the other two moods of the same figure.1 In the same way the second figure receives also two new ones. Thus the first and the second have six; the third has had six always; the fourth was given five, but it is found to have six also by the same principle of addition. But we must know that logical form does not bind us to this order of propositions which we commonly use, and I am of your opinion, sir, that this other arrangement is superior in value: All A is B, All B is C, therefore all A is C, which would be particularly by the sorites, which are a chain of such syllogisms. For if there were one more of them: All A is C, All C is D, therefore all A is D, we may make a chain of these two syllogisms, which avoids the repetition by saying: All A is B, All B is C, All C is D, therefore all A is D, wherein we see that the useless proposition All A is C is neglected, and the useless repetition of this same proposition which the two syllogisms would demand is avoided; for this proposition is henceforth useless, and the chain is an argument perfect and in good form without this same proposition when the force of the chain of reasoning has once for all been demonstrated by means of these two syllogisms. There is an infinite number of other chains of reasoning more complex, not only because a greater number of simple syllogisms enter therein, but also because the ingredient syllogisms exhibit greater differences among themselves, for there may be made to enter into them not only simple categoricals, but also copulatives, and not only categoricals, but also hypothetical; and not only com plete syllogisms, but also enthymemes, wherein the propo sitions believed evident are suppressed. And all this joined with the asyllogistic conclusions, and with the transposi tions of the propositions, and witli a multitude of turns and thoughts which conceal these propositions through the natural inclination of the mind to abridge, and by the properties of language appearing in part in the employment of the parti cles, will make a chain of reasoning which will represent the entire argumentation indeed of an orator, but emaciated 1 Cf. Difficult at es quasdam lor/iae, Gerhardt, 7, 211-217, Erdmann, 101-104; also Leibnitz's letter to Bourguet, March 22, 1714, G. 3, 509-70, E. 723 b. Tbe youthful demonstration referred to in this letter is found in the Dis- sertatio de Arte Conibiimtoria, 1GM, Problem II., § VI., G. 4, 4<i sq., E. 13 b. 5.7., Dutens, 2, Ft. I., 3T>2 sq., and is Leibnitz's most thorough and elaborate treatment of the moods and figures of the syllogism. — TK.
562 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv and stripped of its ornaments and reduced to logical form, not scholastic-ally, but always sufficiently to recognize its force, according to the laws of logic, which are none else than those of good sense, placed in order and in writing, and which differ no more than the custom of a province differs from what it had been when from unwritten as it was, it has become written, except that being put in writing and being capable of being better seen at once, it furnishes more light to enable it to be pushed and applied; for natural good sense without the aid of art, making the analysis of certain reasoning, will sometimes be a little in trouble regarding the force of conclusions, finding some, for example, which include some mood, valid for truth but less ordinarily vised. But a logician who wished us not to make use of such series, or wished not to make use of them himself, claiming that we must always reduce all the complex arguments to the simple syllogisms on which in fact they de pend, would be, according to what I have already said to you, like a man who wished to compel the merchants of whom he buys something to count for him the numbers one by one, as we count on the fingers, or as we count the hours of the town-clock; a procedure which would indicate his stupidity, if he could not count otherwise, or if he could discover only at his fingers' ends that five and three make eight, or rather it would indicate a caprice if he knew these short methods and did not wish to use them or to allow us to use them. He would be also like a man who wished us not to employ axioms and theorems already demonstrated, claiming that we must always reduce all reason ing to first principles in which is seen the immediate connection of the ideas upon which in reality these mediate theorems depend.
After having explained the use of the forms of logic in the way in which I think it should be understood, I come to your considerations; and I do not see, as you wish, sir, that the syllogism serves merely to exhibit the connection of proofs in a single example. To say that the mind always sees easily the conclusions, is a statement which will not be found true; for we sometimes see some (at least in the reasonings of another) where there is room for doubt at first so long as their demon stration is not seen. Ordinarily, we use examples to justify conclusions, but this method is not always sufficiently sure, CH. xvn] ON HUMAN UNDERSTANDING 563 although there is an art of choosing examples which would not be found true if the conclusions were not valid. I do not believe it would be permitted in well-governed schools to deny without any shame the manifest agreement of ideas, and it does not appear to me that we employ the syllogism to show them. At least this is not its unique and principal use. You will find oftener than you think (in examining the paralogisms of authors) that they have sinned against the rules of logic, and I have myself found by experience sometimes in discussion, even by writing, with persons of good faith, that we began to be understood only when we argued in form in order to disen tangle a chaos of reasonings. It would without doubt be ridic ulous to wish to argue after the scholastic fashion in important deliberations, because of the importunate and embarrassing prolixities of this form of reasoning, and because it is like counting on the fingers. But yet it is only too true that in the most important deliberations regarding life, the state, salva tion, men allow themselves to be dazzled often by the weight of authority, by the gleam of eloquence, by examples badly applied, by erithymemes falsely supposing the evidence of that which they suppress, and even by faulty conclusions; so that a severe logic, but of another turn than that of the School, would be only too necessary for them, among other things, to deter mine upon which side is the greatest probability. For the rest, the fact that the common herd of men ignore artificial logic, and that they do not cease thereby to reason well and sometimes better than the class practised in logic, this fact proves not its inutility any more than it would prove the inutility of artificial arithmetic, because we see that some per sons count well 011 ordinary occasions without having learned to read or write and without knowing how to handle the pen or the tokens as far as to rectify the errors of another who has learned to calculate, but who may be neglectful or confused in the characters and signs. It is true that syllogisms also may become sophistical, but their own laws serve to recognize them; and syllogisms do not convert or indeed conquer always; but this is because the abuse of distinctions and of badly understood terms renders their use prolix until it becomes insupportable, if it must be driven to extremities.
It remains for me here only to consider and to supplement 564 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv your argument, employed as an example of clear reasoning without the form of the logicians: God punishes man (an assumed fact); God punishes justly the one he punishes (a truth of reason which may be regarded as demonstrated); therefore God punishes man justly (a syllogistic conclusion extended asyllogistically a recto ad obliquum); therefore man is justly punished (an inversion of relation, but which is set aside because of its evidence); therefore man is guilty (an enthymeme, in which is suppressed this proposition which in reality is only a definition: he who is punished justly is guilty); therefore man could have done differently (a suppression of this proposition: he who is guilty could have done differently); therefore man was free (a further suppression: he who could have done differ ently was free); therefore (by the definition of freedom} he had the power of self-determination; which was to be proved. Re garding which I remark further that this therefore itself includes in reality both the unexpressed proposition (that he who is free has the power of self-determination) and is useful in avoiding the repetition of terms. And in tins sense noth ing would be omitted, and the argument in this view might pass as complete. You see that this reasoning is a series of syllo gisms entirely in accord with logic; for I do not now wish to consider the matter of this reasoning, wherein there might per haps be some remarks to make or some explanations to demand. For example, when a man cannot do differently, there are some cases in which he might be guilty before God, as if he were very glad to be unable to aid his neighbor in order to have an excuse. To conclude, I admit that the scholastic form of arguing is ordinarily inconvenient, insufficient, badly managed, but I say at the same time that nothing would be more impor tant than the art of arguing in form according to true logic, i.e. fully as to matter and clearly as to the order and force of the conclusions, whether self-evident or predemonstrated.
§ 5. Ph. I thought that the syllogism would be still less useful, or rather of absolutely no use in probabilities, because it pushes only a single topical argument.1 But I see now that 1 Aristotle, Topics, I., 1, 100« 27 sq., designates the "topical argument" as gism, or the syllogism which reasons from the probable in distinction from dn-oSeifi?, or the proof resting upon and leading back to first and necessary CH. xvn] ON HUMAN UNDERSTANDING 565 it must always furnish solid proof of what is certain in the topical argument itself, i.e. the probability therein found, and that the force of the conclusion consists in the form. § (5. But if syllogisms serve only in judging, I doubt whether they are capable of use in invention, i.e. in finding proofs and making new discoveries. For example, I do not think that the dis covery of the 47th proposition of the first book of Euclid is due to the rules of ordinary logic, for we first know it and then are able to prove it in syllogistic form.
Th. Comprising under syllogisms also the series of syllo gisms and everything which I call formal argumentation, we may say that knowledge, not self-evident, is acquired by infer ences which are valid only when they have their due form. In the demonstration of the said proposition which makes the square of the hypothenuse equal to the squares of the two sides, we divide the large square into parts and likewise the two small ones, and we find that the parts of the two small squares may all be found in the large one and neither more nor less. This is the proof of equality in form, and the equality of the parts is also proved by arguments in valid form. The analysis of the ancients was, according to Pappus, to take what is asked and to draw therefrom conclusions until they come to something given or known. I have remarked that for this result the proposition must be reciprocal in order that the synthetic demonstration may return in the contrary direction by the paths of analysis, but it is always a drawing of conclu sions. It is well, however, to remark here that in astronomical or physical hypotheses the return does not take place; but in like manner success does not demonstrate the truth of the hypothesis. It is true it renders it probable, but as this proba bility appears to violate the rule of logic which teaches that the true may be drawn from the false, it will be said that logical rules will not have entire sway in probable questions. I reply that it is possible for the true to be concluded from the truths. Cf. also Topics, VIII., 11, lf>2° 15, where he calls the o-uAAoyio-fibs SiaAeKTiKO? an en-ix^'pW* or attempted proof, and the <rvAAo-yio>cb<r AiroSeucriKOs a <j>i\o(r6<t>ripa or demonstration. On the whole snhject, cf. Zeller, Philos. d. Griech., II., 2 [Vol. 4], 242 sq., 3d ed., 1879; Prantl, Gesch. d. Lor/ik, 1, 95 sq.; Wallace, Outlines of the Philos. of Aristotle, § 2:5, pp. 47-48. Cf. also, New Essays, Bk. II., chap. 21, § <>f>, Th. (2), ante, p. 214, note 1; Bk. IV., chap. 2, § 14, Th., ante, p. 418, note 4. —Tin 566 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv false, but it is not always probable, especially when a simple hypothesis gives a reason for many truths, a thing which is rare and difficult to find. We might say with Cardan,1 that the logic of the probable has other consequences than the logic of the necessary truths. But the probability itself of these con clusions must be demonstrated by the conclusions of the logic of the necessary truths.
§ 7. Ph. You appear to apologize for common logic, but I see clearly that what you bring forward belongs to a more sublime logic, to which the common is only what the alphabet is to scholarship: a fact which makes me remember a passage of the judicious Hooker, who in his book entitled " Ecclesiasti cal Polity," Book I., § 6, thinks that if we could furnish the true helps of knowledge and of the art of reasoning, which in this age passing as enlightened are not much known and for which people put themselves to very little trouble, there would be as much difference as regards maturity of judgment between men who would make use of them and what men now are, as between the men of the present and imbeciles.2 I wish that our con ference may give occasion to some to make a discovery of these true helps of the art of which this great man who had so pene trating a mind speaks. They will not be the imitators who like the cattle follow the beaten track (imitatorum servum pecus).s 1 Girolamo Cardano, 1501-1576, an Italian physician, mathematician, and philosopher, whose complete works appeared at Lyons, Ki63, 10 vols., fol., and an account of whose philosophy will be found in Stockl, Gesch. d. Philos. d. Mittelalters, III. [Vol. 4], 452-458. — TK.
2 Richard Hooker, 1553-1600, attempted, in his Laws of Ecclesiastical Polity, to defend the Episcopal form of government of the Church of Eng land, as established by the Protestant sovereign and Parliaments, against the attacks of the Presbyterians. To this end he gives in the two first books of his work an exposition of the fundamental principles by which the disputed question should be decided, especially of the nature of law in general, as a philosophical basis for the rest of his discussion. It is this portion of his work that gives it its permanent place and value in English literature and philosophy.
The passage here referred to by Locke and Leibnitz runs thus, Eccles. Pol., Bk. I., chap. 6, § 3, Workx, ed. Isaac Walton, Oxford, Univ. Press, 1841, 2 vols., 8vo, Vol. 1, p. 164: " Wherefore if afterwards there might be added the right helps of true art and learning (which helps, I must plainly confess, this age of the world, carrying the name of a learned age, doth neither much know nor greatly regard), there would undoubtedly be almost as great dif ference in maturity of judgment between men therewith inured, and that which men now are, as between men that are now and innocents." — TK.
en. XVH] ON HUMAN UNDERSTANDING 567 Yet I dare say there are in this age some persons of such strength of judgment and of such large extent of mind, that they could discover new paths for the advance of knowledge, if they would take the trouble to turn their thoughts in that direction.
Th. You have well remarked, sir, with the late Mr. Hooker, that the world troubles itself but little about this; otherwise I think there are and have been persons capable of succeed ing therein. We must admit, however, that now we have great helps both on the side of mathematics and of philoso phy, in which the Essay concerning Human Understanding of your excellent friend is not the least. We shall see if we may not be able to profit therefrom.
§ 8. Ph. I must further tell you, sir, that I have believed that there was a visible mistake in the rules of the syllogism; but since we have conferred together you have made me hesitate. I will, however, set before you my difficulty. It is stated that no syllogistic reasoning can be conclusive unless it contains at least one universal proposition.1 But it seems that there are in the syllogism only particular things, which are the immediate object of our reasonings and knowledge; they revolve only about the agreement or disagreement of ideas, each of which has only a particular existence and represents only an individ ual thing.
Th. As far as you conceive the similarity of things you con ceive something more, and the universality consists only in that. Yet you will never propose to me any one of our argu ments without therein employing the universal truths. It is, however, well to remark that (as far as form is concerned) the particular propositions are comprised within the universals. For although it is true that there is only a single St. Peter the 1 Locke's sensistic realism appears in sharp outlines in the present passage and its immediate context; cf. further, Locke, P/iilos. Wks., Vol. 2, pp. 295- 206. He maintains the existence, and consequently the knowledge, of the par ticular and individual only, and that our reasoning, which relates to the agreement or disagreement of things, must accordingly, in order to hit the mark, confine itself to the particular. Leibnitz argues, on the other hand, that our knowledge of things, while beginning with the particular in the sense-act, does not rest there, but through thought, especially through the medium of the linguistic form of our mental creation, gives to the individual and particular at once the character of universality. With Locke the ele ment of universality is accidental; with Leibnitz it is essential. — TR.
568 LEIBNITZ'S CRITIQUE OF LOCKE [UK. iv apostle, we may nevertheless say that whoever was St. Peter the apostle denied his master. Thus this syllogism: St. Peter denied his master, St. Peter was a disciple, therefore some disciple denied his master (although it has only particular propositions), is considered to have them as universal affirma tives, and the mood will be Darapti of the third figure.1 Ph. I wished also to say to you that it appeared to me better to transpose the premises of the syllogisms and to say: All A is B, All B is C, therefore All A is C, than to say: All B is C, All A is B, therefore All A is C. But it seems from what you have said that they do not differ, and that both are counted as one and the same mood. It is always true, as you have remarked, that the disposition different from the common is better adapted to making a chain of several syllogisms.
Th. I am wholly of your opinion. It seems, however, that the belief has been that it was more didactic to begin with universal propositions like the majors in the first and second figures; and there are indeed orators who have this custom. But the connection appears better as you propose. I have before remarked that Aristotle may have had a particular reason for the common disposition. For instead of saying A is B, he was wont to say B is in A. And with this method of statement, the connection itself which you demand will arise for him in the received disposition. For, instead of saying B is C, A is B, therefore A is C, he will state it thus: C is in B, B is in A, therefore C is in A. For example, instead of saying: The rectangle is isogon (or has equal angles), the square is a rectangle, therefore the square is isogon, Aristotle, without trans posing the propositions, will preserve the middle place to the middle term by this method of stating the propositions, which reverses the terms, and will say: The isogon is in the rectangle, the rectangle is in the square, therefore the isogon is in the square. And this mode of statement is not to be despised, for in reality 1 Peter being the middle term, and disciple the subject of the conclusion, the minor premise must be converted, by which process the universal affirma tive, " St. Peter Avas a disciple," becomes the particular affirmative, " Some disciple was St. Peter," from which the particular conclusion, " Some disciple denied his master," immediately follows. The mood Darapti of the third figure thus becomes the mood Darii of the first. The universality of the premises consists in the fact that Peter constitutes the entire class to which he belongs. (Jf. Hamilton, Logic, Boston, 1873, pp. 314-315. — TK.
CH. xvn] ON HUMAN UNDERSTANDING 509 the predicate is in the subject, or rather the idea of the predi cate is included in the idea of the subject. "For example, the isogon is in the rectangle, for the rectangle is the figure all of whose right angles are equal to each other, therefore in the idea of the rectangle is the idea of a figure all of whose angles are equals, which is the idea of the isogon. The common mode of statement regards rather individuals, but that of Aristotle ideas or universals. For in saying, every man is an animal, I mean to say that all men are included in all animals; but I mean at the same time that the idea of animal is included in the idea of man. Animal includes more individuals than man, but man includes more ideas or more formalities; 1 the one has more examples, the other more degrees of reality; the one more extension, the other more intension. It may also be truly said that the entire syllogistic doctrine may be demonstrated by that de continente et contento, the containing and the contained, which is different from that of the whole and the part; for the whole always exceeds the part, but the containing and the contained are sometimes equal, as is the case in reciprocal propositions.2 § 9. Ph. I begin to form for myself a wholly different idea of logic from that I formerly had. I regarded it as a scholar's diversion, but I now see that, in the way you understand it, it is like a universal mathematics. Would to God that it might push on to something more than it yet is, in order that we 1 I.e. essences. " The formality of the vow lies in the promise made to God." — Stillingrleet. — TR.
2 Leibnitz's thought, as Schaarschmidt says, is that sometimes the princi ple, what is predicable of the whole is predicable of the parts — ab universali ad particular?, consequentia valet — is not applicable, as in cases where the concepts found in the conclusion are coordinate rather than subordinate, i.e. coincident or identical in extension. In such cases the coordination or coincidence of the concepts — principium identitatis — might be adduced as a fundamental logical principle. To avoid this, Leibnitz proposes the principle De continente et contento, in which in a certain sense is given the higher unity of subordination and identity, i.e. the subject may always be thought of as contained in the predicate, although coincident with it in extension. The principle, however, necessarily considers "the containing" as more ex tended than the " contained." Cases such as Leibnitz here refers to, in which the coordination or agreement of terms is such as to make them identical — "important cases" "for the most part strangely overlooked" by logicians (•Tevons, Lessons in Logic, p. 124, new ed., 1880) — are discussed by Jevons in his little work entitled T/ie Substitution of Similars, London, Macmillau & Co., 570 LEIBNITZ'S CRITIQUE OF LOCKE [BK. iv might be able to find thereby these true helps of reason of which Hooker spoke, which would raise men far above their present condition. Reason is a faculty which so much the more needs it, as its extent is quite limited and as it fails us in many instances. (1) Because often ideas themselves fail us. § 10. Then (2) they are often obscure and imperfect; whilst where they are clear (and distinct), as in numbers, we find no insurmountable diffi culties, and fall into no contradiction. § 11. (3) Often also the difficulty comes from the fact that mediate ideas are want ing. You know that before algebra, that great instrument and noteworthy proof of human sagacity, was discovered, men regarded with amazement many demonstrations of the ancient mathematicians. § 12. It also happens (4) that the mind builds upon false principles, which may entangle it in difficulties where the reason is more involved and very far from clearing them up. § 13. Finally (5), terms whose meaning is uncertain embarrass the reason.
Th. I do not know whether we so much lack ideas as you think, that is to say, distinct ideas. As for confused ideas, or rather images, or, if you prefer, impressions, as colors, tastes, etc., which are a resultant of many little ideas distinct in themselves, but of which we are not distinctly conscious, we lack an infinite number of them suitable to other creatures rather than to ourselves. But these impressions also serve rather to give rise to the instincts and to establish the observa tions of experience than to furnish matter to the reason, except so far as they are accompanied by distinct perceptions. It is then principally the defect of the knowledge we have of these distinct ideas, concealed within the confused, that stops us, and even when all is distinctly exposed to our senses or to our mind, the multitude of things that must be considered some times perplexes us. For example, when there is a pile of one thousand cannon-balls before our eyes, it is plain that in order properly to conceive the number and properties of this multi tude, it is very useful to arrange them in figures as is done in the magazines in order to have distinct ideas of them and to fix them, indeed, so that we may be spared the trouble of counting them more than once. It is the multitude of consid erations also which causes some very great difficulties in the science of numbers themselves; for short methods are sought