g as it is more or less vivid, and more or less connected with the things we know. And even when we are assured of the principal fact we may often question the circumstances. I remember to have known a certain man, for I feel that his image as well as his voice is not new to me; and this double indication is a better guarantee to me than one of the two, but 1 cannot remember where I have seen him. It happens, how ever, though rarely, that a person is seen in a dream before he is seen in flesh and blood. And I am assured that a lady of a well-known court saw in a dream and described to her friends the person she afterwards married, and the hall in which the betrothal was celebrated, and she did this before she had seen or known either the man or the place. They attributed the circumstance to some indefinite secret presentiment; but chance may produce this effect, since it is quite rare that it happens, besides, dream-images being somewhat obscure, there is more liberty in connecting them afterwards with certain others.
§ 13. Ph. Let us conclude that there are two kinds of prop ositions, the one particular and concerning existence, as, for example, that an elephant exists; the other general, concern ing the dependence of ideas, as, for example, that men should obey God. § 14. The majority of these general and certain propositions bear the name of eternal truths, and, in fact, they all are such. Tin's is not because these are propositions act ually formed somewhere from all eternity, or because they are graven upon the mind after some model, which always existed, but because we are assured that when a creature en riched with faculties and means therefor, applies his thoughts to the consideration of his ideas, he will discover the truth of these propositions.
Th. Your division appears to return to mine of propositions of fact and propositions of reason. Propositions of fact also may become general in a way, but it is by induction or obser vation, so that it is only a multitude of similar facts, as when it is observed that all quicksilver is evaporated by the force of fire; and this is not a perfect generality, because we do not see its necessity. General propositions of reason are CH. xi] ON HUMAN UNDERSTANDING 515 necessary, although the reason also furnishes some which are not absolutely general, and are only probable, as, for example, when we presume an idea to be possible until its contrary is discovered by a more exact research. There are finally mixed propositions, drawn from premises, some of which come from facts and observations, and others are necessary propositions; and such are a number of geographical and astronomical con clusions regarding the globe of the earth and the course of the stars, which spring from the combination of the observations of travellers and astronomers with the theorems of geometry and arithmetic. But as, according to the usage of logicians, the conclusion follows the iveakest of the premises 1 and cannot have more certainty than they, these mixed propositions have only the certainty and generality which belong to the obser vations. As for the eternal truths, it must be observed that at bottom they are all conditional and say in effect: such a thing posited, such another thing is. For example, in saying: every figure ivhich has three sides will also have three angles, I say nothing else than that, supposing there is a figure with three sides, this same figure will have three angles. 1 say this same, and it is in this respect that the categorical proposi tions which may be stated unconditionally, although at bot tom conditional, differ from those called hypothetical, as this proposition would be: if a figure has three sides, its angles are equal to two right angles, in which we see that the antecedent proposition (viz.: the figure of three sides) and the consequent (viz.: the angles of the figure of three sides are equal to two right angles) have not the same subject as they have in the preceding case, in which the antecedent was: this figure has 1 The variously phrased formula: conclusio sequitur partem debiliorem or deteriorem; scctetur partem conclusio deteriorem; pejorem sequitur semper conclusio partem, is the Scholastic expression of the fundamental principle of the categorical syllogism, according to which the conclusion cannot contain more than is contained in the premises, or, as given by Hamilton (Lects. on Logic, p. 219, Boston, 1873), in his third rule of the syllogism, "The conclu sion must correspond in quantity with the subsumption [minor premise], and in quality with the sumption [major premise]." Logicians regarded negative and particular propositions as weaker or worse as related to universal and affirmative propositions, the negative being weaker in quality and the par ticular in quantity, so that in the syllogism if one of the premises is particular the conclusion will be particular, and if one of the premises is negative the conclusion will be negative. For the history of the subject, cf. Prantl, Gesch. d. Logik, I, 371, 587; 2, 275; 3, 48. — TK.
516 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv three sides, and the consequent: the said figure has three angles. Although, again, the hypothetical may often be transformed into the categorical, merely by changing a little the terms, as if instead of the preceding hypothetical, I said: the angles of every figure with three sides are equal to two right angles. The Scholastics have hotly disputed de constantia subjecti, as they called it, i.e. how the proposition made upon a subject can have a real truth, if this subject does not exist. The fact is that the truth is only conditional, and says, that in case the subject ever exists, it will be found such. But it will be further demanded, in what is this connection founded, since there is in it some reality which does not deceive. The reply will be, that it is in the connection of ideas. But it will be asked in reply, where would these ideas be if no mind existed, and what then would become of the real ground of this cer tainty of the eternal truths? This leads us finally to the ulti mate ground of truths, viz.: to that Supreme and Universal Mind, which cannot fail to exist, whose understanding, to speak truly, is the region of eternal truths, as St. Augustine has recognized and expresses in a sufficiently vivid way.1 And in order not to think that it is unnecessary to recur to this, we must consider that these necessary truths contain the de termining reason and the regulating principle of existences themselves, and, in a word, the laws of the universe. Thus these necessary truths being anterior to the existence of contingent beings, must be grounded in the existence of a 1 Aurelius Augustinns, 354-430, grounded his philosophy in the principle of the absolute and immediate certainty of consciousness or inner experience. Qf. De Beata Vita, chap. 7; Solil. II., 1 (ante, p. 410, note 1); De Vera Relig., 39, 72 sq.; De Trin., X., 14, XIV., 7. In this certainty of the individual conscious ness, i.e. in thought itself, is immediately involved the idea of God in whom exist the universal truths as the ideas or norms of all reality. Cf. De Ideis, 2: " Sunt namque ide.c principales formaj quaxlam, vel rationes rerum stabiles et incommutabiles, qu;e 5ps;u formatfe non sunt atque per hoc suternaj ac semper eodem modo se habentes, qnre in divina intelligeiitia contincntur, et quum ipsss neque oriantur neque intereant, secundum eas tameu formari dicitur omue, quod interire potest et omne, quod oritur et interit."
For a good account of Augustine's philosophy, cf. Ueberweg-Heinze, 7th ed., Berlin, 188S, 2, 07-115, especially lOti-7, Eng. trans, from 4th Germ, ed., New York, 1871, 1, 333 sq., especially 339-40; "Windelband, Hist, of Fhilos., trans, by Tufts, 27<> sq. Augustine's works form Vols. 32-47 of the Latin Fathers in Migne, Patrol, cur. compl., Paris, 1835 sq.; Eng. trans, by Dods, 15 vols., Edinburgh, 1871-77, and in Schaff's lib. Nicene and Post-Niccne Fathers, Vols. 1-8, Buffalo, 1881 5-8S. — Tn.
CH. xn] ON HUMAN UNDERSTANDING 517 ~i necessary substance. Here it is that I find the original of the ideas and truths which are graven in our souls, not in the form of propositions, but as the sources out of which applica tion and occasion will cause actual judgments to arise.1 CHAPTER XII OF THE IMPROVEMENT OF OUK KNOWLEDGE § 1. Ph. We have spoken of the kinds of knowledge we have. Now let us come to the means of improving the knowl edge or of finding the truth. It is the received opinion among scholars, that the maxims are the bases of all knowledge, and that each particular science is based upon certain things already known (prcecognita). § 2. I admit that mathematics seem to favor this method by their good success, and you have given considerable support to this view. But it is still doubtful whether it is not rather the ideas which were of service therein through their connection than two or three general maxims which were posited at the beginning. A young lad knows that his body is greater than his little finger, but not by vir tue of this axiom, that the whole is greater than its part. Knowledge commenced by particular propositions; but after wards it was desired to relieve the memory by means of gen eral notions from a cumbersome load of particular ideas. If language were so imperfect that there were no relative terms, whole and part, could he not know that his body is larger than his little finger? I at least give you the reasons of my author, although I think I foresee what you Avill say thereto in con formity with what you have already said.
Th. I know not why you bear the maxims such ill will as to attack them yet again; if they serve to relieve the memory of a multitude of particular ideas, as you admit, they must be very useful, although they had no other use. But I add that 1 For Leibnitz God is the source of all truths as well as of all beings. The idea of God contains in itself potentially all truth, and is the regulative (but not in the Kantian sense of the term), or better, the constitutive, principle of all thought, just as his actuality contains potentially within itself all exist ences, and is the regulative, i.e., constitutive, principle of all being. (Jf. also, 618 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv they do not spring from particular ideas, for they are not found by induction from examples. He who knows that ten is more than nine, that the body is larger than the finger, and that the house is too large to be able to run away with the door, knows each one of these particular propositions, by one and the same general reason which is, as it were, incorpo rated therein and illuminated, just as we see designs adorned with colors in which the proportion and configuration con sists properly in the outlines, whatever the color may be. ISTow this common reason is the axiom itself which is known, so to speak, implicitly, although it does not exist at first in an abstract and separate manner. The examples derive their truth from the incorporated axiom, and the axiom has not its ground in the examples. And as this common reason of these particular truths exists in the minds of all men, you see clearly that it is not necessary that the words tvhole and part be found in the language of him who is imbued therewith.
§ 4. Ph. But is it not dangerous to authorize assumptions under the pretext of axioms? One will assume, with some of the ancients, that all is matter; another, with Polemo,1 that the world is God; a third will assert that the sun is the prin cipal divinity. Judge what a religion we should have, if that were allowed. So true is it that it is dangerous to receive principles without questioning them, especially if they con cern morality. For some one will expect another life, like that of Aristippus,2 who placed happiness in the pleasures of the body, rather than like that of Antisthenes,3 who main- 1 Polemo, the successor of Xenocrates, 396-314 B.C., as scholarch, or head, 1514-270 B.C., of the school of the Old Academy, and the third in that office from Plato (Speusippus holding it from Plato's death in 347 to 339, and Xeno crates from 339-314), devoted himself chiefly to ethics. The statement that he declared the universe to be God — noAe>oi' T'OV KOO^OV Btbv an-e^rji/aTo — rests on the authority of Stobaeus, Ecloyse phys., Bk. I., chap. 2, 5, § 62, p. 15, ed. A. Meiueke, Leipzig, 1855-64. For his philosophy, cf. Zeller, Philos. d. Gnech., II., 1 [Vol. 3], 993-4, 1045-6, 4th ed., Leipzig, 1889. — TR.
2 Aristippus, c. 435-c. 3(>6 B.C., the founder of the Cyrenaic school, made pleasure, which, according to Diog. Laertius, II., 85, 86, he defined as the nevriv...Trjv nev \eiav Kivr)<riv Tyv ySovriv — the end of life, the wise man aiming to enjoy pleasure without being controlled by it. For his writings, cf. Mul- lach, Fragt. philos. Gr., II., 397 sq. On his life and philosophy, cf. Zeller, Philos. d. Griech., II., 1 [Vol. 3], 336 sq., ethical doctrine, 352 sq. — TR.
3 Antisthenes, c. 4407-c. 369 B.C., a pupil of Gorgias and Socrates, was the founder of the Cynic school, and taught, according to LMog. Laertius, VI., 11, en. xn] ON HUMAN UNDERSTANDING 519 tained that virtue suffices to produce happiness. And Arche- laus,1 who will lay it down as a principle that justice and injustice, honesty and dishonesty, are defined only by the laws and not by nature, will no doubt have other measures of moral good and evil than those who admit obligations anterior to human constitutions. § 5. It must be, then, that principles are certain. § 6. But this certainty comes only from the com parison of ideas: thus we have no need of other principles, and according to this rule alone we shall advance much farther than by putting our minds at the disposal of another.
Th. I am astonished, sir, that you turn against maxims, i.e. against evident principles, that which can and must be said against principles assumed gratis. When one demands prte- cognita in the sciences, or anterior knowledge, which serves to ground science, he demands known principles and not arbi trary positions, whose truth is not known; and even Aristotle understands that the inferior and subaltern borrow their prin ciples from other superior sciences in which they have been demonstrated, except the first of the sciences, which we call metaphysics, which, according to him, asks nothing from the others, and furnishes them the principles they need; and when he says: Sfl ma-Tfvf.iv TOV (j.av8a.vovTa,2 the apprentice must that virtue only is a good, and that it is sufficient for happiness — avrapxri yap rrfv aperr)!/ eiWi wpbs evSai/j-Oviav. For his Writings, cf. Mlllhicll, FrU(/t, phtloS.
Gr., II., 201 sq. On his life and philosophy, cf. Zeller, Philos. d. Griech., II., 1 [Vol. 3], 281 sq., ethical doctrine, 303 sq. — TR.
1 Archelaus, the dates of whose hirth and death are unknown, was a physi cist, and the disciple of Anaxagoras, c. 500-428 B.C., whose physical doctrine he seems to have modified in the direction of the Ionic school as represented by Anaximines, c. 588-c. 524 B.C., and Diogenes of Apollonia. Zeller says that the statement, as given by Diog. Laertins, II., 1G, that he derived the distinc tion of good and bad from custom rather than nature — TO Sinaiov elvai «ai TO alaxpov ou (£u'o-6i dAAa vo^w — appears to be due to a mistake in interpreting his language, and that he merely said that men at the beginning were without custom and law, and first attained thereto in the course of time. On his philosophy, cf. Zeller, Phllos. d. Griech., I., 2 [Vol. 2], 1031-1038, 5th ed., 2 Cf. Aristotle, Sophist. Elench., chap. 2, 161, b, 1-3: SiSao-KaAi/coi ^f oi CK Ttav OLKeiiov ap\iii' exda'TOV fiaOrj^taros xai OVK ex Tiav TOV anoKpu'Ofievov Sot-lav crvAAoyi<Jofj.fvoi (ofl yap Tri<rTfvei.i' rbv iJ-arQavovra), i.e. discussions for the purpose of teach ing proceed from the special principles of each science, and do not draw their conclusions from the opinions of the participating pupil; Aristotle's thought being that the pupil will receive a confirmation of the mere faith in the prin ciples demanded of him at the outset, in the course of the explanation and demonstration of these principles in his presence, and in the agreement of the scientific results with the facts and his further knowledge. Leibnitz here 520 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv believe his master, his thought is that he must do it only while waiting, while he is not yet instructed in the higher sciences, so that it is only provisionally. Thus we are very far from receiving gratuitous principles. To this it must be added that even principles whose certainty is not complete may have their use if we build upon them only by demonstration; for although all the conclusions in this case are conditional only, and are valid only upon the supposition that this principle is true, nevertheless this connection itself and these conditional enunciations would at least be demonstrated; so that it were much to be desired that wre had many books written in this way, where there would be no danger of error, the reader or disciple being warned of the condition. And practice will be regulated by these conclusions only as the supposition shall be found verified elsewhere. This method also serves very often itself to verify suppositions or hypotheses, when many conclusions arise from them, the truth of which is otherwise known, and sometimes this gives a perfect proof (retour) sufficient to demonstrate the truth of the hypothesis. Mr. Conring,1 a physician by profession, but a clever man in every kind of learning, except perhaps mathematics, wrote a letter to a friend engaged in reprinting at Helmstadt the book of Viottus,2 an esteemed Peripatetic philosopher who tried to expresses a similar thought, in premising the provisional character of that faitli which the hcgiuncr should have in his teacher. — TK.
1 Hermann Conring, 1WX>-1'>81, one of the most learned men of his age, possessed of vast erudition, and thoroughly informed on medicine, law, the ology, history, physics, philology, etc., taught at Helmstiidt, and wrote an immense number of works, which have heen united in part and puhlished under the title of Opera omnia, Brunswick, 1730, 7 vols., fol. For an account of him, cf. Midland, Elocj. Univ., Vol.!», pp. 447-452. For his correspondence with Leibnitz, cf. Gerhardt, Leibniz, philos. Schrift., 1, 153-2(X>. — TK.
2 Bartolommeo Viotto, or Viotti, surnamed a Clivolo, son of a distin guished surgeon, Tommaso Viotto, who was the first in the University of Turin to receive the laurel crown in surgery from the Decurions of Trino, was a philosopher and physician of Turin, and, in the five years preceding 1552, public professor of logic in that city. lie died in 1508. He was author of De balneorum naturalium viribus lib. IV., Lugduni, 1552, reprinted in De balncis omnia qusc extant apud Crxcos, Latinos, et Arabas, fol. Venetiis, 1553, pp. 247-71; and of the work here and elsewhere referred to by Leibnitz, Uemonsfrationum in mcthodum mcdendi lib. V., 8vo, Parisiis, 15(>0, and under the editorship of A. Frolingius, Helmstadt, Mil, Braunschweig, 1(!84. Cf. Correspondence of Leibnitz and Conring, (ierhardt, Leibniz. philos. Schrift., 1, 184-, 187; of Leibnitz and Place-ins, Dutens, Leibnit. op. om., <i, 45.
Couring, Introd. in univ. art. incd., Hahe et Lipsiai, 1720, p. 23, says of cii. xn] ON HUMAN UNDERSTANDING 521 explain the demonstration and " Posterior Analytics " of Aristotle. This letter was appended to the book, and in it Conring criticised Pappus when he said that analysis proposes to discover the unknown by assuming it, and by reaching therefrom, by inference, known truths; 1 a method which is contrary to logic (he said) which teaches that from falsehood we cannot infer truths. But I made known to him afterwards that analysis makes use of definitions and other reciprocal propositions which furnish means of making the proof (retour), and of discovering synthetic demonstrations.2 And even when this proof is not demonstrative, as in physics, it is nevertheless sometimes highly probable, when the hy pothesis explains easily many phenomena, difficult without it and very independent of one another. I hold to the truth, sir, that the principle of principles is in a way the good use of ideas and of experience; but by examining it thoroughly we shall find that, as regards ideas, it is nothing else than the union of definitions by means of identical axi oms. Nevertheless, it is not always an easy thing to come to this ultimate analysis, and whatever desire the geometers, at least the ancient geometers, have shown to succeed therein, they have not yet been able to do so. The celebrated author him: " Certe qui necessitatem ejus in medieina simul ct ipsam artem demon- strandi post Galeuum ostenderit, haetenus nemo inventus est, si excipias unum Bartholomseum Viottum hominem longe doctissimum; cujus de deiuon- stratione pneclarum opus ante centum annos prodiit." Cf., also, G. Pasch, De novis inventis, 2d ed., 4to, Lipsiaj, 1700, p. 2(>; J. A. van der Linden, De scriptis medicis, 8vo, Amstelredami, 1(>37, p. 82, Linden, renovat., 4to, Norim- bergaj, 1<>8(>, pp. 114, 119; Kestner, Medicinisches-Gelehrten-Lexicon, 4to, Jena, 1740, p. 897; G. G. Bouiiio, JJiografta medico, piemontese, 8vo, Torino, 1824, 1 Pappus of Alexandria was a Greek geometer " of a very high order," who flourished, according to the best recent opinion, in the reign of Diocletian, 284-.'305, and whose 2in/ayuy>j, or Collection, is of very great value in the his tory of mathematics. From Bk. VII. of this work is derived a large part of our knowledge of Greek geometry. The best ed. of the whole 'work is F. Hultsch, Pappi Alexandrini Collectionis quse supersunt, 3 vols., Berlin, 1876-78.
Pappus' explanation of the nature of analysis and synthesis, which Con- ring erroneously criticised, is found in the preface of Bk. VII. of the 2wayu)y>j, cf. Hultsch, op. tit., Vol. 2, pp. <>34-<>; C. I. Gerhardt, Der Sammlung des Pappus von Alexandrien, siebentes u. achtes Buck, Halle, 1871, pp. 2-4. Ac cording to Schaarschmidt, this explanation is perhaps the clearest and best concise statement that has been made of the nature of the analytic and syn thetic method. — TR.
2 Cf. Correspondence of Leibnitz and Conring, Letter of Jan. 3d, 1(!78, Gerhardt, Leibniz, philos. Schrift., 1, 187-8; also, ibid., 185, 190, 193 sq. — TR.
622 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv of " The Essay on Human Understanding, " would give them much pleasure if he would complete this investigation, a little more difficult than we think. Euclid, for example, has put among the axioms one which amounts to saying: that two straight lines can meet only once. The image derived from the experience of the senses, does not permit us to picture to ourselves more than one meeting of the two lines; but it is not upon this that science must Le founded. And if any one believes that this image gives the connection of distinct ideas, he is not sufficiently instructed concerning the source of truths, and a multitude of propositions, demonstrable by others ante rior, would pass with him as immediate. Many of those who have criticised Euclid, have not sufficiently considered this: these kinds of images are only confused ideas, and he who knows the straight lines only by this means will not be capable of demonstrating anything. Euclid, therefore, for want of a distinctly expressed idea, i.e. a definition of a straight line (for that which he gives meanwhile is obscure and of no use to him in his demonstrations), was obliged to return to two axioms which for him took the place of definitions and which he em ployed in his demonstrations: the one that two straight lines have no common part, the other that they enclose no space. Archimedes has given a kind of definition of the straight line, in saying that it is the shortest line between two points. But he tacitly assumes (by employing in his demonstrations ele ments like those of Euclid, based upon the two axioms I have just mentioned) that the properties (affections) of which these axioms speak, accord with the line which he defines.1 Tims if you believe, with your friends, under the pretext of the agree ment or disagreement of ideas, that what these images tell us was allowed and is still to be received in geometry, without seeking that strictness of demonstration by means of defini tions and axioms which the ancients demanded in this science (as I believe many people will believe for lack of information), I will admit, sir, that you may be contented as regards those who trouble themselves only about practical geometry such as it is, but not as regards those who desire to have the science which serves indeed to perfect the practical. And if the ancients had been of this opinion and had relaxed their efforts 1 Gerhardt and Erdmauu read " dcfiuit "; Jacques " decrit." — TR.
CH. xn] ON HUMAN UNDERSTANDING 523 on this point, I tliink they would have made but little advance, and would have left us only an empirical geometry such as that of the Egyptians apparently was, and such as that of the Chinese seems still to be; this would have deprived us of the most worthful physical and mechanical knowledge which geometry has caused us to discover, and which is unknown wherever our geometry is unknown. It is also apparent that in following the senses and their images we should fall into errors; much the same as we see that all those who are not instructed in exact geometry receive as an indubitable truth upon trust in their imagination, that two lines continually approaching each other, must finally meet; while geometers give contrary instances in the case of certain lines called asymptotes. But besides this we should be deprived of what I value most highly in geometry as related to reflection, viz.: permitting us to catch a glimpse of the true source of eternal truths and of the means of making us comprehend their neces sity, a matter which the confused ideas of the sense-images could not show us distinctly. You will say to me that Euclid was obliged, however, to confine himself to certain axioms whose evidence is seen only confusedly by means of the