3 A strange remark for Leibnitz to make, who had so thoroughly studied Aristotle in his youth, and in later years Plato, whose works contain demon strations inferior in no respect certainly to the precision of the Pandects. The only explanations that seem to touch the case are that Leibnitz had in mind the stringency and completeness of mathematical demonstration, which in form, and sometimes in content also, is apparently, and sometimes really, superior, though not necessarily so merely because mathematical, to the demonstrations of philosophy; or, as he seems to suggest in the immediately following con text, that metaphysics being a matter of pure thought and ethics largely an ideal not as yet realized in the actual, their demonstrations cannot, like those of mathematics, be experimentally verified, and must thus be regarded as, in a sense, lacking in completeness as demonstrations. — TR.
4 Cf. ante, p. 108, note 2. Leibnitz's remark concerning Proclus has its justification in the fact that his philosophical system, while embracing the entire philosophy and theology of his predecessors methodically elaborated with great dialectic art and skill, is yet purely formal in its completeness, its thought exhibiting little freedom or creative power, and wholly lacking in any real scientific basis and character. Though presenting here and there evidence of deep speculative ability on the part of its author, his philosophy is never theless wholly wanting in such demonstration as is found in his mathematical work. — TR.
CH. n] ON HUMAN UNDERSTANDING 417 physics experiments demand labor and expense. Now men at once relaxed their attention, and as a consequence were led astray when they were destitute of this faithful guide, experience, who aided and sustained them in their walk, as that little revolving machine does, which prevents children from falling when walking. There was a succeclaneum,1 but it is something that has not been and is not yet sufficiently con sidered. And I shall speak of it in its place. For the rest, blue and red are scarcely capable of furnishing matter for demonstration by means of the ideas we have of them, because these ideas are confused. And these colors do not supply matter for reasoning so long as in experience they are found accompanied by some distinct ideas, but in which the con nection with their own ideas does not appear.]
§ 14. Ph. Besides intuition and demonstration, which are the two degrees of our knowledge, all the rest is faith or opinion, and not knowledge, at least as regards all general truths. But the mind has also another perception, regarding the particular existence of finite beings outside of us, and this is sensitive knoivledge.2 Th. [Opinion, based on probability, deserves perhaps the name knowledge also; otherwise nearly all historic knowledge and many other kinds will fall. But without disputing about terms, I hold that the investigation of the degrees of probability is very important, that we are still lacking in it, and that this lack is a great defect of our logics.3 For if the question can not always be decided absolutely, the degree of resemblance ex datis can always be determined, and consequently one can reasonably judge what view is the most likely. And when 1 I.e., a substitute. The expression was much used by the later Roman jurists. — TK.
2 Locke's word is " sensitive," Philos. Wks. (Bonn's ed.), Vol. 2, p. 141, adfin. His three degrees of knowledge are intuitive, demonstrative, and sensitive, cf.
3 Cf. Leibnitz's letter to Kestner, No. 11, Jan. 30, 1711, § 3 (Dutens, Leibnit. op. om. 4, Pt. III., 264, and Kortholt, Leibnit. epist. ad diversos, 3, 251): "Ea vero pars Logicse, qua sc. gradus verisimilitudinum et argumentornm pondera eonstituerentur, nuspiam hactenus reperitur traditur. Ego juvenis aliquando aggressus sum, sed per varia dissipatus, fere intra voluntatem steti. Topica Aristotelis scopo meo non respondet. Congerit regulas, quae occasionem aliquam praibere possunt de argumentis cogitandi, sed qua) non possunt dor-ere, quantum cuique argumeuto aut judicio ponderis iusit." — TR.
418 LEIBNITZ'S CRITIQUE OF LOCKE [me. iv our moralists (I mean the wisest of them, such as the present (modems) General of the Jesuits)1 unite the safest and the most probable, and prefer even the safe to the probable,2 they are not far in fact from the most probable; for the question of safety is here that of the little probability of an evil to be feared. The fault of the moralists lax upon this article 3 has largely been, that they have had a too limited and too inade quate notion of the probable, which they have confounded with the Endoxon 4 or the probable (opinable) of Aristotle; for Aris totle in his " Topics " did not mean to accommodate himself to the opinion of others, as did the orators and sophists. Endoxon is with him what has been received from the greatest number or the most authoritative: he is wrong in having restricted his " Topics " to this, and this view caused him to adhere only to received maxims, for the most part vague, as if he wished 1 Leibnitz probably refers to Tirso Gonzalez, General of the Jesuits from 1G87-1705, and author of a work on probabilism, opposing the doctrine and maintaining that the Jesuits did not originate it, entitled Fundamentum theoloyise moralis, id est tractatus theolof/icus de recto usu opinionam proba- bilium^to, Dillingen, 1(589, Naples, 1094. An abridgment with the title. Synop sis tract, theol. de recto usu opinionum probabilium, concinnata a theoloyo quodam Soc.Jesu: cm accessit logistica probabilitatum, 3d ed., appeared at Venice, 169(5, 8vo. Cf. Michaud, Bioa. Univ. 18, 111-112, Du Pin, Biblioth. des out. eccles. du XVII. sie'clc, and, for the De recto usu opin. prob., Migue, Theol.
2 The theory of moral probabilism is, perhaps the most celebrated question discussed in Moral Theology, and formed one of the chief subjects of contro versy between the Jansenists and the Jesuits of the seventeenth century. The aim of moral probabilism is to find some rule by which action may be determined in that portion of the moral realm in which certainty is impossible, and probability only can be attained. The probable opinion being that which has a certain number of arguments in its favor, either intrinsic, i.e., grounded in reason, judgment in regard to which was restricted to men of considerable education and especially to those versed in moral theology, or extrinsic, i.e., resting on some external authority, such as that of some theologian of repute; and the safe opinion, that which conforms to the moral law, casuists distinguish the following doctrines: 1. Prribabilism, which permits action in accord with the opinion which is least probable and least safe; 2. Probabilorism, or the preference of the most probable opinion, regardless of its relative safety; 3. Tutiorism, or the choice of the safest opinion, without regard to its rela tive probability. On the whole subject, cf. the dissertation of Pierre Nicole annexed to his Latin trans, of Pascal's Lettres prorinciales, and Janet, La Morale, Bk. III., Chap..">, Paris, 1874, Eng. trans., The Theory of Morals, pp. 292-308, New York, Chas. Scribner's Sons, 1883.— TR.
3 According to Janet, the casuists refuted by Pascal. — TR.
CH. n] ON HUMAN UNDERSTANDING 419 to reason only by means of quodlibets l or proverbs. But the probable or the likely is more extended: it must be drawn from the nature of things; and the opinion of persons whose authority has weight is one of the things which may contribute to render an opinion probable, but not what completes the en tire verisimilitude. At the time when Copernicus 2 was almost alone in his opinion, it was still incomparably more probable than that of all the rest of the human race. Now T do not know but that the establishment of the art of estimating probabilities5 would be more useful than a majority of our demonstrative sciences, and I have thought of this more than once.]
Ph. Sensitive knowledge, or that which establishes the exist ence of particular beings without us, goes beyond bare proba bility; but it has not all the certainty of the two degrees of knowledge of which we have just spoken. Nothing is more certain than that the idea we receive of an external object is in our mind, and this is intuitive knowledge: but the knowl edge whether from this we can certainly infer the existence of anything without us corresponding to this idea, this it is which certain persons think may be questioned, because men may have such ideas in their minds, when no such thing actu ally exists. For myself I believe, however, that there is a degree of evidence which elevates us beyond doubt. One is unalterably convinced that there is a great difference between the perceptions which he has when by day he looks at the sun, and when by night he thinks about it; and the idea which is 1 The Mediaeval Latin " quodlibetum " was a very elaborate and subtle scholastic argumentation upon a question chosen at pleasure — " quod libet " — but almost always of a theological or philosophical character. Such ques tions were called " quodlibetariae qurestiones "; they were proposed chiefly for the exercise of students, and their discussion was carried on to satisfy curiosity or for entertainment, and, for the most part, served rather to exhibit the skill and dexterity of the dialectician than to establish truth. The French word "quolibet," starting from the scholastic use of the term in the sense of an argumentative subtlety, came by a debasing extension of this meaning to signify a witty, but not always appropriate commonplace, a bad joke, a pun, an epigram; and it is in this sense that Leibnitz, coupling the word with "proverbs," uses the term. — TR.
2 Nicolas Copernicus, 1473-1543, published his theory of the planetary system in his De orbium cvelestium revolutionibus lit. VI., Nuremberg, 1543, 2cl ed., Basle, 1500, both fol. 3d ed., with notes by Nicolas Muler in his Astronomia Instaurata, Amsterdam, 1017 and 1G40, 4to. — TR.
3 Cf. ante, p. 213, note 2, p. 214, note 1; also Erdmann, Leibnit. opera philos., 84. — TR.
420 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv renewed by recourse to the memory is very different from that which actually comes to us by means of the senses. Some one will say that a dream may produce the same effect. I reply in the first place that it matters little that I remove this doubt, because if all is but a dream, reasoning is useless, truth and knowledge nothing at all. In the second place, he will ac knowledge, in my opinion, the difference between dreaming of being in a fire, and being actually in it. And if he persists in appearing sceptical, I shall tell him that it is enough that we certainly find pleasure or pain following the application to ourselves of certain objects, true or dreamt of, and that this certitude is as great as our happiness or misery; two things beyond which we have no interest. Thus I think we may count three sorts of knowledge: intuitive, demonstrative and sensitive. Th. [I think you are right, sir, and I also think that to these species of certitude or certain knoivledge you can add the Jcnoidedge of the probable; thus there will be two sorts of knowledge, as there are two sorts of proofs, the first of which produce certitude, and the second end only in probability. But let us come to this dispute of the Sceptics and the Dogmatists upon the existence of things without us. We have already touched upon it, but we must return to it here. I formerly discussed the subject a great deal viva voce and in writing with the late Abbe Foucher,1 Canon of Dijon, a learned and 1 Simon Foucher, 1644-1696, a devoted student of the Platonic philosophy, in consequence of which he was called " the restorer of the philosophy of the Academy." His Critique de la Recherche de la Verite, here mentioned by Leibnitz, appeared at Paris, 1675. It was based upon the sceptical principles of the Middle Academy, and was subjected to a very sharp criticism by Male- branche in the Preface to the next edition of the Recherche de la Verite. Foucher also wrote Dissertation sur la recherche de la verite ou sur la philo sophic des academiciens, Paris, 1673, said to be his best work, and De la Sagesse des anciens, Paris, 1683. For Foucber's " objections " (published in the "Journal des Savans " of Sept. 12, 1695) to Leibnitz's doctrine of pre- established harmony as set forth in the Systeme nouveuu (" Jour, des Savans," June 27, 1695), cf. Gerhardt, 1,424, and 4, 487, Erdmann, 129, Dutens, 2, Pt. I., 102, trans. Duncan, 81; and for Leibnitz's reply (" Jour, des Savans," April 2 and 9, 1696), cf. G. 4, 493, E. 131, Dutens, 2, Pt. I., 67, trans. Duncan, 85. The correspondence of Foucher with Leibnitz was first published by Foucher de Careil in his Lettres et opuscules inedits de Leibniz, Paris, 1854, pp. 27-131 (cf.
Introd. pp. 22-41, where the controversy over Malebranche is thoroughly con sidered), and more recently, 1875, after a new comparison with the originals in the Royal Library at Hannover, by Gerhardt, Leibniz, philos. Schrift., 1, CH. 11] ON HUMAN UNDERSTANDING 421 subtile man, but a little too prepossessed in favor of his Acad emicians, which sect he was very desirous of reviving, as Gas- sendi1 had brought upon the stage that of Epicurus.2 His critique upon " The Search after Truth," 3 and the other minor treatises which he afterwards published, have made their author quite well known. He published also in the " Journal des Savans " some objections to my System of Pre-established Harmony, when I gave it to the public after having digested it for many years; but death prevented him from replying to my answer. He always preached the necessity of guarding against prejudice and of using great accuracy, but besides the fact that he himself did not make it his duty to carry out his counsel to others, in which he was perhaps excusable, it seems to me that he was not careful whether another did it, antici pating doubtless that no one would ever do it. Now I showed him that the truth of sensible things consisted only in the connection of phenomena, which must have its reason and is that which distinguishes them from dreams; but that the 1 Cf. ante, pp. 64, note 2, G5, n. 3. Gassendi published on the life and phi losophy of Epicurus: De vita, moribus et doctrina Epicuri, Lugd. Bat., 1647; Animadversiones in libr. X. Dioy. Laert. de Epicuro, Lugd. Bat. 1(349; Syn tagma philos. Epicuri, The Hague, 1055. For his philosophy, cf. his Syntayma philosophicum, Vols. 1 and 2 of his Opera omnia; also Stockl, Gesch. d. Phi- los. d. Mittelalters, III. [Vol. 4], 316-327; Lange, Gesch. d. Materialismus, Vol. 1, Eng. trans. Vol. 1, pp. 253-209; R. Adamson, article "Gassendi," in Encyclop. Brit., 9th ed. — TK.
2 Cf. ante, p. 126, note 1. On his life and philosophy, cf. Zeller, Philos. d. Griech., III., 1 [Vol. 5], 363 sq., 3d ed., Leipzig, 1880; Lange, Gesch. d. Materi alismus, Vol. 1, Eng. trans., Vol. 1, pp. 98 sq.; Benu, The Greek Philosophers, Vol. 2, pp. 53 sq.; Win. Wallace, Epicureanism, in the series of " Chief Ancient Philosophies," pub. by the Society for promoting Christian Knowl edge, London, 1880. — Tn.
3 The De la Recherche de la Verite', the principal work of Malebranche, 1638-1715, appeared in 1674-1679. The most recent edition is that of F. Bouil- lier, with an introduction and notes, 2 vols., Paris, 1880. On Malebranche's philosophy, cf. Bouillier, Histoire de la Philos. Cartesienne, Paris, 1854; Olle- Laprune, La Philos. de Malebranche, 2 vols., Paris, 1870-1872; Kuuo Fischer, Gesch. d. n. Philos., 3d ed., I., 1, Eng. trans, by J. P. Gordy, New York, Scrib- ners, 1887; Martineau, Ti/pes of Ethical Theory, 2d ed., Vol. 1, p. 159 sq. For a critical account of Malebranche's place in the history of philosophy, cf. Edward Caird, article " Cartesianism," in Encyclop. Brit., 9th ed. For Leib nitz's correspondence witli Malebranche, cf. Gerhardt, Leibniz, philos. Schrift., 1, 315-361; for his discussion of Malebranche's philosophy, cf. Gerhardt, 3, 656-660, Erdmann, 735-737, Dutens, 2, Pt. I., 213, trans. Duncan, 233-237; G. 6, 579-594 (cf. also 481-483), E. 690-697, U. 2, Pt, I., 201; G. 6, 574-578 (cf. also 480-483; Locke's examination of Malebranche is in his Philos. Works, Vol. 2, 413-458, Bohii's ed.), E. 450-452, trans. Duncan, 185-189. — Tu.
422 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv truth of our existence and the cause of phenomena is of a different nature, because it establishes substances, and that the Sceptics spoiled what they rightly say by carrying it too far, and by wishing indeed to extend their doubts even to immediate experience, and to the geometrical truths, a thing which Foucher did not do however, and to the other truths of reason, which he did a little too much. But to return to you, sir, you are right in saying that there is ordinarily some difference between feelings and imaginations; but the Sceptics will say that the more or less does not alter the species. Be sides, although feelings are wont to be more vivid than im aginations, it is nevertheless a fact that there are cases where imaginative persons are impressed as much or perhaps more by their imaginations than another is by the truth of things; so that I think the true criterion concerning the objects of the senses is the connection of the phenomena, i.e. the connection of that which takes place in different places and times, and in the experience of different men who are themselves, each to the others, very important phenomena in this respect. And the connection of the phenomena which guarantees the truths of fact in respect to sensible things outside of us, is verified by means of the truths of reason; as the phenomena of optics are explained by geometry. It must, however, be admitted that none of this certitude is of the highest degree, as you have well recognized. For it is not impossible, metaphysically speaking, that there may be a dream continuous and lasting like the life of a man; but it is a thing as contrary to reason as would be the fiction of a book which should be formed by chance by throwing together the type pell-mell. For the rest, it is also true that, provided the phenomena are connected, it does not matter whether they are called dreams or not, since experience shows that we are not deceived in the measures we take concerning phenomena when they are understood accord ing to the truths of reason.1] 1 Of. New Essays, Bk. III., chap. 4, § 2, Th., ante, pp. 318, 319, notes 1 and 2, and Bk. IV., chap. 11, § 10, Th., infra, p. 512. The principle of the "con nection of the phenomena," their constant occurrence in the same order and relations, giving them a certain measure of objectivity in pur consciousness and enabling us to predict the appearance of other members of the series when one member presents itself, is for Leibnitz the guarantee of the truth of our sense-knowledge and the ground of our greatest possible certainty therein; en. in] ON HUMAN UNDERSTANDING 423 §15. Ph. For the rest, knowledge is not always clear, though ideas may be. A man who has as clear ideas as any mathe matician in the world of the angles of a triangle and of equality to two right angles, may yet have a very obscure perception of their agreement.
Hi. [Ordinarily when ideas are thoroughly understood their agreements and disagreements appear. I admit, however, that at times some of them are so complex, that much care is needed to develop what they conceal; and in this respect certain agreements or disagreements may still remain obscure. As to your example,' I remark that if we have in the imag ination the angles of a triangle we do not on that account have clear ideas of them. The imagination cannot furnish us an image common to acute-angled and obtuse-angled triangles, and yet the idea of triangle is common to them: thus this idea does not consist in images and it is not as easy as you may think thoroughly to understand the angles of a triangle.]
CHAPTER III OF THE EXTENT OF HUMAN KNOWLEDGE § 1. Ph. Our knowledge does not extend beyond our ideas, § 2. nor beyond the perception of their agreement or dis agreement. § 3. It cannot always be intuitive, because we cannot always compare things immediately, for example, the size of two triangles upon one and the same base, equal, but very different. § 4. Our knowledge, also, cannot always be demonstrative, for we cannot always find mediate ideas. § 5. Finally, our sensitive knowledge regards only the existence of things which actually strike our senses. § 6. Thus not only our ideas are limited, but also our knowledge is more limited than our ideas. I do not doubt however that human knowl edge can be carried much farther if men will devote thembut lie holds that this guarantee is " verified," and the consecutions of experi ence supplemented, "by means of the truths of reason," and particularly by the use of the principles of logic. The position here taken is also that of the modern scientist, who keeps strictly within the scientific realm and does not pass on to consider the ultimate metaphysical nature and grouud of the phenomena he investigates. — TR.
424 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv selves sincerely to discovering the means of perfecting truth, with entire freedom of mind and with all the application and industry they employ in coloring or maintaining falsehood, in defending a system in favor of which they have declared themselves, or else a certain party and certain interests, with which they find themselves united. But after all our knowledge can never embrace all we may wish to know concerning the ideas we have. For example, we shall never perhaps be able to find a circle equal to a square, and know certainly that it is so. Th. [There are confused ideas in which we cannot promise ourselves a complete knowledge, like those of certain sensible qualities. But when they are distinct, there is room to hope for all. As for the square equal to the circle, Archimedes has already shown that "there is one. For it is the one whose side is the mean proportional between the semi-diameter and the semi-circumference. He has also determined a straight line equal to the circumference of the circle by means of a straight line tangent to the spiral, as others by the tangent to the quadratrix; a method of quadrature with which Clavius l was wholly content; not to speak of a thread applied to the cir cumference and then stretched out, or of the circumference which revolves to describe the cycloid and is changed to a straight line. Some demand that the construction be made by employing only the ruler and the compasses; but the majority of geometrical problems cannot be constructed by this means. The question then is rather that of finding the proportion between the square and the circle. But this pro portion not being capable of expression in finite rational num bers, it has been necessary, in order to employ only rational numbers, to express this same proportion in an infinite series 2 1 Christopher Clavius, 1537-1012, a Jesuit and distinguished mathematician, Professor of Mathematics at Rome, and called " the Euclid of the sixteenth century," was employed by Pope Gregory XIII. in the reformation of the calendar, for which he made the principal calculations. Among his works are: Eudidis elementorum, Rome, 1574; Sinus linese tangentes, etc., Rome, 158(), 4to; Romani Calendarii a Gregorio XIII. P.M. restituti Explicrttio, Rome, KiO.'i. His Opera mathematica, containing these and several other works, appeared at Mayence, 1G12, 5 vols., fol. — TK.
2 Leibnitz's infinite series, which, according to Schaarschmidt, he had dis covered before he became acquainted with Huygens, and also before his discovery of the infinitesimal calculus, is =1 —,; ~l~ ^o •"> an^ en. in] ON HUMAN UNDERSTANDING 425 of these numbers, which I have assigned in a manner quite simple. Now we should like to know whether there is not some finite quantity, although it be irrational only, or more than irrational, which can express this infinite series, that is to say, whether we can find exactly an abbreviated expression for this series. But finite, especially irrational, expressions, if we proceed to the most irrational of all, may vary in too many ways for us to be able to make an enumeration of them or to determine easily all that they are capable of. There might be perhaps a means of doing it if this irrationality should be ex plained by an ordinary, or even more, an extraordinary equaas related to unity it expresses the proportion obtaining between the circle and the circumscribed square. Cf. De vera proportione circuit ad quadratum circumscriptum in numeris rationalibus, "Acta Enid. Lips.," February, 1682, p. 41 sq., Gerhardt, Leibniz, math. Schrift., II., 1 [Vol. 5], 118, Dutens, Leib- nit. op. om., 3, 140 sq.; Quadratura arithmetica, "Acta Erud. Lip.," April, 1(591, p. 180, Gerhardt, Leibniz, math. Schrift., II., 1 [Vol. 5], 130, Dutens, 3, 242; also letter to Conring, Jan. 3, 1678, Gerhardt, Leibniz, philos. Schrift.,