312 LEIBNITZ'S CRITIQUE OF LOCKE [BK. m or the next general term; and this is for the purpose of spar ing ourselves the trouble of counting the different simple ideas which this genus signifies, or sometimes perhaps for the pur pose of sparing ourselves the disgrace of being unable to make this enumeration. But although the shortest way of defining is by means of genus and difference, as the logicians say, it may be doubted, in my opinion, whether it is the best; at least it is not the only way. In the definition which states that man is a rational animal (a definition which is perhaps not the most exact, but which serves well enough the present pur pose), instead of the word animal you might put its definition. And this shows the little necessity of the rule which requires that a definition must be composed of genus and difference,1 and the little advantage there is in its strict observance. Thus languages are not always made according to the rules of logic, so that the meaning of each term may be exactly and clearly expressed by two others. And those who made this rule have done ill in giving us so few definitions conformable to it.
Th. [I agree with your remarks; it would be advantageous, however, for many reasons, if definitions might consist of two terms: it would without doubt greatly shorten them, and all divisions could be reduced to dichotomies which are the best species of divisions, and are particularly useful for invention, judgment, and memory. I do not, however, think logicians always demand that the genus or the difference be expressed in a single word; for example, the term regular polygon may pass as the genus of the square, and in the figure of the circle the genus might be a plane curvilinear figure, and the dif ference might consist in the fact that all points of the circum ference are equally distant from a certain point as centre.2 2 Leibnitz rightly takes exception to Locke's censure of Aristotle's rule regarding definition, given in the preceding note, viz.: that it must consist of the genus and the species-forming difference, remarking that genus and dif ference may very often be interchanged, the possibility of this interchange depending upon the principle on which, or the point of view from which, the classification is made, or upon the closeness with which the genus and the species-forming difference approach each other, it being essential to valid interchange that they be actually alike, or so nearly so that the difference is en. ni] ON HUMAN UNDERSTANDING 313 For the rest, it is also well to remark that very often the genus may be changed into a difference and the difference into a genus. For example, the square is a regular quadrilateral, or rather a four-sided figure that is regular, so that the genus or the difference seems to differ only as the substantive and adjective; as if, instead of saying that man is a rational living being (animal raisonnable), language allowed the statement that man is a living rational being (rational animable), i.e. a rational substance endowed with an animal nature; while genii * are rational substances whose nature is not animal or common with the animals. And this interchange of genera and differentia depends upon the variation of the order of the sub-divisions.]
§ 11. Ph. It follows from what I have just said, that what is called general and universal belongs not to the being (exist ence) 2 of tilings, but that it is a work of the understanding, § 12, and the essences of each species are only abstract ideas.
Th. [I do not quite see this consequence. For generality consists in the resemblance of separate things among them selves, and this resemblance is a reality.]
§ 13. Ph. I was going myself to say to you that these species are founded upon resemblances.
Th. [Why, then, not seek therein also the essence of genera and species?]
§ 14. Ph. You will be less surprised to hear me say that these essences are the work of the understanding, if you con sider that there are at least complex ideas which in the minds of different persons are often different collections of simple ideas, and thus what is avarice in the mind of one man is not so in the mind of another.
practically of no account. Cf. New Essays, Bk. III., chap. 3, ante, p. 30$. Such definitions, while not strictly logical or scientific in the full sense of these terms, hut tentative rather, and, as it were, popular, are nevertheless useful, and indeed necessary, in ordinary life and in science, where we must classify to a certain extent for the sake of relative clearness, but where strict logical definition is not essential, or is impossible because of the insufficiency of our knowledge. Logically exhaustive definition, save in the realm of pure thought and in such sciences as the pure mathematics, is possible only to an infinite mind who possesses exhaustive knowledge of all principles and facts involved. Exhaustive knowledge of an individual demands an exhaustive knowledge of all other individuals. Cf. N. E., Bk. III., chap. 3, § (i, Th., ante, p. 309.— TK.
1 I.e. angels and archangels. — TR.
2 Locke has: " real existence," Philos. Wks., Vol. 2, p. 14 (Bolm'sEd.). — TK.
314 LEIBNITZ'S CRITIQUE OF LOCKE [BK. in Th. [I admit, sir, that there are few cases in which I have less understood the force of your inferences than here, and this troubles me. If men differ in the name, does it change the things or their resemblances? If one applies the name avarice to one resemblance, and another to another, there will be two different species designated by the same name.]
Ph. In that species of substance which is most familiar to us and with which we are most intimately acquainted, it has many times been doubted whether the offspring brought into the world by a woman was a man,1 even to discussing whether he should be fed and baptized. This could not be if the ab stract idea or the essence, to which the name man belongs, were the work of nature, and not a diverse, uncertain collection of simple ideas which the understanding put together, and to which it attached a name, after having made it general by way of abstraction. So that at bottom each distinct idea, formed by abstraction, is a distinct essence.
Th. [Pardon me for telling you, sir, that your language perplexes me, for I do not see its connection. If we cannot always discern by the outside the internal resemblances, are there less of them in nature? When we doubt whether a monster is a man, we doubt whether it has reason. When we know it has, the theologians will order it to be baptized, and the jurisconsults, to be fed. It is true that we may dispute about the lowest species logically considered, which vary by accidents in one and the same physical species, or species by direct descent (tribu de generation'),'2' but we do not need to determine these; we may, indeed, vary them infinitely, as is seen in the great variety of oranges, lemons, and citrons, which experts know how to name and distinguish. The same thing was seen in tulips and pinks when these flowers were in fashion. For the rest, the fact that men unite these or those ideas, or even that nature actually unites them or not, makes no difference as regards essences, genera, or species, since the question only concerns possibilities, which are independent of our thought.]
1 Cf. Locke, Philos. Works, Vol. 2, p. 17, and note (Bonn's Ed.). — TR.
2 Cf. New Essays, Bk. III., chap. 6, § 14, Gerhardt, 5, 288, line 14; Erdmann, 313, a; Jacques, 1, 234. The term "species," in Leibnitz's day, denoted not merely similarity of external form and characteristics, but more essentially the genetic relationship of common descent. — TR.
CH. in] ON HUMAN UNDERSTANDING 315 § 15. Ph. The species of each thing is ordinarily supposed to have a real constitution, and it is beyond doubt that some real constitution must exist upon which every collection of simple ideas or qualities co-existing in this thing must depend. But as it is evident that things are ranked in sorts or species under certain names only as they agree with certain abstract ideas to which we have attached these names, the essence of each genus or species comes thus to be nothing else than the abstract idea signified by the general or specific name, and we shall find this to be the import of the word essence, according to its most ordinary use. It would not be a bad thing, in my opinion, to designate these two kinds of essences by two different names, and to call the one real, and the other, nominal essence.
Tli. [It seems to me that our language makes extreme inno vations in the method of expression. AVe have indeed spoken hitherto of nominal and causal or real definitions, but not within my knowledge of essences other than real, at least by nominal essences have not been understood false and impos sible essences, which appear to be essences, but are not; as, for example, would be that of a regular decahedron, i.e. of a regular body comprised within ten planes.1 Essence is at bottom nothing less than the possibility of that which we think. What we assume as possible is expressed by the defi nition; but this definition is only nominal when it does not express at the same time, possibility; for then we may doubt whether this definition expresses anything real, i.e. possible, until experience comes to our aid to make us know this reality a posteriori,2 when the thing is actually found in the world: and this suffices for the defect of the reason, which made us know the reality a priori 2 by exposing the cause or the possible generation of the definite thing. It does not then depend on us to unite ideas as seems good to us; at least, this combination is not justified either by reason which shows it as possible, or by experience which shows it as actual, and consequently, also possible. In order the better to distinguish, also, essence and 1 This figure is impossible, the only possible regular polyhedrons being the tetrahedron, hexahedron, octohedron, dodecahedron, and icosahedron. — TR.
310 LEIBNITZ'S CRITIQUE OF LOCKE [BK. in definition, you must consider that there is only one essence of the thing, but that there are many definitions which express one and the same essence, as the same structure or the same city may be represented by different scenographies according to the different sides from which it is regarded.]
§ 18.1 Ph. You will, I think, agree with me that the real and the nominal are always the same in simple ideas and in the ideas of the modes; but in the ideas of substances, they are always entirely different. A figure which bounds a space by three lines is the real as well as the nominal essence of the triangle; for it is not only the abstract idea to which the general name is annexed, but the essence or proper being of the thing, or the foundation whence proceed its properties, and to which they are annexed. But it is wholly otherwise as regards gold. The real constitution of its parts, upon which its color, weight, fusibility, firmness, etc., depend, is unknown to us; and, having no idea of it, we have no name that is its sign. Yet these are the qualities which cause the matter to be called gold, and are its nominal essence, i.e. which give it a right to the name.
Tli. [I should prefer to say, in accord with received usage, that the essence of gold is that which constitutes it and which gives it these sensible qualities, which make it known and which make its nominal definition, while we should have the real and causal definition if we could explain this contexture or internal constitution. But the nominal definition is here found real also, not by itself (for it does not make known a priori the possibility or the genesis of bodies), but by experi ence, because we have experience of a body in which these qualities are found together: but without this we might doubt whether so much weight would be compatible with so much malleability, as it may be doubted, even at present, whether a glass malleable by cold is possible in nature.2 I am not, for the rest, of your opinion, sir, that there is here the difference 1 § 18, in Locke, Philos. Works, 2, p. 19 (Bolm's ed.); so Gerhardt: Erdmann, Jacques, and Schaarsohmidt in his German translation, have § 19. — TR.
2 Cf. Pliny the Elder, 23-79, Histor. Natur., Bk. 3(i, chap. GO; Eng. trans. (Bolm's Class. Lib.), Vol. 6, p. 381, London, 1857. " In the reign of Tiberius, it is said, a combination was devised which produced a flexible glass...This story, however, was, for a long time, more widely spread than well authenti cated " — " fama crebrior quam certior." — TR.
cir. m] UN HUMAN UNDERSTANDING 317 between the ideas of substances and the ideas of predicates, as if the definitions of predicates (i.e. of the modes and the objects of simple ideas) were always real and nominal at the same time, and that those of substances were only nominal. I quite agree that it is more difficult to have real definitions of bodies, which are substantial existences because their con texture is less sensible. But it is not the same with all sub stances; for we have a knowledge of true substances or unities (as God and the soul) as intimate as we have of the most of the modes. Besides, there are some predicates as little known as the contexture of bodies; yellow or bitter, for example, are objects of simple ideas or notions (phantasies1}, and yet we have only a confused knowledge of them.2 The case is the same in mathematics, where one and the same mode may have a nominal as well as a real definition. Few people have clearly explained in what consists the difference between these two definitions which must distinguish, also, essence and prop erty. In my opinion, this difference is that the real shows the possibility of the thing defined, and the nominal does not.3 1 Schaarschmidt translates: " die Gegenstiinde einfacher Vorstellungen oder Phantasiebilder." — TR.
2 Cf. New Essays, Preface, ante, p. 48, ad fin, and Bk. IV., chap. G, § 7, Th. (2), infra, p. 458. According to Leibnitz, sense-knowledge is confused, and needs to be developed into clearness and consistency by the discriminative analysis and unifying power of thought. Phenomena such as colors, sounds, etc., the subjective counterpart or resultant of specific sense-energies, resist all further analysis, and while clear as wholes, are composite, insoluble, and so confused as regards their single elements. Such wholes admit only descriptive, not, strictly speaking, logical definition. Cf. Med. de Cor/., Ver., et Id. ad init., Gerhardt, 4. 422, Erdniann, 78, a, trans. Duncan, Philos. Works of Leibnitz, 27.
3 Of. ante, pp. 17, 201, and Mad. de Cor/., Ver., et Id, Gerhardt, 4, 424, Erdmann, 80, b, trans. Duncan, Philos. Works of Leibnitz, 30; also G. 6, 40"), E. <>:>", a, Dutens, Leibnit. opera omnia, 1, 43'J; G, 44; G. 7. 104 and note. As the nominal definition explains a thing according to the name, we may have nominal definitions of objectively non-existent or of impossible things, as centaurs, griffins, or any of the creatures of the fancy or the imagination, or the decahedron mentioned in § 15, Th., of this chapter, ante p. 315. The real definition explains the thing to be defined by exhibiting its cause or generation, its rise out of its conditions, i.e., its possibility; it is thus identical witli the genetic definition, and Leibnitz accordingly calls it the causal definition, ante p. 31(>. Cf. also Dewey, Leibniz's New Essays, 210; Hamilton, Lor/ic, 343; Trendelenburg, Uebcr d. Element d. Definition in Leibniz. Philosophic in Histor. Beitr. z. Philos., Berlin, 18G7, Vol. 3, pp. 48-G2. Trendelenlmrg calls special attention to the fact that Leibnitz, in definition, has in mind especially the analytical element, explaining definition as an unfolding of the concept, 318 LEIBNITZ'S CRITIQUE OF LOCKE [BK. in The definition of two parallel straight lines, which states that they are in one and the same plane and will not meet although continued to infinity, is only nominal, for we could at once doubt whether that is possible. But when we have under stood that we can draw a straight line in a plane parallel to a given straight line provided we take care that the point of the style describing the parallel remains always equally distant from the given line, we see at once that the thing is possible, and why they have this property of never meeting, which con stitutes their nominal definition, but which is the sign of the parallelism only when the two lines are straight, while if one at least were curved, they might be by nature unable ever to meet, and yet not on that account be parallel.
§ 19. Ph. If essence was something else than the abstract idea it would not be ingenerable * and incorruptible. A uni corn, a mermaid, a perfect circle, perhaps do not exist in the world.
Th. [I have already told you, sir, that essences are perpetual, because here the question concerns only the possible.]
CHAPTER IV OF THE NAMES OF SIMPLE IDEAS § 2. Ph. I confess I have always believed that the forma tion of the modes was arbitrary; but as regards simple ideas and those of substances, I have been persuaded that, besides possibility, these ideas should signify a real existence.
Th. [I see no necessity for it. God has ideas before creating the objects of these ideas, and nothing prevents Him from being able also to communicate such ideas to intelligent creat ures: there is also no exact demonstration proving that the objects of our senses and of the simple ideas which the senses or its resolution into several concepts equivalent to the one concept — " definire est explicare notionem, resolvere in plures notiones uni aequivalentes; " cf. Dutens, op. cit.,4, (>8: " definitio nihil aliud, quam accurata nominis explicatio est"; G. 4, 140, E. GO, b: "definitio enim nihil aliud est, quam signincatio verbis expressa, sive brevins, si^nifieatio significata." — TB.
CH. iv] ON HUMAN UNDERSTANDING 319 present to us are outside us.1 This fact has especial weight in the case of those who believe with the Cartesians and with our distinguished author, that our simple ideas of sensible qualities have no resemblance to that which is outside us in the objects; there would then be nothing requiring these ideas to be grounded in any real existence.2] §§ 4, 5, 6, 7. Ph. You will grant me at least this other difference between simple and complex ideas, that the names of simple ideas cannot be defined, while those of complex ideas can be. For definitions should contain more than one term, each of which signifies one idea. Thus you see what can or cannot be defined, and why definitions cannot go on to infinity; a remark which no one, so far as I know, has up to this time made.
Th. [I have also made the statement in the brief Essay upon Ideas? inserted in the " Actes de Leipzic " about twenty years since, that simple terms cannot have nominal definitions; but I have there added at the same time the statement that terms, when they are simple only as regards us (because we have no means of analyzing them so as to reach the elementary / 1 The demonstrability of the reality of that which lies at the basis of the phenomena of the senses is one of the most difficult problems in the theory of knowledge — Erkenntnisslehre. Leibnitz seems nowhere to have discussed the question, at least in this form, nor to have asked himself how, agreeably to his philosophical system, a knowledge of the reality of the external world could be demonstrated or a belief therein justified. So far as his system sug^""\ gests any answer consistent with itself, that answer is found in his doctrine of I pre-established harmony, in the consciousness of which we pass immediately I from our inner representative world of ideas to belief in the reality of the I external things thus ideally represented. This, however, like Descartes^) attempt to bridge the chasm from the subjective to the objective by his doctrine of God's veracity, is mere assumption, not " exact demonstration." The problem belongs to both psychology and metaphysics, and is satisfactorily discussed and solved only when considered in these two aspects. Leibnitz was an idealist in psychology, and a realist in metaphysics, and never really har monized or united these two points of view. For him, therefore, there could be ''no exact demonstration" of the external reality of "the objects of our senses and of the simple ideas which the senses present to us." (Jf. Discours df, Metaphysique, §§ 2<! sq., Gerhardt, Leibniz, philos. Krhrift., 4. 451 «</., E. Caird, The Crit. Philos. of Immanuel Kant, 1, 8(3-95. New York, Macmillan 2 Cf. New Essays, Bk. II., chap. 8, §§ 21, 24, ante, pp. 133-135; also Bk. IV., chap. 11. The constancy of sense-phenomena is the constraining reason for referring them to something real. Cf. Dewey, Leibniz's New Essays, 173 sq.; Gerhardt, Leibniz, philos. Schrift. 7, 319. 07. — TR.
320 LEIBNITZ'S CRITIQUE OF LOCKE [UK. in perceptions of which they are composed), as heat, cold, yellow, green, can receive a real definition which would explain their cause. Thus, the real definition of green is that of an entity composed of blue and yellow thoroughly mixed,1 although green is no more susceptible of a nominal definition by which we may recognize it than blue or yellow. Terms 011 the other hand which are simple in themselves, i.e. whose conception is clear and distinct, cannot receive any definition, whether nominal or real. You will find in this little Essay, placed in the " Actes de Leipzic," the foundations of a large part of the doctrine concerning the understanding, briefly explained.]
§§ 7, 8. Ph. It were well to explain this point and to indi cate what can be defined, what not. And I am tempted to believe that often great disputes are raised and much nonsense introduced into men's discourse from a failure to consider this matter. These celebrated trifles about which so much stir is made in the schools have arisen from the fact that no attention has been paid to this difference which is found in ideas. The greatest masters in the art have been constrained to leave the majority of simple ideas without defining them, and when they have undertaken to define them, they have not succeeded. What more superfine nonsense, for example, could the mind of man invent than that which is contained in this definition of Aristotle: Motion is the realization of that which is possible so far as it is possible?2 § 9. And the moderns who define motion as passage from one place into another, merely put one synonymous word in the place of another.
Th. [I have already remarked in one of our past conferences that you consider many ideas as simple which are not so. Motion is of this number which I believe to be definable; and the definition which states that it is a change of place is not to be despised. Aristotle's definition is not so absurd as you 1 This is true of pigments, but not of lights. Blue and yellow lights when mixed produce white light. — TR.
2 Cf. Neio Essays, Bk. II., chap. 21, § 1, Th. ante, p. 174. For Aristotle's Kivriffit effTiv, also 33; Wallace, Outlines of the Philos. of Aristotle, § 42, p. 77; Zeller, Philos. d. Griec., 3d ed., 1879, II., 2 [Vol. 4], p. 350 $q., with the notes.
en. iv] ON HUMAN UNDERSTANDING 321 think, this supposed absurdity arising from the failure to understand that the Greek Kivyvis with him did not signify what we call motion, but what we would express by the word change, whence it comes that he gives it a definition so abstract and metaphysical, while what we call motion is called by him cf>opd, latio, and is found among the species of change (rr/s Kivr/a ecos ).
§ 10. Ph. But you will not apologize, at least, for the same author's definition of light as the action of the transparent.2 Th. [I find it, as you do, very useless; 3 and he makes too frequent use of his action, which does not tell us much. Diaphanous is for him a medium across which we can see; and light is, according to him, that which consists in the actual passage. Well and good.]
§ 11. Ph. We agree, then, that our simple ideas cannot have nominal definitions, as we cannot know the taste of pine apples by the accounts of travellers, unless able to taste things by the ears, as Sancho Panza had the power to see l)ulcinea by hearsay,4 or as that blind man who, having been heard to speak boldly of the brilliancy of scarlet, thought it must resemble the sound of the trumpet.
Th. [You are right; and all the travellers in the world 1 Cf. Phys. AcrOCtS., VII. 2, 243a, 0 sq.: ***'<• Se rpeis eio-t (avijo-eis, j) re Kara roirov Kai Kara TO woicy /cai Kara TO noaov, dcay/cr) (cai T<i Kivov^tva. Tpi'a. 17 fikv oiiv Kara, ronov </>opa, r; 5e Kara. TO iroiov oAAocioais, r; 6e Kara TO noaov ai"f>)o-t9 «ai <j>di<T(.<;, Et/l. NlC. X., 3, 1174a,."0: ei yap iariv r; <£opa KiV7)<ris noOev TTOI (Alex. Grant, The EthicS Of Aristotle, Vol. 2, p..'524, line 17, 3d ed., London: Longmans, Green, & Co., 1874); Wallace, Outlines, § 42; Zeller, Philos. d. Griec., 3d ed., 1879, II., 2 Psychology in Greek and English w. Introd. and Notes, Cambridge: Univ. Press, 1882, pp. 95, 97, translates the two passages: " Light then is the expres sion of the pellucid qua pellucid," "The full play of this pellucid constitutes light," and, in his Introd., p. Ixxi., combines them thus: " Light therefore may itself be defined as the actual expression or full play of the pellucid as pellucid." Cf. also Zeller, Philos. d. Griec., 3d ed., 1879, II., '2 [Vol. 4], p. 477, note 2.
8 Schaarsohmidt calls attention to "a bad typographical error" in the text of Raspe's edition of the Nouveaux Essais at this point. Raspe reads " fort ufcile," for which Schaarschmidt proposes "futile." Gerliardt, Erdmann, and Jacques all read " fort inutile," which gives the requisite sense, and is accord ingly followed in the translation. — TR.
4 Cf. Cervantes, 1547-1010, Don Quixote, Pt. 2, chap. 9, ad med.; also, Pt. 1, Y 322 LEIBNITZ'S CRITIQUE OF LOCKE [UK. m could not give by their words what we owe to a gentleman of this country who cultivates successfully pine-apples three leagues from Hannover, almost upon the bank of the Weser, and who has found means of multiplying them to such an extent that some day we can perhaps have them of our own growing in as great abundance as the oranges of Portugal, though there would apparently be some loss in the flavor.]
§§ 12, 13. Ph. It is wholly otherwise with complex ideas. A blind man can understand what a statue is; and a man who had never seen the rainbow could understand what it is, pro vided he had seen the colors which compose it. § 15. But though simple ideas are inexplicable, they are the least doubt ful. [For experience accomplishes more than definition.]
Th. [There is, however, some difficulty as to the ideas which are only simple as regards us. For example, it would be diffi cult to indicate precisely the limits of blue and of green, and in general to discriminate colors closely approaching one another, while we can have precise notions of the terms used in arith metic and geometry.]
§ 16. Ph. Simple ideas have further this peculiarity that they have very little subordination in what the logicians call the line of predication (ligne predicamentale),l from the lowest