obtain what is called restitutio in integrum l contrary to the decision that has been given. And likewise in our own affairs, especially in matters very important, where it is still allowable to embark or to put back, and where it is not preju dicial to suspend their execution and to proceed bridle in hand, the decisions of our minds based upon probabilities should never so pass in rein judicatam,2 as the jurisconsults call it, i.e. to a settlement, that we may not be disposed to the revision of the reasoning when new counter reasons of weight present themselves. But when there is no more time for delib eration, we must follow the judgment we made with as much firmness as if it were infallible, but not always with so much strictness.3 § 4. Ph. Since, then, men cannot avoid exposing themselves to error in judgment and having different opinions, since they cannot look at things from the same points of view, they must maintain peace between themselves and the duties of humanity amid this diversity of opinions without claiming that another should promptly change a rooted opinion upon our objec tions, especially if there is room for supposing that his adversary acts from interest or ambition or from some other private motive. Most frequently those who would impose upon others the necessity of yielding to their opinions have examined things with but little thoroughness. For those who have entered beforehand sufficiently into the discussion to extricate themselves from doubt are so few in number, and find so little reason to condemn others, that nothing violent is to be expected on their part.
Th. Really that which one has the most right to censure in men is not their opinion, but their rash judgment in censuring 1 Cf. Paulus, Sententiarum, Lib. I., Tit. VII. 1.: "Integri restitutio est ro- dintegrandsB rei vel causse actio. 2. Integri restitution em prajtor tribuit ex his causis, qua? per metum, doluin et status permutationem, et jnstum errorem, et abseiitiam necessariam, et infirmitatem aetatis gesta esse dicuntur; " also Digest, Lib. XLIL, Tit. I. 33.
'2 Cf. Digest, Lib. XLIL, Tit. I. 1: " Res judicata dicitnr, quse finem con- troversiam pronunciations judicis accipit: quod vel condemnatione vel abso- lutione eontingit." — Tit.
3 Janet cites as a parallel passage Descartes, Discours de la Methodc, Ft. III.: " Ma seconde maxinie etait d'etre le plus ferine et le plus resolu eu nies actions que je pourrais, et de ne suivre pas moius constaniment les opinions les plus douteuses lorsque je m'y serais uue fois determine que si elles eussent ete tres-assurees." — Tu.
en. xvi] ON HUMAN UNDERSTANDING 535 that of others, as if it were necessary to be stupid or wicked to judge differently from themselves; a condition of things which, in the authors of these passions and hatreds who spread them among the public, is the effect of a mind haughty and unfair, which loves to rule and cannot suffer contradiction. uSTot that there is not, in truth, reason very often for censuring the opinions of others, but it must be done in a spirit of fair ness, and sympathy with human weakness. It is true that we are right in taking precautions against bad doctrines, which are influential upon manners and upon practical piety: but we must not attribute them to people to their prejudice without having good proofs of the same. If fairness wishes to spare persons, piety demands the representation, where it is fitting, of the bad effects of their dogmas when they are in jurious, as those are which are contrary to the providence of a perfectly wise, good, and just God, and contrary to that immortality of souls which renders them susceptible of the effects of his justice, not to speak of other opinions dangerous as regards morality and the police. I know that excellent and well-meaning men maintain that these theoretic opinions have less influence upon practice than is thought, and I also know that there are persons of an excellent disposition whom these opinions will never make do anything unworthy of themselves: as also those who have reached these errors by speculation, are by nature wont to be farther removed from the vices to which men in general are susceptible, besides the fact that they are careful of the dignity of the sect in which they are, as it were, chiefs; and it may be said that Epicurus and Spinoza, for example, have led a life wholly exemplary. But these reasons cease most frequently in their disciples or imitators, who, believing themselves released from the trouble some fear of an overseeing Providence and of a menacing future, give loose reins to their brutish passions, and turn their mind to the seduction and corruption of others; and if they are ambitious and of a disposition somewhat harsh, they will be capable, for their pleasure or advancement, of setting on fire the four corners of the earth, as I have known from the character of some whom death has swept away. I find also that similar opinions insinuating themselves little by little into the minds of men of high life who rule others and upon 536 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv whom affairs depend, and slipping into the books in fashion, dispose all things to the general revolution with which Europe is threatened, and accomplish the destruction of what still remains in the world of the generous sentiments of the ancient Greeks and.Romans, who preferred love of country and of the public good, and regard for posterity to fortune, and even to life. These public spirits, as the English call them, are fast diminishing, and are no longer in fashion; and they will diminish still faster when they are no longer sus tained by the good morality and true religion which even natural reason teaches us. The best of the opposite character who are beginning to rule have no other principle than that they call honor. But the mark of the honest man and of the man of honor with them is only to do no baseness as they understand it. And if for the sake of power or through caprice anyone poured forth a deluge of blood, if he turned every sense upside down, that would be counted as nothing, and a Herostratus * of the ancients or a Don Juan in the " Festin de Pierre " 2 would pass for a hero. Boldly they scoff at the love of country, they ridicule those who care for the public, and when any well-mean ing man speaks of what will become of posterity, they reply: we shall see when the time comes. But these persons will pos sibly experience themselves the evils they think reserved for others. If, however, this disease of an epidemic mind whose bad effects begin to be visible is corrected, these evils will perhaps be prevented; but if it goes on increasing, Providence will correct men by the revolution itself which must spring there from: for whatever may happen, everything will always turn out for the better in general at the end of the account, although that ought not and cannot happen without the punishment of those who have contributed even to the good by their bad acts. But I return from a digression into which the consideration of truthful opinions and of the right of censuring them has led me.
1 Herostratus, an Ephesian, who, for the sake of making his name famous, as he himself confessed on being put to torture, set fire to the temple of Ar temis at Ephesus, on the night in which Alexander the Great was horn, 2 The Don Juan ou le Festin de Pierre, 1665, a comedy of Moliere, 1622- 1673, the principal character of which is Don Juan. The play, written in prose, was versified in 1677, at the request of Moliere's widow, by Thomas en. xvi] ON HUMAN UNDERSTANDING 537 Xow as in theology censures go very much farther than else where, and as those who lay great stress upon their orthodoxy, often condemn their adversaries, to whom those in the same party who are called syncretists by their adversaries are opposed, this opinion has caused civil wars to spring up between the rigid and condescending in one and the same party. But, as to refuse eternal salvation to those who are of another opinion is to encroach upon the rights of God, the wisest of those who condemn, only indicate the peril in which they think they see erring souls, and leave to the peculiar mercy of God those whose wickedness does not render them incapable of profiting therefrom, and on their part believe themselves obliged to make all imaginable efforts to withdraw them from a condition so dangerous. If these persons who thus judge of the perils of others have come to this opinion after a suitable examination and there are no means of dis abusing them of it, their conduct cannot be censured so long as they use only fair means. But as soon as they go farther, they violate the laws of equity. For they should consider that others persuaded like themselves have an equal right to maintain their views, and even to spread them if they think them important. Opinions must be excepted which teach crimes that should not be allowed, and which it is right to suppress by stringent means, if it should be true, indeed, that he who maintains them cannot be rid of them; 1 as it is right to destroy even a poisonous animal, wholly innocent as it is. But I speak of suppressing the sect and not men, since we can prevent them from doing harm and dogmatising.
§ 5. Ph. To return to the ground and degrees of assent, it is proper to remark that propositions are of two kinds. Some are of fact, and, depending upon observation, may be based upon human testimony; others are speculative, and, regarding things which our senses could not discover, are incapable of similar testimony. § 6. When a particular fact is in conformity with our constant observations, and with the uniform report of others, we rest upon it as firmly as if it were certain knowl- 1 Gerhardt reads: " ne peut point s'en defaire." Erdmann, Jacques and Janet read: "ne pent point s'en faire," and Janet in his note says: "supply ' d'autres.' " With this reading the meaning is: " cannot procure for himself others." — TR.
538 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv edge, and where it is in conformity with the testimony of all men, in all ages, so far as can be known, it is the first and highest degree of probability; for example, that fire warms, that iron sinks to the bottom of the water. Our belief built upon such foundations rises to assurance. § 7. In the second place, all historians relate that such an one has preferred his individual interest to that of the public, and as it has ahvays been observed that this is the custom of the majority of men, the assent I give to these histories is confidence. § 8. Thirdly, when there is nothing either for or against it in the nature of things, a fact, vouched for by the testimony of unsuspected people, for example, that Julius Csesar lived, is received with a firm belief *. § 9. But when the testimony is found contrary to the ordinary course of nature or the witnesses vary among themselves, the degrees of probability may vary infinitely, whence arise these degrees which we call belief, conjecture, doubt, uncertainty, distrust; and there it is that exactness is necessary to form a right judgment and to proportion our assent to the degrees of probability.
Th. Jurisconsults in treating of proofs, presumptions, con jectures, and indices, have said a number of good things on this subject, and have gone into some considerable detail. They begin with notoriety, in which there is no need of proof. Afterwards they come to complete proofs, or those which pass as such, upon which they pronounce sentence, at least, in a civil process, but upon which in some places they are more reserved in a criminal process; and they are not wrong in demanding in such case proofs more than complete, and espe cially as regards what is called corpus delicti, according to the nature of the act. There are then proofs more than complete, and there are also ordinary complete proofs. Then there are presumptions, which pass provisionally as complete proofs, i.e. so long as the contrary is not proved. There are proofs more than half complete (to speak precisely), in which the one who relies upon them is allowed to swear to make them good (the juramentum suppletoriuni); there are others less than half complete, where wholly to the contrary the oath is adminis tered to him who denies the act, to purge himself (the jura mentum purf/ationis). Beyond this there are many degrees of conjectures and indices. Particularly in a criminal process CH. xvi] ON HUMAN UNDERSTANDING 539 there are indices (ad torturani) to proceed to tlie torture, which itself has its degrees indicated by the formulas of arrest; there are indices (ad terrenduni) sufficient to show the instru ments of torture and to prepare things as if they intended to come to it. There are some (ad capturam) to make sure of a suspected man; and (ad inquirendum) to make inquiries secretly and without noise. And these differences may be of use also on other similar occasions. The entire form of judi cial procedure is nothing else in fact than a species of logic applied to questions of law. Physicians also have a number of degrees and differences in their signs and indications which may be seen among them. The mathematicians of our times have begun to calculate chances upon the occasion of games. Chevalier de Mere,1 whose " Agremens " and other works have been printed, a man of penetrating mind who was both a player and a philosopher, gave them an opportunity by form ing questions regarding the profits in order to know how much the game Avould be worth, if interrupted at such or such a stage. In this way he induced Pascal, his friend, to examine these things a little. The question made a stir and gave Huygens the opportunity to produce his treatise "de Alea."2 1 Cf. ante, p. 213, note 2; also Response, (Replique) aux reflexions contenues dans la seconde Edition du Dictionnaire Critique de M. Bayle, Gerhardt, 4, 570, Erdmaun, 190, Janet, 2, f>93, Dutens, 2, Pt. I., 92. Antoine Gombault, chevalier de Mere, c. 1610-1(>84, was erroneously confounded with a Georges Brossin, chevalier de Mere, belonging to another family, by all biographers since Moreri, until the special researches of M. de Bremont d'Ars proved the error and assigned him his right name. He had an inordinately exalted idea of his own importance and attainments, especially in mathematics. His Ar/rements, discours de M. le chevalier de Mere a Mme **, appeared iii ll>77, 12mo, and in the collected edition of all his works, entitled (Envres du chevalier de Mere, Amsterdam, 1692, 2 vols., 12mo. A volume of (Euvres posthumes, 12mo, appeared at Paris, 1700, and again at The Hague, 1701. For further account of him, cf. Larousse, Grande Diet. Univ. de XIXme Siecle, Vol. 11, p.
2 Cf. ante, p. 150, note 3. Huygens' De ratiociniis in aless ludo, dated The Hague, 1057, is found in F. van Schooten, Exercitat. math. lib.V., pp. 514-539, Lugd. Bat. l(j.">7, 4to. It was written by Huygens in Dutch and translated into Latin by Schooten. There are two English translations, one attributed to Motte, but probably by Arbuthnot; the other by W. Brown. Cf. I. Todhunter, Hist, of the Math. Theory of Probability, pp. 22-23, Cambridge and London, Macmillan & Co., 18G5. Leibnitz, Misce.llan. Leibnit., No. CXIIL, cf. Dutens, (i, Pt. I., 1518, says of it: " Christian] Hugenii ratiocinia de lusu alex, Franc. Schotenii script is mathematicis adjecta, snnt elegans specimen ratiocinationis de gradibus probabilitatis."
Spinoza also discussed the calculation of probabilities in games of chance, 540 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv Other learned men entered into the subject. Some principles were established of which the Pensioner De Witt also availed himself in a brief discourse printed in Dutch on annuities.1 The foundation on which they have built goes back to the prosthaphceresis,2 i.e. the taking of an arithmetical mean be tween several equally receivable suppositions. Our peasants also have made use of it for a long time according to their natural mathematics. For example, when some inheritance or land is to be sold, they form three bodies of appraisers; these bodies are called Schurzen in Low Saxon, and each body makes an estimate of the property in question. Suppose, then, that the first estimates its value to be 1000 crowns, the second 1400, the third 1500; the sum of these three estimates is taken, viz. 3900, and because there were three bodies, the third, i.e. 1300, is taken as the mean value asked for; or rather, they take the sum of the third part of each estimate which is the same thing. This is the axiom: ceqiialibus cequalia, equal suppositions must have equal consideration. But when the suppositions are unequal they compare them with each other. Suppose, for example, that with two dice, the one ought to win if it makes 7 points, the other if it makes 9, the que'stion is asked what proportion obtains between their probabilities of winning? I reply that the probability of the last is worth only two-thirds of the in a letter to Jan van der Meer. Cf. Epistola No, 38 (formerly 43), Spinoza, Opera, ed. Van Vloten and Land, 2, 145-149 (in Latin and Dutch): Spinoza's Brief wechsel, in J. H. v. Kirchmann's Philos. Bibliothek, Vol. 46, pp. 145- 1 Cf. ante, p. 426, note 2. John De Witt appears to have been " the first to apply scientific principles to the calculations connected with annuities, which are analogous to those connected with assurances." His report on this sub ject was presented to the States General, July 30, 1(571. It was entitled De vanlye van de llf-renten na proportie van de los-renten, and appeared at La Haye, 1(571. An abstract of it, showing exactly how De Witt reasoned on the subject, will be found in M. Nicolas Struyck, Inleiding tot het alr/enteine geo- f/raphy, etc., p. 345, Amsterdam, 1740, 4to, and an English translation of the tract is printed in Contributions to the Hist, of Insurance by Frederick Hendriks in the "Assurance Magazine," Vol. 2 (1852), p. 231. For some remarks on De Witt's hypothesis as to the rate of mortality, cf. the same vol., 2 Prosthaphseresis — Trpoo-ea^acpeo-i? — = a previous subtraction. The term here signifies " the fundamental principle for the ascertainment of the degree of probability which requires us to take the arithmetical mean of the existing suppositions estimated according to their relative value." — TR.
CH. xvi] ON HUMAN UNDERSTANDING 541 probability of tlie first, for the first can make 7 in three ways with two dice, viz.: by 1 and 6, or 2 and 5, or 3 and 4; and the other can make 9 in two -ways only, by throwing 3 and 6, or 4 and 5; and all these methods are equally possible. Then the probabilities, which are as the numbers of equal possibilities, will be as 3 to 2, or as 1 to f. I have more than once said that a new kind of logic would be required which would treat of the degrees of probability, since Aristotle in his " Topics " has done nothing less than this, and has con tented himself with putting in a certain order certain popular rules distributed according to the common topics, which may be of use" on some occasion where the question concerns the amplification of the discourse and the giving to it probability without putting it to the trouble of furnishing us a necessary balance for weighing probabilities and forming thereupon a solid judgment.1 It would be well for him who should treat of this matter to pursue the examination of games of chance; and in general I wish that some skilful mathematician would produce an ample work with frill details and thoroughly reasoned upon all sorts of games, which would be very -useful in perfecting the art of invention, the human mind appearing to better advantage in games than in the most serious matters.
§ 10. Ph. The law of England observes this rule, that the copy of an act received as authentic by Avitnesses is a good proof, but the copy of a copy, however attested, and by wit nesses the most credible, is never admitted as a proof in a trial. I have never yet heard any one censure this wise pre caution. This observation at least may be drawn from it, that testimony has less force in proportion as it is farther removed from the original truth which is in the thing itself; while among certain peoples use is made of it in a directly contrary manner, opinions acquiring force as they grow older, and what would not at all have appeared probable a thousand years ago to a reasonable man a contemporary of the one who first certified it, passes at present as certain because many have related it upon his testimony.
Th. Historical critics have great regard for contemporary witnesses of things: but a contemporary even merits belief chiefly as regards public events only; but when he speaks of 542 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv motives, secrets, hidden forces, and things which may be dis puted, as, for example, poisonings, assassinations, we acquaint ourselves Avith what many have believed. Procopius is very credible when he speaks of the war of Belisarius against the Vandals and the Goths, but when he retails horrible scandals against the Empress Theodora in his " Anecdotes," he may believe them who will.1 Generally, we should be very re served in believing satires; we see some published in our times which, although wholly improbable, have nevertheless been greedily swallowed by the ignorant. And some day perhaps it will be said: Is it possible that one would have dared to publish these things at that time, if there had been any appar ent foundation for them? But if this statement is some day made, the judgment will be a very erroneous one. The world, however, is inclined to indulge in satire; and, to quote but one example, the late Mr. Marnier, the son,2 having published, from some caprice, in his memoirs printed some years since, certain, things wholly without foundation against the incom parable Hugo Grotius, ambassador from Sweden to France, stirred apparently by some unknown circumstance against the memory of this illustrious friend of his father, I have noticed that many authors have repeated them from envy, although the negotiations and letters of this great man sufficiently make known the contrary. We have emancipated ourselves indeed from writing romances in history, and he who produced the last life of Cromwell thought that in order to enliven the subject he was allowed, in speaking of the life, still private, of this clever usurper, to make him travel in France, where he follows him into the public houses of Paris as if he had 1 For critical discussion of the authorship of the Ta 'AveKSora — Anecdota or Historia Arcana — of Procopius, and of the credibility of its contents, cf. J. H. Reinkens, Anecdota sintne scripta a Procopio Csesariensi inquiritur, Breslau, 1858, who denies, and F. Dahn, Prokopius von Ciisarea, Berlin, 18(55, who affirms, that Procopius is the author. Prof. James Bryce gives a brief account and estimate of the work in his article on "Procopius," in the Encyclop. Brit.!)th ed. Cf. also M. Debidour, Thesis, 1877, who tries to make out the best cas'e he can for Theodora, and Prof. Bryce in the " Contemporary 2 Louis Aubery du Maurier, the historian, died 1087, was the son of Benjamin Aubery, an ambassador from France to Holland, and published Meinoires pour servir a I'Histoire de Hollande, Iii80, Menioires de Hamburg, de Lubeck, de Holstein, etc. Leibnitz refers to him in his letter to Bierling, Oct. 24, 1709, Gerhardt, 7, 487. — Tu.
CH. xvi] ON HUMAN UNDERSTANDING 543 been liis master.1 But it appears by the history of Cromwell written by Carrington, a well-informed man, and dedicated to his son.Richard when he acted the part of the Pro tector, that Cromwell never went out of the British Isles. Detail especially is uncertain. There are almost no good accounts of battles; the majority of those of Titus Livius appear to be imaginary, as well as those of Quintus Curtius. It would be necessary to have on both sides the accounts of exact and capable men, who indeed would draw up plans of them like those which the Count of Dahlberg, who had already served with distinction under the King of Sweden, Charles Gustavus, and who, being Governor-General of Livonia, re cently defended Riga, has had engraved touching the actions and battles of this prince. We must not, however, at once decry a good historian at a word from some prince or minister who has exclaimed against him on some occasion, or in regard to some subject not to his taste or wherein there really is per haps some fault. The story is told that Charles the Fifth, wishing to have something of Sleidan2 read, said: "Bring me my story-teller (menteiir)," and that Carlowitz, a Saxon gentle man, of good repute at that time, said that the history of Slei