Th. [In fact this last kind of certainty will also suffice with out the use of words, and is nothing else than a perfect knowl edge of the truth; while the first kind of certainty appears to be nothing else than the truth itself.]
§ 4. Ph. Now as AVC cannot be assured of the truth of any general proposition, unless we know the precise limits of the signification of the terms of which it is composed, it will be necessary for vis to know the essence of each species, which is not difficult as regards the simple ideas and the modes. But in substances wherein a real essence distinct from the nominal is supposed to determine the species, the extent of the gene ral term is very uncertain, because we do not knoAv this real essence; and consequently in this sense ive cannot be assured of any general proposition made upon the basis of these sub stances. But when we suppose the species of substances to be nothing else than the reduction of substantial individuals into certain sorts, arranged under different general names according as they agree with the different abstract ideas which we designate by these names, we cannot doubt whether a prop osition, well known as it should be, is true or not.
Th. [I do not know why you, sir, return again to a point sufficiently discussed by us, and which I believe an empty one. But, after all, I am very glad of it, because you give me an op portunity very suitable (it seems to me) to disabuse you anew. I say then to you that we can be assured, for example, of a thousand truths regarding gold, or that body whose internal essence makes itself known by the greatest weight known here below, or by the greatest ductility, or by other marks. For we say that the body of the greatest known ductility is also the heaviest of all known bodies. It is true that it is not impossible that all which has hitherto been noticed in gold will some day be found in two bodies distinguishable by other new qualities, and that thus gold would no longer be the low est species, as it has hitherto been regarded provisionally. We might also, if the one kind remained rare, and the other became common, think it proper to reserve the name of en. vi] ON HUMAN UNDERSTANDING 455 true gold to the single rare species, in order to retain it in use as money by means of new assays wliich would be suited to it. After which we shall not doubt, also, that the internal essence of these two species is different; and if indeed the definition of an actually existing substance should not be fully determined in all respects (as in fact, that of men is not as regards the external figure), we should not cease to have an infinite number of general propositions upon its subject, which would follow from reason and the other qualities which we recognize in it. All that we can say regarding these gen eral propositions is, that in case man is taken as the lowest species and restricted to the race of Adam, we shall have no properties of man such as are named in quarto modo,1 or may 1 The term in quarto modo, here used by Leibnitz, refers to a classification of propria — ISm, properties — existent in the time of Porphyry, 2,'53-304, though not accepted by him, — cf. Eio-aywyTj, chap. 4, 4°, 14 (in Aristotle, ed. Berl.
Acad., Vol. 4, p. 4): TO 5e ISiov SiaipoC<T<. reTpaxws...(18.) TerapToi/ Se €</>' ou <rvv- Se&pafjuriKe TO fj.6v<a xai navri Kai aei, <o« raj ivdpiaitia TO yeAaffTiKoi'...(22.) raura 6e Kal Kvpi'ws ISia <j>r)<Tii>, on (cai di/TKjTpe^ei — and due, perhaps, to some one of the old Peripatetics, and prevalent in different forms in the Middle Age, according to which classification as given by Porphyry there were four classes: 1. Propria belonging to one species only, but not to every individual thereof, as gram matical to man; 2. Propria belonging to every individual of the species, but not to this species alone, as biped to man; 3. Propria belonging to one species only and to every individual thereof, but not always, as hoary to man; 4. Pro pria belonging to one species only, to every individual thereof, always, as risibility or risible to man.
The propria of this fourth class — quartus modus — are, each, of equal breadth with its subject, and, though no part of the essence of the species of which they are predicated, — man, for example, without theproprium risible, still being man, — as a matter of fact belong to every individual of the species on all occasions, and to no individual of any other species. Propositions predi cating such propria are judgments in A, according to Archbishop Thomson's terminology, of the type "Common Salt is Chloride of Sodium," and are of coiirse convertible.
Propria of this fourth class alone, i.e. propria each of which would be coinci dent with its subject so as to be enouncible in a judgment in A — reciprocal — con stitute the fourth practicable, and answer to the lSi.ov of Aristotle and Porphyry, and the proprium of Appuleius, Marcianus Capella and Boetliius. These writers, with the exception of Aristotle, to whom probably the four-fold divis ion of propria was unknown, regard the other three classes, which were pro pria according to the Middle Age schoolmen, as accidents, — accidentia, <ri>/x|3e- Prj/cdra, — a fact which explains the somewhat peculiar language of Leibnitz: " We shall have no properties of man such as (of the sort that) are named in quarto modo," etc. Leibnitz's thought is this: " In the case of ' man ' " taken as the lowest species — species infima — and " limited to Adam's race, there is, except provisionally, no such proprium. ' Sole-rational-animal ' would be, provisionally, such a proprium, because up till now we know no men whom it 456 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv be enounced concerning him by a reciprocal or simply conver tible proposition, unless provisionally, as in saying: man is the only rational animal. Taking man as those of our race, the provisional consists in the assumption that he is the only rational animal of those known to us; for we might some day find other animals who would have in common with the posterity of men of the present time all that which we have hitherto observed in them, but who would have another origin. It is as if the so-called Australians should overrun our coun tries: in all likelihood we should then discover some means of distinguishing them from ourselves. But in case this should not happen, and supposing that God had forbidden this mixt ure of these races, and that Jesus Christ had redeemed ours only, it would be necessary to try to make some artificial marks in order to distinguish between them. There would doubtless be an internal difference, but as it would not make itself recog nizable, we should be reduced to the extrinsic denomination of birth alone which we should try to accompany with a durable artificial mark that would give an intrinsic denomination,, and a constant means of distinguishing our race from the others. These are all fictions, for we have no need to recur to these distinctions, being the only rational animals of this globe. Yet these fictions are useful in knowing the natures of ideas, substances, and truths general in their character. But if man were not taken as the lowest species nor as that of the rational animals of the race of Adam, and if, instead of that, he signified a genus common to several species, which belonged now to a single known race, but which might belong also to others distinguishable either by birth or even by their natural marks, as, for example, in the case of the supposed Australians; then, I say, this genus would have reciprocal propositions, and the present definition of man would not be provisional. It is would not fit, and know of no other species any of whose individuals it would fit. Only provisionally, however, for future discoveries may show, in either of these respects, that ' sole-rational-animal,' and ' man ' are not exactly coinci dent concepts." On the whole subject, c/. Prantl, Gesch. d. Lof/ik, Vol. 1, pp. 343, 395, 425, 581, 584, 030, 674, G7G, (596, Vol. 2, pp. 342-343, Vol. 3, p. 102, Vol. 4, p. 241, note 383; Aldrich, Artis Logicas Rudimenta, ed. Mansel, I would add that for much of the material as well as of the language of the above note, I am indebted to the kindness of Pres. E. B. Andrews of Brown University. — TR.
on. vi] ON HUMAN UNDERSTANDING 457 the same with gold; for suppose that some clay there were two kinds of it distinguishable, the one rare and hitherto unknown, the other common and perhaps artificial, discovered in the course of time; then suppose that the name gold should continue for the present species, i.e. for the natural and rare gold, in order to preserve by its means the commodity of gold money, based upon the rarity of this substance, its definition known hitherto by intrinsic denominations would have been provisional only, and should be augmented by new marks which will be discovered, to distinguish the rare gold or the ancient species from the new artificial gold. But if the name gold should then remain common to the two species, i.e. if by gold you mean a genus of which up to the present time we know no subdivision, and which we now take as the lowest species (but only provisionally until the subdivision is known) and if some day a new species were found, i.e. an artificial gold, easy to make, and which might become common; I say that in this sense the definition of this genus should not be judged provisional, but perpetual. And indeed, without troubling ourselves with the names man or gold, whatever name is given to the genus or to the lowest known species, and even if none should be given them, what has just been said would be always true of ideas, genera or species, and species will be defined provisionally only by the definitions of genera. But it will always be allowable and reasonable to assume, by means of a reciprocal proposition, that there is a real internal essence belonging either to the genus or the species, which makes itself known ordinarily by external marks. I have assumed hitherto that the race does not degenerate or change; but if the same race passed into another species, we should be so much the more obliged to recur to other marks and denominations intrinsic or extrinsic, without confining ourselves to the race.
§ 7. Ph. Complex ideas, which the names we give to the species of substances justify, are collections of ideas of certain qualities which we have observed coexisting in an unknown sub stratum which we call substance. But we cannot know cer tainly what other qualities coexist necessarily with such com binations, unless we can discover their dependence as regards their primary qiialities.
458 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv Th. I have already remarked before that the same (diffi culty) is found in the ideas of accidents, whose nature is a little abstruse, as, for example, are the figures in geometry; for when the question concerns, for example, the figure of a mirror which collects all the parallel rays into one point as a focus, many properties of this mirror may be found before its construction is known, but we shall be uncertain about many other relations it may have, until we find in it that which corresponds to the internal constitution of substances, i.e. the construction of this figure of the mirror, which will constitute as it were the key to ulterior knowledge.]
Ph. But if we had known the internal constitution of this body, we should have found therein only the dependence which the primary, or what you call manifest, qualities may have, i.e. you would know what size, figure, and moving force depend thereupon; but we should never know the connection which they may have with the secondary or confused qualities, i.e. with the sensible qualities, as colors, tastes, etc.
Th. The fact is, you still assume that these sensible quali ties, or rather the ideas we have of them, do not depend upon figure and movement in a natural way, but only upon the good pleasure of God, who gives us these ideas. You appear to have forgotten, sir, the remonstrance I have more than once made to you against this opinion, in order to make you think rather that these sensitive ideas depend in detail upon the fig ures and movements, and express them exactly, although we cannot distinguish therein this detail in the confusion of too great a multitude and minuteness of mechanical actions which strike our senses. But if we had reached the internal constitution of some bodies, we should see also how they must have these qualities, which would themselves be reduced to their intelligible reasons; although it would never be in em power to recognize them sensibly in these sensitive ideas which are a confused resultant of the actions of bodies upon us, as, now that we have the perfect analysis of green into blue and yelloAV, * and have scarcely anything more to ask in regard to it save as related to these ingredients, we are, however, incapable of analyzing the ideas of blue and yellow in our 1 Cf. ante, p. 320, note 1; also Leibnitz's letter to Th. Burnett, without date, but written, according to Gerhardt, in 1699, G., Leibniz, philos. Schrift., 3, CH. vi] ON HUMAN UNDERSTANDING 459 sensitive idea of green, for the very reason that it is a con fused idea. It is much the same as we cannot analyze the idea of the teeth of the wheel, i.e. of the cause, in the percep tion of an artificial transparency, which I have noticed among the clock-makers, made by the rapid rotation of a cog-wheel, which makes the teeth disappear, and an imaginary continu ous transparency appear in their place, composed of the suc cessive appearances of the teeth and their intervals, but in which the succession is so rapid that our phantasy cannot dis tinguish it. We find then, indeed, these teeth in the distinct notion of this transparency, but not in this confused sensitive perception, whose nature is to be and to remain confused; otherwise if the confusion ceased (as if the motion were so slow that we could observe its parts and their succession) this notion, i.e. this phantasm1 of a transparency would no longer exist. And as there is no need of imagining that God for his good pleasure gives us this phantasm, and that it is independent of the movement of the teeth of the wheel and their intervals, and as, on the contrary, we conceive it to be only a confused expression of what takes place in this movement, an expression, I say, that consists in the fact that these successive things are confounded in an apparent simul taneity: it is thus easy to think that it will be the same as regards other sensitive phantasms, of which we have not as yet so perfect an analysis, as of colors, tastes, etc. For, to speak the truth, they deserve this name phantasms rather than that of qualities or even of ideas. And it would suffice us in all respects to understand them as well as this artificial trans parency, without its being reasonable or possible to claim a further knowledge of them; for to desire these confused phantasms to abide, and yet to distinguish therein their in gredients by the phantasy itself, is a contradiction, is a desire to have the pleasure of being deceived by an agreeable per spective, and to desire that at the same time the eye see the de ception, which would destroy it. It is a case, in short, where — nihilo plus agas Quam si des operam, ut cum ratione insanias.2 1 Cf. ante, p. 445, note 1. Schaarschmidt here translates: " Phantasie- Erscheinnng "; in line 17 of this page, " Phantasievorstellung "; in lines 24, 26, 31, " Erscheinnngen." — TR.
400 LEIBNITZ'S CRITIQUE OF LOCKE [I?K. iv F>ut it often happens that men seek nodum in scirpo 1 and make difficulties where there are none, by demanding the impossible, and afterwards complaining of their impotence and of the limits of their light.
§ 8. Ph. All gold is fixed is a proposition, the truth of which we cannot certainly know. For if gold signifies a species of things, distinguished by a real essence, which nature has given it, we are ignorant what particular substances are of this species. Thus, although this may be gold, we cannot affirm it with certainty. If we take gold as a body endowed with a cer tain yellow color, malleable, fusible, heavier than any known body, it is not difficult to know what is or is not gold; but with all that, no other quality can be affirmed or denied with certainty of gold, than that which has a connection with this idea, according to a connection or incompatibility which may be discovered.2 Now fixity having no known connection with color, weight, and the other simple ideas which I have sup posed to constitute the complex idea we have of gold, it is impossible that we can know with certainty the truth of this proposition, that all gold is fixed.
Th. We know almost as certainly that the heaviest of all bodies known here below is fixed, as we know certainly that it will be light to-morrow. This is because we have tried it a hundred thousand times; it is an experimental certainty, and of fact, although we do not know the bond which unites the fixity with the other qualities of this body. Moreover, it is unnecessary to oppose two things which agree and amount to the same thing. When I think of a body, which is at the same time yellow, fusible, and which resists the cupel, I think of a body whose specific essence, although unknown in its interior, makes these qualities emanate from its depths, and makes itself known confusedly at least by means of them. I see nothing wrong in that, nor anything which requires you to return so often to the charge in order to attack it.
§ 10. Ph. It is enough for me now that this knowledge of the fixity of the heaviest of bodies is not known to us by the 2 According to the texts of Gerhardt and Erdmann. Jacques and Janet read: "Que ce qui a avec cette idee une connexion on une incompatibilite qu'on pent decouvrir "; i.e. than that which has a discoverable connection or incompatibility with this idea. — TR.
en. vi] ON HUMAN UNDERSTANDING 401 agreement or disagreement of ideas. And I for myself think that among the secondary qualities of bodies and the powers relating to them there cannot any two be named whose neces sary coexistence or incompatibility can be known with cer tainty, except the qualities which belong to the same sense and necessarily exclude one another, as when you can say that what is white is not black.
Th. I believe, however, that you might perhaps find them; for example, every palpable body (or that which may be felt by touch) is visible. Every hard body makes a noise when struck in the air. The tones of strings or wires are semi-pro portional to the weights which cause their tension. It is true that what you ask succeeds only as far as you conceive distinct ideas united with confused sensitive ideas.
§ 11. Ph. It is not always necessary to think that bodies have their qualities by themselves independently of anything else. A piece of gold, separated from the impression and influence of every other body, would immediately lose its yellow color and weight; perhaps, also, it would become friable and lose its malleability. You know how vegetables and animals depend upon the earth, air, and sun; how do you know whether the very distant fixed stars have not also an influence upon us?
Th. This is a very excellent remark; and if the contexture of certain bodies were known to us, we could not judge wholly of their effects without knowing the interior of those which touch and traverse them.
§ 13. Ph. Our judgment, however, may go further than our knowledge. For people sedulous in making observations can penetrate farther, and by means of certain probabilities resulting from an exact observation and by certain hints pur posely put together, often make just conjectures regarding that which experience has not yet discovered to them; but it is always only conjecture.
Th. But if experience justifies these consequences in a con stant manner, do you not find that you can acquire certain propositions by this means? Certain, I say, at least as those which assert, for example, that the heaviest of our bodies is fixed and that the one which is after it the heaviest is volatile, for it seems to me that the certainty (understanding it as moral 402 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv or physical), but not the necessity (or metaphysical certainty) of these propositions which are learned by experience alone and not by analysis and the bond of ideas, is established among us and with reason.1 CHAPTER VII OF PROPOSITIONS CALLED MAXIMS OB AXIOMS § 1. Ph. There is one species of propositions which under the name of maxims or axioms pass as principles of science, and because they are self-evident, we have been contented to call them innate) although no one that I knoiv of has ever tried to show the reason and ground of their extreme clearness, which forces us, so to speak, to give them our consent. It is not, however, useless to enter into this investigation and to see whether this great evidence is peculiar to these proposi tions alone, as also to examine how far they contribute to our knowledge.
Tli. This investigation is very useful and very important. But you must not suppose, sir, that it has been entirely neglected. You will find in a hundred places that the Scho lastics have said that these propositions are evident ex ter- minis, as soon as the terms are understood, so that they were persuaded that the force of conviction was grounded in the knowledge of the terms, i.e. in the connection of their ideas. But geometers have done very much more: that is 1 Metaphysical and moral or physical certainty differ as the certainty of the truths of reason and the truths of fact. The truths of reason ground them selves in the necessities of thought, and their certainty is accordingly absolute. The truths of fact, in Leibnitz's view, rest upon the divine choice of the best, and have an evidence merely relative and established with the aid of experi ence; their necessity is accordingly only hypothetical. Cf. New Essays, Bk. II., chap. 21, § 8, Th., ante, pp. 179-180, and § 18, Th., ante, p. 183. The prin ciple upon which the whole matter depends is the famous distinction of the mediaeval scholastics between the understanding and the will of God, a prin ciple to which Leibnitz very often recurs, especially in order to maintain the contingency of the world, and to escape from the universal fatalism of Spinoza. According to this principle, the understanding of God is the source of the necessary truths, and the will of God the source of the contingent truths. The distinction, however, does not solve the problem either of the contingency of the physical universe or of the moral freedom of man. — Tn.
CH. vn] ON HUMAN UNDERSTANDING 463 they have undertaken very often to demonstrate them.1 Pro- clus already attributes to Thales of Miletus, one of the oldest known geometers, the wish to demonstrate the proposi tions which Euclid has since assumed as evident.2 It is said that Apollonius has demonstrated other axioms, and Proclus has also done so. The late Mr. Roberval, already eighty years old or thereabouts, intended to publish the new ele ments of geometry of which I think I have already spoken to you.3 Perhaps the "New Elements" of Arnauld, which at that time made some stir, had contributed thereto.4 He exhibited specimens of them in the Royal Academy of Sciences, and some found fault that assuming this axiom, if equal mag- 1 Leibnitz frequently refers, both in the New Essays and elsewhere, to the demonstrability of the axioms, and the thought was evidently a favorite one with him. It is a weighty thought, too; for all real advance in specula tive and truly and lastingly constructive thinking rests upon just this " work ing-over of the notions," as Herbart expresses it, this deeper penetration into their real meaning and content, and its exposition in the simplest possible intelligible forms. — TK.
2 Proclus cites Thales of Miletus in prop. XV., theor. VIII., of his In primum Euclidis Elementorum lib. Cornmentarii, ex recog. G. Friedlein, p. 299. Thales, c. 624-c. 550 B.C., was the founder of the Greek geometry, astron omy, and philosophy. For his geometry, cf. G. J. Allman, Greek Geometry from Thales to Euclid, Dublin, 1889; for his philosophy, cf. Zeller, Philos. d.
4 The work of Antoine Arnauld, 1G12-1694, here referred to is the Nouveaux Siemens de Ge'ome'trie, Paris, 1661, mentioned among the most prominent books of that time by Ch. Wolf in his Kurzer Unterricht v. d. vornehmsten math. Schrift., Wien, 17G3. Arnauld was an excellent mathematician, an able philosopher and theologian, a celebrated controversialist, and the indefatigable champion and mouthpiece of the Jansenists against the Jesuits. A zealous Catholic, he repeatedly tried to convert Leibnitz to that faith. Leibnitz's correspondence with him contains important matter regarding his own philos ophy. It was originally edited and published by C. L. Grotefend, Briefwcchsel z. Leibniz, Arnauld u. d. Landgrafen Ernst v. Hessen-Rheinfels aus d. Hand- schriften der Kb'nigl. Ribliothek z. Hannover, Hanover, 1846, and was re printed conformably to Grotefend's text by Janet, (Euvres philos. de Leibniz, Vol. 1, pp. 577-691, and, with a new comparison of the original Mss., by Ger- hardt, Leibniz, philos. Schrift., Vol. 2, pp. 11-138; cf. also his Einleitung, ib. p. 5 sq., and Vol. 1, p. 65, and for Leibnitz's first letter, unanswered, to Ar nauld, ib. 08-82 (Grotefeud, op. cit. 137 sq.).
Arnauld's (Euvres completes, with a life by Larriere, appeared at Paris.and Lausanne, 1775-1783, 45 vols., Vols. 38-40 containing the philosophical works. Of these the most important are: Des vraies et desfausses ide'es, 1683, directed against Malebranche, in which Arnauld develops his doctrine of perception and attacks the theory of representative ideas, on which cf. Hamilton's Reid, 8th ed., Vol. 1, pp. 295-298, Vol. 2, pp. 823 b, 963; Reflexions philos. et theolog. sur le nouveau systeme de la nature et de la grace du P. Malebranche, 1685- LEIBNITZ'S CKITIQUE OF LOCKE [HK. iv