him: Hitherto I have believed you as a man of good faith; now I see that you lie. § 6. But if the testimony of others can render a fact probable, the opinion of others should not pass of itself as a true ground of probability. For there is more error than knowledge among men, and if the belief of those whom we know and esteem is a legitimate ground of assent, men have reason to be Heathen in Japan, Mahometans in Turkey, Papists in Spain, Calvinists in Holland, and Luther ans in Sweden.
Th. The testimony of men is no doubt of more weight than their opinion, and in reason it is also the result of more reflection. But you know that the judge sometimes makes them take the oath de credulitate, as it is called; that in the examinations, we often ask witnesses not only what they have seen but also what they think, demanding of them at the same time the reasons of their judgment, and whether they have reflected thereupon to such an extent as behooves them. Judges also defer much to the views and opinions of ex perts in each profession; private individuals, in proportion as it is inconvenient for them to present themselves at the appropriate examination, are not less compelled to do this. Thus a child, or other human being whose condition is but little better in this respect, is obliged, whenever he finds him self in a certain situation, to follow the religion of the coun try, so long as he sees nothing bad therein, and so long as he is not in a condition to find out whether there is a better. A tutor of pages, whatever his sect, will compel them each to go to the church where, those who profess the same belief as this young man go. The discussions between Nicole 1 and others on the argument from the great number in a matter of 1 Pierre Nicole, l(>2f>-l(>95, one of the most distinguished of the Port-Royal ists, and, with the exception of Arnauld (c/. ante, p. 4(>.'5, note 4) and Pascal, the most accomplished member of the school, was author with Arnauld of the fa- CH. xv] ON HUMAN UNDERSTANDING 531 faith may be consulted, in which sometimes one defers to it too much and another does not consider it enough. There are other similar prejudyments by which men would very easily exempt themselves from discussion. These are what Tertul- lian, in a special treatise, calls Prescriptiones,1 availing him self of a term which the ancient jurisconsults (whose lan guage was not unknown to him) intended for many kinds of exceptions or foreign and predisposing allegations, but which now means merely the temporal prescription when it is in tended to repel the demand of another because not made with in the time fixed by law. Thus there was reason for mak ing known the legitimate prejudgments both on the side of the Roman Church and on that of the Protestants. It has been found that there are means of opposing novelty, for example, on the part of both in certain respects; as, for example, when the Protestants for the most part abandoned the ancient form of ordination of clergymen, and the Eomanists changed the ancient canon of the Old Testament books of Holy Scripture, as I have clearly enough shown in a discussion I had in writing, and from time to time, with the bishop of Meaux, whom we have just lost, according to the news which came, some days since.2 Thus these censures being mutual, the novelty, although it presents a suspicion of error in these matters, is not a certain proof thereof.
inous L' Art de Penser or the Port Royal Logic. His most important work is his Essais de Morale, Paris, Ki71-74. It was about his De V unite de Veylise ou refutation du nouveau systeme de Jurien, Paris, Ki87, that the theological controversies here alluded to by Leibnitz centred, and " in which the question was considered, whether Roman Catholicism allows itself to engage in the — undoubtedly questionable — argument of the ' majority of professors.'" An account of Nicole's De VuniU de I'er/lise will be found in Bayle's Diet., Eng. transl., Vol. 4, p. 3(53, London, 1737. — TR.
1 Tertullian, 150-160 — 220-240, sought in his De Prsescriptione Hsereticorum to produce a formal general argument against all heresies — "adversns luere- ses omnes " — his object being to prevent heretics, in accordance with certain just and necessary rules (prsescriptiones), from appealing to Scripture in sup port of their views. For an account of the work, cf. Smith and Wace, Diet, of (Jhrist. fiioy., Vol. 4, p. 837 a, sq. — Tn.
2 Leibnitz hero refers to his correspondence with Jacques Benigne Bossuet, 1(527-1704, Bishop of Meaux from 1(181 till his death. This correspondence was irenic in character, and extended, with some interruptions, over a period of about 25 years, but was without result, because Leibnitz would not suffer the freedom of scientific inquiry to be taken away, while Bossuet desired sub jection to the infallible authority of the church. The entire correspondence has been published by Foucher de Careil, (Envn-s de Leibniz, Vols. 1, 2, 532 LEIBNITZ'S CRITIQUE OF LOCKE [HK. iv CHAPTER XVI OF THE DEGREES OF ASSENT § 1. Ph. As for the degrees of assent, we must take care that the grounds of probability we have do not operate beyond the degree of likelihood found therein or which has been found therein when they are examined. For we must admit that assent cannot always be based upon an actual view of the rea sons which have prevailed with the mind, and it would be very difficult even for those * who have an admirable memory Paris, 1859-60. A portion of the same is found in Dutens, Leibnit. op. om., 1, 507 sq. The letters especially referred to are (1) of Leibnitz: Dec. 11, 1699, (Foucher de Careil, CEnvres de Leibniz, 2, 274—277; Dutens, Leibnit. op. om., 1, 594-596), May 14 and 24, 1700 (F. 2, 314-369; D. 1, 612-642); (2) of Bossuet: Jan. 9 and 30, 1700 (F. 2, 278-306; D. 1, 596-611), Aug. 17, 1701 (F. 2, 396-426; D. 1, 657-673). For an account of the controversy, cf. Pichler, Die Theologie des The present passage is important, as it enables us to determine the date of the composition of the New Essays, or at least of this portion of them. Bos- suet died April 12, 1704. This passage must then have been written in the second half of April, 1704; and from other data (for which cf. Guhrauer, Leibniz. Eine Biographic, Bk. II., p. 282 and Anmerkungen z. zweiten Buche, pp. 38-39; and Gerhardt's Introduction to the New Essays, ante, pp. 8, 9, and notes) it is evident that the entire work was substantially completed in 1704, though the revision of the French style, and possibly some minor additions or alterations, occupied Leibnitz to a certain extent after this date.
In this connection it is to be noted that the date given, ante, p. 9, line 15, 1709, should be 1704 (cf. Gerhardt, Leibniz, philos. Schrift., 3, 297, note *), and that Gerhardt's remark, ante, p. 9: "On the other hand, he remarks, well- nigh it seems in the opposite sense," etc., as well as that by the Translator, ante, p. 101, note l,prope.jin.: " As Leibnitz was occupied...with the com position and revision of his Neto Essays, from 1700...to 1709 and perhaps later...possibly even as late as 1714 or 1716,'' should be modified accord ingly. — TR.
1 Gerhardt's text reads: " Sur une veue actuelle des raisons, qui ont prevalu sur Vesprit, et il seroit tres difficile, meme a cenx, qui out une memoire ad mirable," etc. The words italicised above are not found in the texts of Raspe, Erdmann, Jacques and Janet; and Janet restores the sense of "this incorrect phrase "thus: "...Sur une vue actuelle des raisons, comme il arrive chez ceux qui ont une memoire admirable, capable de toujours retenir..." Gerhardt's reading agrees with Locke's text, cf. Philos. Wks., Vol. 2, p. 271, Bonn's ed., and is therefore to be preferred. — TR.
en. xvij UN HUMAN UNDERSTANDING 533 always to retain all the proofs which have compelled them to a certain assent, and which sometimes might fill a volume on a single question. It suffices that they have once examined the matter minutely with sincerity and with care, and that they have, so to speak, cast up the account. § 2. Without this men must be very sceptical, or change their view at every moment, in order to yield themselves to every man who, having exam ined the question of late, offers them arguments which they cannot at once wholly answer, for lack of memory or of appli cation at leisure. § 3. It must be admitted that this often makes men obstinate in error: but the fault is, not that they rely upon their memory, but that they have badly judged be fore. For often the remark that they have never thought otherwise takes the place of an examination and of reason with men. But ordinarily those who have least examined their opinions hold them most tenaciously. Holding to what one has seen is praiseworthy, but not always to what one has believed, because some consideration may have been left behind capable of overturning all. There is perhaps no one in the world who has the leisure, patience, and means of assembling all the proofs on both sides of the question upon which he has his opinions in order to compare these proofs and safely to conclude that nothing more remains for him to know for his more ample instruction. But the care of our life and of our more important interests cannot bear the delay, and it is abso lutely necessary that our judgment be determined upon the points when we are incapable of attaining to a certain knowl edge.
Tli. There is nothing but what is good and solid in what you, sir, have just said. It would be desirable, however, for men to have at certain junctures written abstracts (in form of memoranda) of the reasons which have led them to an impor tant opinion, which they are obliged often to justify after wards to themselves or others. Besides, although in a matter of justice it is not usually allowable to retract the judgments which have been passed, and to revise the verdicts agreed upon (otherwise there would necessarily be perpetual unrest, which would be so much the more intolerable as the accounts of things past cannot always be preserved), yet one is some times allowed upon new light to sue for justice, and also to 534 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv