UBRARY OF CONGRil^, 
 
 S-helf.,....k.§ 
 
 UNITED STATES OF AMERICA. 
 
 MAY 7 188/ 
 
Digitized by the Internet Archive 
 in 2011 with funding from 
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 http://www.archive.org/details/outlinesoflogicoOOIo.tz 
 
M 
 
LOTZE'S 
 
 Outlines of Philosophy 
 
 VI 
 
 LOGIC 
 
 AND 
 
 ENCYCLOPAEDIA OF PHILOSOPHY 
 

OUTLINES 
 
 OF 
 
 LOGIC 
 
 AND OF 
 
 ENCYCLOPEDIA OF PHILOSOPHY 
 
 DICTATED PORTIONS 
 
 U, fLJi 
 
 OF THE 
 
 / 
 LECTURES OF HERMANN LOTZE 
 
 
 > M 
 
 TRANSLATED AND EDITED BY 
 
 GEORGE T. LADD 
 
 PROFESSOR OF PHILOSOPHY IN YALE COLLEGE 
 
 BOSTON 
 
 GINN & COMPANY 
 
 1887 
 

 THE LIBRARY 
 Of CONGRESS 
 
 WASHINGTON 
 
 Entered according to Act of Congress, in the year 1887, by 
 
 GEORGE T. LADD, 
 in the Office of the Librarian of Congress at Washington. 
 
 J. S. Cushing & Co., Printers, Boston. 
 
 
EDITOR'S PREFACE. 
 
 This volume is a translation of the second Ger- 
 man edition of Lotze's " Outlines of Logic and En- 
 cyclopaedia of Philosophy," which appeared in 1885. 
 The second edition differed from the earlier one 
 chiefly in the abbreviation of certain parts of the 
 Encyclopaedia of Philosophy. The matter thus 
 omitted consisted largely either of opinions ex- 
 pressed elsewhere in the Philosophical Outlines, or 
 of a somewhat special criticism of certain views of 
 Schelling, Fichte, and Herbart. It has therefore 
 been thought best to take for translation the more 
 recent but somewhat less voluminous German text. 
 
 Although Lotze dealt with the subject of Logic 
 in a large and technical treatise, which constituted 
 one of the two volumes of his System of Philosophy, 
 completed by him before his death, it must be said 
 that his contributions to it are perhaps less distinc- 
 tive and valuable than those to any other of the 
 several branches of philosophy upon which he wrote 
 and lectured. Notwithstanding this, his views upon 
 some important topics under the general subject will 
 be found very suggestive and valuable. This seems 
 
VI EDITOR S PREFACE. 
 
 to me particularly true of the chapter on the " For- 
 mation of Concepts/' There can be little doubt that 
 the distinction between the association of mental 
 images and the definitely logical processes of the 
 mind is far too little drawn and too loosely held by 
 certain English writers on Logic. 
 
 Part Second, which treats of the " Encyclopaedia 
 of Philosophy," so-called, will be found to contain a 
 number of articles which throw considerable addi- 
 tional light upon the author's general philosophical 
 position. His peculiar doctrine of "Values," as dis- 
 tinguished from a knowledge of what is necessitated 
 or real, his view of the general method of philosophy-, 
 and of the relation in which the Theory of Cognition 
 stands to the whole of Metaphysics, and his attitude 
 toward philosophical Scepticism and Criticism, will 
 doubtless receive some elucidation from the careful 
 study of these sections. 
 
 A first draught of the translation of §§ 6-38 of the 
 
 Pure Logic was made by John F. Crowell, graduate 
 
 student of Philosophy in Yale University, 1885-86. 
 
 The rest of the work upon the volume is by my 
 
 own hand. With this sixth number of the series 
 
 of Lotze's Philosophical Outlines, I regard my task 
 
 as completed. 
 
 GEORGE T. LADD. 
 
 New Haven, March, 1887. 
 
TABLE OF CONTENTS. 
 
 PAGE 
 
 I. LOGIC. 
 
 Introduction i 
 
 FIRST PRINCIPAL DIVISION. PURE LOGIC. 
 Chapter I. The Formation of Concepts . 9 
 
 Chapter II. Of Judgments .... 
 
 A. Preliminary Remarks and the Customary 
 
 Division of Judgments .... 24 
 
 B. System of the Forms of Judgment . . 31 
 
 C. Immediate Inferences from Judgments . 48 
 Chapter III. Of Syllogisms .... 56 
 
 A. The Aristotelian Figures .... 56 
 
 B. The Forms of Calculation .... 75 
 
 C. Systematic Forms ..... 84 
 SECOND PRINCIPAL DIVISION. APPLIED LOGIC. 
 
 Chapter I. Application of the Forms of the 
 
 Concept 97 
 
 Chapter II. Concerning the Adducing of Proof, 106 
 Chapter III. The Process of Thought in Discovery, 120 
 
 II. ENCYCLOPAEDIA OF PHILOSOPHY. 
 
 Introduction 145 
 
 Section I. Theoretical Philosophy . . .155 
 Section II. Practical Philosophy . . . 179 
 
 Section III. Philosophy of Religion . . .182 
 
I. LOGIC 
 
 INTRODUCTION. 
 
 § l. According to the combination in which the 
 external stimuli happen to act upon us, there arise 
 within us manifold ideas, simultaneous or succes- 
 sive, which do not always have an interior coherence 
 that agrees with the nature of their Content. And, 
 further, since memory and recollection retain and 
 reproduce these ideas in the same connections which 
 they had at their origin, certain ideas that are quite 
 foreign to each other and without any interior cohe- 
 rence, very often appear in our mental train in a 
 connection which, although it is matter of fact, is 
 without any real reason. 
 
 § 2. Besides, perception by the senses affords us 
 the impressions of at least one sense, — namely, that 
 of sight, — in an arrangement with reference to each 
 other which has space-form ; and this arrangement is 
 not, like the connection referred to above, a merely 
 accidental coexistence of the single colored points, 
 
OUTLINES OF LOGIC, 
 
 but undoubtedly depends upon the peculiar nature 
 of what is perceived. Nevertheless, we do not call 
 this ' thought ' but ' intuition/ — and for the very 
 reason that, while we discover the arrangement of 
 the single points to be unalterable, we yet perceive 
 it as a bare matter of fact without understanding 
 the reasons on account of which each point has its 
 position toward others. 
 
 § 3. We are accustomed to distinguish thought 
 both from the aforesaid train of ideas and also from 
 such process of intuition, as a higher and self-coher- 
 ing activity, which elaborates, shapes, and connects 
 the material of ideas furnished by both of the others. 
 Its essential tendency can be expressed as follows ; — 
 that the thinking spirit is not satisfied to receive 
 the ideas simply in those combinations in which 
 what is accidental to the physical mechanism has 
 brought them to it. Thought is rather of the nature 
 of a continuous ' critique,' which the spirit practises 
 upon the material of the train of ideas, when it sep- 
 arates the ideas whose connection is not founded 
 upon some such justification for the combination as 
 lies in the very nature of their content ; while it not 
 only combines those ideas whose content permits or 
 requires some connection, but likewise reconstructs 
 their combination in some new form of apprehen- 
 
THE TRAIN OF IDEAS. 
 
 sion and expression, from which the justification of 
 this connection admits of being discerned. 
 
 § 4. If we assume (not as a positive assertion, but 
 only as an aid to the exposition of the subject) that 
 the animals, although possessing the train of ideas 
 alluded to, do not possess thought specifically ; then 
 the distinction between these two achievements would 
 lie in what follows. 
 
 In the animal, with the idea of the stick when 
 swung, the idea of the pain that follows thereupon 
 is connected ; and the renewal of the first alone is 
 sufficient to reproduce in anticipation the second 
 also, and to determine the behavfor of the animal 
 in some purposeful way. 
 
 Practically, therefore, the animal obtains fairly well 
 from the mere association of ideas the same service 
 as though it had, by thinking in the strict meaning 
 of the word, expressed its experience in the form of 
 judgments and conclusions, as follows: 'The stick 
 strikes — the stroke smarts — therefore, etc/ Still 
 in each of these logical judgments there would be 
 involved an apprehension of the state of the case 
 quite other and more profound than is involved in 
 such mere association. That is to say, when we 
 apprehend the stick as the subject or cause from 
 which the stroke proceeds, we do not merely repeat 
 
OUTLINES OF LOGIC. 
 
 the psychological fact that the ideas of the two 
 occur in connection, but likewise express the adjunct 
 thought that both belong together by an inner bond 
 uniting their content, — in this case, by a causal 
 relation. The same thing is true in all cases, as will 
 subsequently be shown in particular. 
 
 Thought, therefore, carries the merely subjective 
 association of ideas — that is, their mere occurrence 
 together in consciousness as a matter of fact — back 
 to principles that govern the objective synthesis of 
 their content. 
 
 § 5. In order that the process of thinking may 
 be able to accomplish such an achievement, it must 
 have in its possession the principles for it, — that 
 is to say, certain universal rules or grounds of right, 
 according to which, in general, the content of differ- 
 ent ideas may, or may not, be capable of connection. 
 Or, to express the same thing in another way : if we 
 are to be able to distinguish truth and untruth, then 
 there must exist within us some absolutely valid and 
 universal standard determining what is permissible, 
 and what is not permissible, as to the connections 
 of ideas. Moreover, the general principles contained 
 in it must stand in a very close connection with the 
 presuppositions which we are compelled to make 
 concerning the nature and the reciprocal relations 
 of all 'Things.' 
 
THOUGHT AND "THINGS." 
 
 These latter we are accustomed to style metaphys- 
 ical principles. And, accordingly, a near relation- 
 ship would exist between logical and metaphysical 
 truths. This Introduction is not the place to treat 
 this relationship exhaustively; the following remark 
 is sufficient at this point. 
 
 We assume that the process of thinking is deter- 
 mined so as to lead to the knowledge of the true 
 nature of ' Things.' Now every means must be 
 directed, on the one hand toward the object which 
 it is to work out, and on the other hand toward 
 the nature of that which is to employ it. On this 
 account, the forms and the laws also, in which and 
 according to which thought connects the ideas, must 
 be such that by means of them the knowledge of 
 truth can be conclusively attained ; but they need 
 not be such that the ideas shall directly copy the 
 essence of the ' Things' themselves. The rather, 
 since it is man who, by means of them, is to arrive 
 at the truth, must they attach themselves to the 
 nature and stand-point of man ; and accordingly they 
 must have peculiarities which are comprehensible 
 only from this fact, and not from the nature of the 
 ' Things ' which are to be known. 
 
 In other words (to answer, at least in a prelimi- 
 nary way, a question which is not to be exhaustively 
 treated in this place) : The forms and laws of thought, 
 
OUTLINES OF LOGIC. 
 
 with which we are to become acquainted, have neither 
 a ' merely formal ' nor a ' perfectly real ' significance. 
 They are neither mere results of the organization of 
 our subjective spirit, without respect to the nature 
 of the objects to be known, nor are they direct copies 
 of the nature and reciprocal relations of these objects. 
 They are rather ' formal ' and ' real ' at the same time. 
 That is to say, they are those subjective modes of 
 the connection of our thoughts which are necessary 
 to us, if we are by thinking to know the objective 
 truth. 
 
First Principal Division. 
 
 PURE LOGIC 
 
First Principal Division. 
 
 PURE LOGIC. 
 
 CHAPTER I. 
 
 THE FORMATION OF CONCEPTS. 
 
 § 6. It is well known that most of the operations 
 of thought consist in acts connecting together differ- 
 ent simple ideas. Wherever, then, some such * con- 
 nection ' is spoken of, the question at once arises, 
 How must the simple elements themselves be formed 
 in order to be able to enter at all into the connection 
 designated ? Out of purely spherical elements it is 
 impossible to make a coherent structure. That can 
 be done only by means of prismatic elements which 
 present to each other surfaces that are definitely laid 
 out. Just so, from mere impressions, in so far as 
 they are nothing more than our affections (moods, 
 that is, of our feeling), no logical connection is to 
 be established ; but each individual impression, in 
 
IO OUTLINES OF LOGIC. 
 
 order to be capable, in the logical sense, of being 
 combined with another into a thought, must be already 
 apprehended by the spirit in such a quite definite 
 form as renders this combination possible. 
 
 § 7. This, the first work of logical thought, be- 
 comes most distinctly apparent to us in the circum- 
 stance, that almost all languages divide the whole 
 stock of the content of ideas into definite, formally 
 different classes ; and that even those languages 
 which do not distinguish externally this difference 
 between substantives, adjectives, verbs, etc., still 
 cherish, in forming each one of their words, the 
 adjunct thought, that its content must be conceived 
 of either substantively, as something in itself valid, 
 permanent, independent of every other; or adjec- 
 tively, as quality dependent and presupposing some 
 other to which it adheres ; or verbally, as a move- 
 ment or relation passing between different contents. 
 In the first place, by means of these forms in 
 which they are cast by the act of thinking, ideas 
 become elements of a thought ; and, like the pris- 
 matic stones in the comparison made above, they 
 turn toward one another definite surfaces which 
 allow a connection in the logical sense. So long, 
 on the other hand, as ideas are only different modes 
 of being apprehended in our consciousness, although 
 
LOGICAL ACT OF THOUGHT. II 
 
 they can, of course, like tones in music, be signifi- 
 cantly connected with one another in other ways 
 (in this case, cesthetically), yet as such no thought 
 arises from them. 
 
 § 8. The next question seems necessarily to be, 
 How must thought always proceed in order to ac- 
 complish this arrangement of any content whatever 
 in one of these forms taken by the parts of speech ? 
 Since the question relates quite generally to every 
 content, simple as well as composite, this second 
 logical act of thought must consist in a very sim- 
 ple process which can occur in both cases. 
 
 Now it does consist in the following : — As often 
 as language forms a word for some content, which 
 is to be ascribed to this particular content and to it 
 alone, it necessarily expresses therewith the presup- 
 position that this content is something which holds 
 good of itself, is identical with itself, and different 
 from others ; that, on this very account, it is able 
 to bear a name of its own. That is, when the sec- 
 ondary thought, which occurs along with the act 
 of thinking, forms in speech a word for a thing 
 (that is, apart from speech, when it fixes some con- 
 tent, and distinguishes it from others), it consists 
 particularly in this, that it conceives of it as a whole 
 which in itself belongs together, and as thus belong- 
 ing together is marked off from every other. 
 
12 OUTLINES OF LOGIC. 
 
 Expression in speech permits this act to be man- 
 ifest in different classes of words with different 
 degrees of distinctness. An adjective, as 'blue/ 
 expresses least of this logical import. Verbs sig- 
 nify by means of their ending, that the content 
 indicated by them is thought of as a unity in a def- 
 inite sense, — namely, in that of the verbal relation. 
 In the case of substantives, certain languages make 
 it most palpable that the content designated should 
 be thought of as something identical with itself, 
 exclusive, one and entire, by means of the prefixed 
 article. 
 
 § 9. This logical form of the * idea ' (so we will 
 call this second act of thought) accordingly appre- 
 hends its content, be it simple or composite, only in 
 such a way that it comes in general to be regarded 
 as unity or as totality. 
 
 In reference to simple content, that which admits 
 of being realized at all stands highest. For exam- 
 ple ; the impressions, 'blue/ 'sweet/ 'warm/ cannot 
 undergo any other logical elaboration than that of 
 being apprehended as having a content which is 
 identical with itself, different from others, and of 
 course adjective in its nature. 
 
 For the composite content, on the other hand, this 
 form of the idea which asserts in a general way 
 
GENERAL IDEA AND CONCEPT. 1 3 
 
 nothing more than that its parts belong together, 
 without rendering cognizable the kind, the ground, 
 and the rule of the same, is an unsatisfactory mode 
 of apprehension ; although we very frequently cannot 
 get beyond this in the ordinary course of thought. 1 
 The words ' nature,' 'life,' 'state,' 'government,' 
 indicate for the majority of men nothing but the 
 consciousness that in every case a manifold of phe- 
 nomena and events is united into a totality ; without 
 their being able to specify the definite plan, the laws 
 and the forces, according to which and through 
 which this totality is produced. These same words, 
 however, will indicate a higher apprehension of their 
 content, a 'concept' of the same, in case, besides the 
 bare fact that the parts of the content belong to- 
 gether, some reason for the latter is also thought. 
 
 §10. Now it is this principle of 'belonging to- 
 gether' which thought seeks to discover; since it 
 has regard either to that which, in several ideas 
 that differ from each other, appears as common 
 and homogeneous (the universal) ; or to that which, 
 throughout all changes of one and the same con- 
 
 1 Especially useful kinds of expression for anything thought of merely 
 in the form of idea, are such as these : in the Greek the neuter plural, — 
 ra (pva-LKa, r a T)9iKa, ra iro\ir lkol) in the German, compounds 
 with . . . ' wesenl — Munzwesen, Zollwesen, Heerwesen, etc. 
 
14 OUTLINES OF LOGIC. 
 
 tent, continually remains homogeneous (the constant). 
 For there naturally seems to lie in both, somewhat 
 which coheres together more firmly and legitimately 
 than the other changing and heterogeneous marks, 
 and which, just for these marks, composes the prin- 
 ciple of their coexistence and determines the kind 
 of their combination. 
 
 Should a composite content be thought, however, 
 in such a way that somewhat universal or constant, 
 but distinct from the sum-total of its 'marks/ be 
 thought along with it as the determining law on 
 which that whole circle of marks is dependent ; then 
 is that content thought in the form of a concept. 
 
 The name 'linden/ 'oak/ and the like, moreover, 
 designates for the ordinary course of thought a con- 
 tent apprehended in accordance with a concept. For 
 every one conceives of the general image of ' tree/ 
 or the still more general image of 'plant/ as the 
 outline, the schema, or the norm, according to 
 which all parts of the afore-mentioned individual 
 ideas are bound together into a whole. So, too, 
 all nomina propria of persons are real concepts. 
 ' Alcibiades/ or ' Napoleon/ never means merely 
 a totality of parts ; but both are explained and 
 conceived of under the accompanying universal men- 
 tal image of ' man/ 
 
CONCEPT AS UNIVERSAL. 1 5 
 
 § 11. Very rarely will such a general image admit 
 of being produced from several comparable individual 
 ideas through the retention of their marks that 
 are completely alike, and the simple omission of those 
 unlike. For the marks of ideas are not wont to be 
 alike and unlike, but similar and dissimilar. If 
 indeed we should merely retain what little is pre- 
 cisely alike, we should arrive at a meaningless uni- 
 versal which would sustain a relation of complete 
 indifference toward the omitted constituents, and 
 not that of a principle regulating them. 
 
 But in fact we do not so proceed. The compari- 
 son of several bodies does not result in the general 
 image of body, — because one is blue, hard, elastic, 
 light, and the other is yellow, soft, ductile, and 
 heavy, — by omitting all of these properties ; as 
 though the idea of ' body ' would have any meaning 
 at all regardless of 'color,' 'cohesion,' and 'weight.' 
 Of these dissimilar marks the comparison omits 
 merely what is different, but retains what is common 
 to them (for example, in this case, ' color in general,' 
 ' weight in general ') ; and it combines these general 
 marks themselves into the desired general image of 
 a body, to which it is therefore quite essential that it 
 should have some color, some cohesion, some weight, 
 or other. 
 
l6 OUTLINES OF LOGIC. 
 
 § 12. The ordinary theory of logic is accustomed 
 simply to teach that, from comparable individual 
 ideas (iiotiones speciales) we ascend to the more uni- 
 versal one (notio generalis) by 'abstracting' from 
 the unlike marks (notae) of the former, and retain- 
 ing only the like ones. This theory adds the 
 statement, therefore, that the content {materia com- 
 plexus) of a general idea is ' poorer/ that is, can 
 count fewer marks than that of the particular ones 
 out of comparison of which it arose. 
 
 The foregoing remark must at all events be im- 
 proved upon to this extent, that each universal has 
 exactly so many marks, which it is indispensable 
 should be thought together, as belong to the indi- 
 viduals corresponding to it. Nevertheless, while all 
 these marks are perfectly defined in the particular or 
 in the individual, as respects both kind and quantity ; 
 in the universal, certain general or undefined marks 
 have taken the place of many of them. The universal, 
 as compared with the particular, is therefore poorer 
 in defined marks, but not poorer in marks in general. 
 
 § 13. We distinguish, therefore, two different kinds 
 of universals. In the first place, there is the afore- 
 said general image, through the entrance of which 
 into the group of marks belonging to an idea, this 
 idea is itself raised to a concept ; and, besides this, 
 
FORMATION OF THE CONCEPT. 1 7 
 
 those universal marks out of whose connection to- 
 gether the general image itself arises. 
 
 These latter, the universal marks, in the simplest 
 case require no special logical work of thought for 
 their origin, but arise out of the immediate impres- 
 sion without our logical assistance. That 'green/ 
 'blue/ 'red/ for example, have something in common, 
 is a matter of immediate experience ; and although 
 this common possession may not admit of being sep- 
 arated by a logical operation from that by which 
 these impressions are distinguished; still the name 
 ' color ' points to this as to the something experienced 
 as common. So, too, differences of magnitude are 
 immediately perceived as true ; and the general name 
 of magnitude expresses, side by side with these dis- 
 tinctions, the common characteristic. 
 
 In this manner there arise from the consideration 
 of the different marks, which are presented in the 
 individual ideas, the general marks as the elements 
 out of which the aforesaid general image is then 
 composed ; and the latter holds good for those 
 individual ideas as a common type comprising 
 them all. 
 
 § 14. For the formation of a 'concept' it is not 
 sufficient that its general marks, nor indeed for the 
 formation of the 'idea/ is it enough that its indi- 
 
1 8 OUTLINES OF LOGIC. 
 
 victual marks, be merely present in general ; but the 
 essential thing is their mode of combination. No 
 idea, and no concept, consists of a mere summation 
 of marks in such a way that every first one should 
 enter into combination with every second one just as 
 the second with every third ; but in the universal 
 the marks limit, define, or determine one another in 
 such manifold and characteristic ways, that a first 
 one is connected with the second otherwise than the 
 second is connected with the third, or the third with 
 the fourth. 
 
 In the case of mere ideas which only combine 
 marks in general into a totality, without logically 
 characterizing the way in which they belong to- 
 gether, the intuitions of time and space take the 
 place of such strictly logical work. Through 
 these intuitions we then know in what way, for in- 
 stance, the distinctive marks of an animal — color, 
 skin, head, swiftness, etc. — are to be brought to- 
 gether and combined. If, on the other hand, we 
 form an abstract concept of ' motion/ for example, 
 and designate it as ' constant change of place/ then 
 it is seen that no one of these three marks is thought 
 as of like species with the other ; but, strictly speak- 
 ing, simply the general idea of ' change/ in so far as 
 it is restricted by reference to the idea of 'place/ 
 and through the mark belonging to it is defined 
 
THE CONCEPT AND ITS NAME. I9 
 
 as 'constant/ forms the content of the concept of 
 motion. 
 
 The general image which arises out of the com- 
 parison of several individual ideas is formed, not 
 simply when the general marks are put in the place 
 of the particular, but also when a general mode of 
 connection corresponding to them is put in the place 
 of the particular modes of connection among the 
 marks. 
 
 The general mental image ' metal ' — for instance 
 — connects together the general marks of ' color/ 
 'weight/ etc., in a form, or according to a scheme, 
 of which the modes of combination are only par- 
 ticular examples, wherein gold combines the color 
 yellow, its specific gravity, etc., copper the color red, 
 and its specific gravity, etc. 
 
 § 15. To recapitulate the foregoing ; we give the 
 name of l concept' to an idea whenever, in addition 
 to its group of marks, a universal is thought along 
 with it as an explanatory law. 'Gold' or 'Caitis' 
 is thus thought as concept, in so far as the marks 
 of both are regulated by the general schemata, 
 'metal' and 'man/ respectively. 
 
 The universal itself, by whose entrance into it the 
 idea becomes the concept, is not necessarily hor 
 always itself thought as concept, but frequently only 
 
20 OUTLINES OF LOGIC. 
 
 as idea. It is then, indeed, concept only when its 
 own marks also are not merely thought in general 
 as a whole belonging together, but as combined by 
 means of a new universal in accordance with some 
 definite scheme. 
 
 There are accordingly just as much individual, 
 singular concepts (notiones singulares) — like all 
 names of persons, for instance — as there are uni- 
 versal concepts (notiones generates) in manifold gra- 
 dations. 
 
 The name of higher general concept is given to 
 that one, which is thought as an explanatory schema 
 in addition to the marks of another concept, which 
 latter is then the lower of the two. 
 
 It is then said that the content {materia) of the 
 higher general concept (genus) is ' contained ' in the 
 content of the lower (species) ; that is, that all the 
 marks which are essential to the genus occur also 
 in the species. But, conversely, the content of the 
 species is not entirely contained in that of the genus ; 
 but the former possesses, besides the particular 
 marks of the latter, certain ones peculiar to it as 
 species. On this matter a corrective remark is made 
 above (§ 12). 
 
 It is further said — and rightly, too — that each 
 higher general concept occurs in a greater number 
 of kinds or individual concepts (or holds good of 
 
RELATION OF EXTENT AND INTENT. 21 
 
 them) than the lower concept. The name of ' extent ' 
 (ambitus) is given to the number of these lower 
 concepts, of which the higher holds good. And 
 since to the latter there is ascribed, as previously 
 remarked, a smaller number of marks or smaller 
 content (materia complexus) ; therefore it is said that 
 "the extent and the content of two concepts are 
 in inverse ratio to each other " : the one poorer in 
 content — that is, the more general — commands a 
 greater aggregate of individual cases ; the one richer 
 in content occurs in fewer kinds, perhaps only in a 
 single individual. 
 
 According to the foregoing, this proposition would 
 correctly run thus : A concept with clearly defined 
 marks is always individual. In case it has undefined 
 or general marks besides the defined ones, then with 
 the number of the undefined marks (or, conversely, 
 with the number of the defined ones), the number 
 of cases increases in which it is valid, — that is, its 
 extent. 
 
 § 16. Two relations of subordination, since they 
 are essentially different logically, are to be held as 
 excluding each other. That is to say, every concept 
 can be ranked in respect to one part of it, under its 
 higher concept of species, — for example, ' gold ' (G) 
 under ' metal ' (M) ; in respect to another part, under 
 
22 OUTLINES OF LOGIC. 
 
 any one of its marks at pleasure, — for example, 
 'gold' (G) under < fusible' (F). 
 
 Fig. I. Fig. 2. 
 
 The first of the foregoing relations (Fig. i.) is 
 called subordination. In this case the whole nature 
 of G is included in the universal M, in such a man- 
 ner that there is in G no part, no mark and no com- 
 bination of marks, which may not be essentially 
 comprehended by means of the universal principle 
 M ; for example, the ' yellow ' of gold is a certain 
 lustrous yellow peculiar to the metal, which does 
 not occur otherwise. Within this M, finally, G- is 
 found * co-ordinated ' with its natural kindred (copper, 
 lead, silver, — C, Ii, — etc.) ; that is, it stands in the 
 same logical relation to M with all the rest of them. 
 
 The other species of arrangement of one concept 
 under another (Fig. 2) is called subsumption. Here 
 G touches upon the universal concept F with only 
 one part of its content; the remaining parts of its 
 content lie outside F and are not defined by F. Be- 
 sides, G (gold) is found in this case to be co-ordi- 
 
SUBORDINATION AND SUBSCRIPTION. 23 
 
 nated, in reference to F (fusible), not merely with 
 its own related species, but also with other con- 
 cepts of content altogether heterogeneous (sugar, 
 pitch, sulphur, — S, P, — etc.). 
 
 § 17. If we ascend by continued abstraction to 
 more and more general concepts, we shall, accord- 
 ing to a frequent assertion, reach one single highest 
 general concept, — that of the 'thinkable.' Such 
 an abstraction, however, would only be performed 
 through subsiimption (Fig. 2), if the concept should 
 have entirely let go of the characteristic content of 
 the concepts, and confined itself simply to a common 
 mark through which its content is not defined. 
 
 If we proceed by way of subordination, then it 
 is found that our system of concepts does not ter- 
 minate in one point, but in several independent 
 points. The substantive concepts lead to one 
 highest concept of Being ; the verbal to that of 
 Becoming; the adjective to that of Property, etc.; 
 and there is absolutely no concept still higher, to 
 which these fundamental concepts may be referred 
 as to a common principle of their content. As for 
 the rest, it is obvious, — and the reason why it 
 must be so needs no explanation, — that these 
 fundamental concepts are nothing more than the 
 meanings belonging to the different parts of speech. 
 
CHAPTER II. 
 
 OF JUDGMENTS. 
 
 A, Preliminary Remarks and the Customary Division 
 of Judgments, 
 
 § 18. The consideration of the subject up to this 
 point leads to a new problem. In the concept we 
 have distinguished the universal and the special 
 circle of marks. Concerning the reciprocal rela- 
 tions of these two members we had, however, only 
 expressions characteristic of like species. The uni- 
 versal served us only as a nucleus, as a normative 
 principle, as a rule for the disposition and combi- 
 nation of the marks. The question now arises ; 
 what this means, when taken strictly, and what 
 power the universal can exercise over the marks, 
 and in what way. 
 
 We consequently seek for an explanation of the 
 relation of the two members to each other. Every 
 assertion which thought can utter on this question, 
 and by means of which it can answer the same, 
 must consequently take this form ; that it connects 
 two members S and P through the affirmation of a 
 definite mode of relation X. This is essentially 
 
NATURE OF THE JUDGMENT. 25 
 
 the form of a proposition or a judgment, in which 
 S is subject, P is predicate, and X copula between 
 the two. 
 
 § 19. The ground of the fact that different im- 
 pressions belong together, however, we have sought, 
 not merely in somewhat universal which is common 
 to the different impressions, but likewise in some- 
 what constant which appertains to one and the 
 same content of the idea, while it experiences 
 changes in other respects by accession or diminution 
 of its marks. This relation, too, of an unchanging 
 nucleus, which is at once the ground of the possi- 
 bility of the changing marks and the law of their 
 connection, requires a similar investigation. We 
 must know how any P can ' adhere ' to an S, and 
 how it is possible that it disappears again and 
 another mark, P', occupies its place, — and every 
 assertion on this matter must bear the form of 
 the judgment, 
 
 § 20. Apart from such systematic coherency, the 
 doctrine of judgment may be introduced as fol- 
 lows : — In the train of ideas it must frequently 
 occur that, in the first place, two impressions a 
 and b, which have for us become united in part 
 (as, for example, the shape of a tree and its green 
 
26 OUTLINES OF LOGIC. 
 
 ■ — — — ^ — ■ . > 
 
 color), are apprehended as a whole whose distinguish- 
 able parts are not actually distinguished, because 
 all reason for it is wanting. If now, by a second 
 experience, the tree is shown without leaves, then, 
 in a third instance in which it is again seen to be 
 green, the two ideas of its shape and color will 
 no longer form an undivided whole in the same 
 naiVe way; on the contrary, the recollection of 
 their being separable will keep them apart from 
 each other; and therewith arises the idea of two 
 impressions which are combined, instead of that of 
 one impression, in which there is no inner difference. 
 This process of the simultaneous association and 
 separation of two ideas without doubt takes place 
 in animals also. It supplies for them the place of 
 the logical judgment of human thought ; yet it is 
 not such itself, but only the occasion of a judgment. 
 If we, for instance, affirm in judgment, 'the tree is 
 green' or 'is not green/ then we interpret the co- 
 existence of separable ideas and do not simply 
 express over again the fact of such coexistence. 
 When we conceive of the tree as subject (or in this 
 case as substance) and the predicate green as attri- 
 bute or accident, we point to that inner connection 
 in which, according to our view, the property stands 
 related to the i Thing' or the accident to its subject, 
 as in each case constituting the legitimate ground 
 
CLASSIFICATION OF JUDGMENTS. 2/ 
 
 according to which both of the ideas ' tree ' and 
 'green' do not merely exist together, but belong 
 together precisely as they are together, — to wit, 
 as separable yet conjoined. 
 
 § 21. The essential part of a judgment is, then, 
 precisely this secondary thought which the process 
 of thinking has, when it connects subject and predi- 
 cate in definite form. As many as are the essentially 
 different points of view, grounds, or models, to which 
 this process of thought rightly refers the combina- 
 tion of S and P, — that is, as many as the essentially 
 different meanings of the copula actually are ; so 
 many are the essentially different logical forms of 
 the judgment which are to be systematically devel- 
 oped later on. 
 
 We previously made mention of a classification of 
 the judgment usually given, — namely that by Kant. 
 According to him, every judgment must at the same 
 time be determined in four different respects, and 
 must in each of these have one of the three mutually 
 exclusive forms ; namely, is — 
 
 i) According to quantity either universal or par- 
 ticular or singular. 
 
 2) According to quality it is either affirmative or 
 negative or limitative. 
 
 3) According to relation, — that is, the meaning of 
 
28 OUTLINES OF LOGIC. 
 
 the connection between S and P — either categorical 
 or hypothetical or disjunctive, 
 
 4) According to modality, — that is, the relation of 
 the whole content to actuality — either problematic 
 or assertory or apodictic. 
 
 § 22. These differences are not of equal value : 
 
 1) To begin with, in the three quantitative forms : 
 
 This S is P, 
 
 Some S are P, 
 
 All SareP,— 
 the kind of combination between S and P is entirely 
 the same ; and they differ simply in respect to the 
 number of the subjects, and consequently in respect 
 to the material, to which this entirely identical con- 
 nection is extended. Accordingly, although the quan- 
 titative differences remain of great importance for 
 other purposes, — for example, the drawing of con- 
 clusions from judgments, — they are nevertheless not 
 essentially different steps in the development of the 
 judgment as such. 
 
 2) As to what further concerns the qualitative 
 
 forms, it is obvious that the affirmative and the 
 
 negative judgment, 
 
 S is P, 
 
 S iS not P, 
 
 must understand the kind of combination that takes 
 
QUALITY OF JUDGMENTS. 29 
 
 place between S and P, in the same manner. 
 For the negative judgment could not be the exact 
 opposite of the affirmative, if it did not deny pre- 
 cisely what the latter asserts. This judgment is there- 
 fore fitly presented in such a way that, to one entirely 
 identical thought of a combination of S and P, there 
 is added the two secondary judgments; — it is true, 
 or it is not true. They differ then in their content 
 very essentially, but not in their form. — The limita- 
 tive judgment should attach a negative predicate to 
 S by means of a positive copula, and so have the form 
 
 S is non-P. 
 On the other hand, it must be kept in mind that 
 non-P is a definite idea and not of any use at all to the 
 predicate, only in those cases where it does not merely 
 indicate that which is in general not P, but that 
 which is co-ordinated with P under a higher general 
 concept, and therefore has a meaning of its own, — 
 as for instance, ' not-round ' in so far as it must still 
 always have some form, either straight or angular 
 and the like. If, on the contrary, non-P is intended 
 to comprehend everything that is simply not P in 
 general, — for example, the ' not-round ' is to include, 
 besides the angular, things like the ' bitter/ the 
 ' future/ the ' cheap/ etc.; then non-P is no longer 
 an idea at all, such as could be apprehended and 
 given to some subject S as its predicate. The 
 
30 OUTLINES OF LOGIC. 
 
 attempt to do this invariably has in time this issue, 
 that S is excluded from the circle of the predicate 
 P, and the judgment consequently, according to its 
 meaning, is negative. 
 
 3) The third distinction, that according to rela- 
 tion, is of such essential significance that it is passed 
 by here in order to be thoroughly examined later. 
 
 4) The differences of modality, likewise, have no 
 essentially logical value ; since the possibility of the 
 combination of S and P in the problematical judg- 
 ment, and its necessity in the apodictic judgment, is 
 expressed only by means of the auxiliary verbs, 
 
 S may be P, 
 
 S must be P. 
 They are both therefore, after all, properly speaking, 
 only assertory judgments ; that is, they affirm, exactly 
 as does the strictly assertory judgment, 
 
 S is P, 
 an actuality — in the former case, that of possibility ; 
 in the latter, that of necessity. 
 
 But neither of the two admits of being brought 
 forward immediately as a consequence of the pecu- 
 liar mode of relation of S and P. This kind of 
 modality, therefore, belongs to the content, but not 
 to the logical form of the judgment; and there may 
 be set beside it yet many other forms of precisely 
 equal rank ; as, for instance, S should be P, S ought 
 
SIMPLEST FORM OF JUDGMENT. 3 1 
 
 to be P, S will be P, etc. Now, in what way the 
 judgments are capable of expressing, by means of 
 their form, at the same time a claim to the possi- 
 bility, actuality, or necessity of their content, will be 
 shown by what follows. 
 
 B. System of the Forms of Judgment. 
 
 § 23. In the classification of the forms of judg- 
 ment, we start from the point of view that thought 
 should declare itself as to how it conceives of the 
 coherency of that previously so-called 'nucleus' of an 
 idea with its own circle of marks ; or, in other words, 
 of an S with P. Every such declaration will be ex- 
 pressed by a separate form of judgment ; and the 
 series of the forms of judgment must therefore form 
 a series of increasingly better attempts at the com- 
 plete and adequate expression of the aforesaid rela- 
 tion between S and P. 
 
 § 24. The simplest form of judgment is the 
 impersonal. In the propositions, 'It lightens,' 'It 
 thunders/ etc., the whole content of the judgment 
 is completely contained in the predicate. The indefi- 
 nite pronoun i it ' adds nothing thereto, but formally 
 marks the place of the concept of the subject, which 
 is missing. But just this alone — that the process of 
 thinking is not satisfied with the bare reproduction 
 
32 OUTLINES OF LOGIC. 
 
 of the simple content which stands in the predicate, 
 that it consequently does not employ for its expres- 
 sion the infinitive 'to thunder/ but inflects the word 
 and joins it as predicate to the 'it' — proves most 
 evidently this fundamental necessity of analyzing 
 every content of an idea into two component parts, 
 the one of which is the regulative principle, and the 
 other the phenomenon dependent on it. Of course, 
 this requirement is here only formally satisfied. For 
 the case does not admit of specifying any subject, 
 with complete content, to which the phenomenon is 
 attached. We are, therefore, under the necessity 
 of joining the phenomenon taken as predicate to 
 itself taken as subject. 1 
 
 § 25. The next advance must consist in this, that 
 the separation of the ideated content in S and P, 
 which is here only indicated, is brought to comple- 
 
 1 According to their modality, the impersonal judgments are naturally 
 assertory; that is, affirmations of actuality. In the natural process of 
 thinking, they uniformly express perceptions. The ' it ' in the subject is, 
 according to its content, either nothing more than the predicate, or, if it is 
 to be distinguished from it, is only the thought of the universal Being, which 
 in the different phenomena is defined now in one way and now in another. 
 One might therefore say, instead of ' it lightens,' ' the Being is [now] light- 
 ening,' or conversely, 'the lightning is.' That is to say, it is possible to 
 convert the impersonal judgments into existential propositions, in which 
 * to be ' is the predicate. Such conversion is, however, an artificial work of 
 the schools. The natural process of thought never apprehends the indi- 
 vidual phenomenon as subject and the Being as predicate, but only univer- 
 sal Being as subject and the phenomenon as a single predicate of the same. 
 
THE CATEGORICAL JUDGMENT. 33 
 
 tion by the rise of a special conception of the subject 
 as different from the predicate. 
 
 This gives the so-called categorical form of judg- 
 ment, S is P, in which P is unconditionally and 
 without further justification asserted of S (Kai]«yop€iT<H, 
 Aristotle). The only available justification of this 
 connection, — namely, that it takes place according 
 to the type of the relation between ' Thing'' and 
 property, Substance and attribute (Kant) — does 
 not suffice ; since, metaphysically considered, this 
 relation itself is not a perfectly clear truth but an 
 enigma. 
 
 We can then distinguish two kinds of this judg- 
 ment. One, the so-called analytic, connects with S 
 a P which is itself included in the very concept of 
 S; as, for example, 'Gold is heavy/ For the con- 
 cept of 'gold' is not a completed product of thought 
 until it includes the mark 'heavy.' Accordingly, this 
 judgment, strictly speaking, simply asserts that, when 
 we think the concept S, we think along with it that 
 of P as a constituent part of it. But how the con- 
 tent of the P as a matter of fact adheres to the con- 
 tent of the S, in such a way that, just in order to 
 think S, we must think P along with it, — this the 
 form of judgment does not explain, but merely asserts 
 as a fact. 
 
 The second kind, the so-called synthetic or histor- 
 
34 OUTLINES OF LOGIC. 
 
 ical judgment, connects S with a P that does not 
 lie thus within the concept, and consequently is a 
 changeable mark of it ; for example, ' Caesar fled/ 
 'The dog is mad/ Here it is far less clear through 
 the form of the judgment, by what right two concep- 
 tions which stand in no constant relation are brought 
 into such a relation. But here also the combination 
 is expressed unconditionally as a fact to be taken for 
 granted. 
 
 § 26. On occasion of this doubt arising and as the 
 ground of it, the first universal law of thought comes 
 to consciousness : The law of identity and of con- 
 tradiction (Principium identitatis et contradictionis). 
 
 Its simplest logical expression is this : In a cate- 
 gorical judgment of the form S is P it is absolutely 
 forbidden to combine unconditionally, as subject and 
 predicate, two different concepts S and P, whatever 
 they may be. The rather can only the two propo- 
 sitions i S is S ' and ( P is P' always hold good ; but 
 never <S is P' or <P is S/ 
 
 The usual form of the proposition 'A = A', (Propo- 
 sition of identity), and the negative 'A not = non-A' 
 (Proposition of contradiction) both express this sim- 
 ple truth, that every thinkable content is equal to 
 itself and different from every other one. 
 
 This simple logical meaning of the proposition 
 
PROPOSITION OF IDENTITY. 35 
 
 must without fail be distinguished from other theo- 
 rems, partly true and partly doubtful, which, although 
 they spring from the application of the universal logi- 
 cal proposition of identity, still do so only from its 
 application to a definite real content, and are not on 
 a par with the proposition itself. For example, that 
 every * Thing ' is like itself, or that it is unchange- 
 ably like itself, is a metaphysical proposition which 
 arises from an application of the logical proposition 
 of identity to the concept of the 'Existent/ The 
 logical proposition itself says nothing at all of 
 * Things/ It is also valid of events that happen, 
 of conditions that take place, of the real as truly as 
 of the unreal. And of all of them it merely says, 
 that to be is to be, the changeable is changeable, 
 the contradictory is contradictory, the impossible is 
 impossible. 
 
 § 27. Briefly expressed, then, the proposition of 
 identity asserts, that all categorical judgments of 
 the form 'S is P' are false and inadmissible. Now 
 since such judgments nevertheless very frequently 
 occur, and we are sufficiently convinced of their 
 admissibility, their defect can only consist in the 
 fact, that they express a correct sentiment with 
 formal imperfection. And an interpretation of them 
 must be given by which they can be justified before 
 the law of identity. 
 
36 OUTLINES OF LOGIC. 
 
 Attempts were first made at this in such a way 
 that a distinction was made between predicates com- 
 patible, and those incompatible with the subject. 
 And as no one is capable of knowing from purely- 
 logical laws, what P is compatible with what S, 
 therefore the general meaning was given to the 
 proposition of identity : Of two incompatible predi- 
 cates only one can belong to one subject. This 
 proposition, correct in itself, nevertheless does not 
 justify the categorical judgment at all. For it in 
 turn always presupposes that an S can be a P. 
 And it is just this which the proposition of identity 
 forbids without exception, no matter in what the 
 P may consist. 
 
 Another attempt at justification makes prominent 
 the fact, that in the proposition ( S is P' (gold is 
 yellow), S and P are by no means interpreted as 
 identical in such a way that the one could be sub- 
 stituted for the other, and consequently the judg- 
 ment be inverted and read, [ yellow is gold.' Between 
 both, the rather, another relation is maintained which 
 is fitly expressed by 'S has P.' Against this rela- 
 tion, that a mark is 'had' by its subject, or a 
 property by the ' Thing,' the proposition of identity 
 raises no protest. This view, also, although it 
 alludes to something that is quite true, does not 
 reach the end desired. It indeed removes the diffi- 
 
PROPOSITION OF IDENTITY. 37 
 
 culty of combining with S the content of P which 
 differs from S. But it does not explain how it is 
 possible to combine with S the conception of ' hav- 
 ing' (although it does explain what is had). For 
 since S is obviously able to ' have ' as well as ' not 
 have/ ' having' is itself in turn a predicate deter- 
 mination differing from that of the mere Being of 
 S; and the question recurs concerning this predicate, 
 how it is compatible with S. The proposition of 
 identity simply says, S is S. Every proposition, 
 S has something or other, therefore declares some- 
 thing different of the S, from the mere proposition 
 that it is S ; and, consequently, is itself defective 
 as respects the proposition of identity. 
 
 § 28. The solution of the above-mentioned diffi- 
 culty lies approximately in this, that all categorical 
 judgments are according to their intent and meaning 
 identical but express this intent in a formally im- 
 perfect way ; since they allude to only single parts, 
 sometimes of the true subject and sometimes of 
 the true predicate. 
 
 For example ; ' Gold is yellow ' means (as in Latin 
 the neuter of the adjective shows) the same as 
 'gold is yellow gold,' — an observation which has 
 been for a very long time expressed in such a way 
 that, in the judgment, the subject is not merely 
 
38 OUTLINES OF LOGIC. 
 
 defined or determined by the predicate, but likewise 
 the predicate by the subject. ' Yellow,' for instance, 
 means here not simply 'yellow in general/ but in 
 particular ' gold-yellow/ 
 
 The proposition ' Some men are black ' is ambig- 
 uous in German. The Latin ' Nonnulli homines 
 sunt nigrV shows that in the predicate homines is 
 to be supplied. Now ■ nonnulli homines ' and ■ nigri 
 homines' undoubtedly seem to be two entirely dif- 
 ferent conceptions. But still it is not meant, that 
 every 'some' men you please, taken out of the 
 totality, so far as they are 'some/ would be 'black' ; 
 but we understand a perfectly definite 'some/ — 
 namely, the negroes. Therefore S and P are wholly 
 identical as respects content, and only indicate in 
 different ways, that in P one instance (S) is char- 
 acterized as part of a more general concept by 
 means of its properties. 
 
 Finally, the historical judgments — for example, 
 ' the dog drinks/ ' Caesar crossed the Rubicon ' — 
 that is, all which express particular facts but not 
 uniformly valid relations, have for their true subject, 
 not the concept simplieiter, which appears at this 
 place, but always such concept together with a multi- 
 tude of secondary ideas, sometimes suppressed and 
 sometimes indicated, which we will call X ; so that 
 they properly have the form 'S + X = P.' Thus in 
 
THE HYPOTHETICAL JUDGMENT. 39 
 
 the foregoing examples, it is not the universal dog 
 which is drinking, but some specific one whose dif- 
 ferences from other dogs are not pointed out ; but 
 which, when we add in thought all its peculiarities, 
 — for instance, its temperament, the nourishment 
 it has previously had, its thirst, and the tempera- 
 ture in which it lives — is then exactly the same 
 dog which in the predicate cannot be thought of as 
 any other than the dog which is drinking. 
 
 These secondary ideas X, in the customary expres- 
 sion of categorical judgments, are wont to be desig- 
 nated mostly through the particular quantity of the 
 subject : for example, 'this S is P' ; 'some S are P' ; 
 or by particular denotation of the predicate, as ' S is 
 sometimes P ' ; ' S was P ' ; and the like. On this 
 account we give to this entire grade the form of the 
 'particular judgments' 
 
 § 29. What these particular judgments indicate, is 
 more expressly alluded to in the more developed form 
 of the hypothetical judgments. Here the accessory 
 circumstances, which are in the previous form sup- 
 pressed or only indicated, are designated in some an- 
 tecedent proposition as the condition which must be 
 fulfilled, if P as predicate is to be capable of being 
 adjoined to the concept of the subject S. 
 
 The simplest form will be this : If to S an X be 
 
40 OUTLINES OF LOGIC. 
 
 added, then S has the predicate P ; that is, antece- 
 dent and consequent propositions have the same con- 
 cept of the subject, which in the antecedent is 
 completed by means of X so as to become the real 
 subject to which in the consequent P must be 
 attached. In the usage of thought, other forms may 
 arise by suppression of the middle terms ; for exam- 
 ple, ' If R is an X, then S is a P/ Nevertheless they 
 always depend upon the foregoing original form. 
 
 In this form, the antecedent proposition being 
 according to its nature problematic, the consequent 
 is in a conditional way apodictic : it is necessarily 
 true if the antecedent, which is in itself only possible, 
 is true. If we wish to express therewith the truth of 
 the antecedent, then the assertory form comes into 
 use: 'Since $ is an X, S is a P.' If we wish to 
 designate that the antecedent is not the condition of 
 the consequent, the negative form arises : Although 
 S is an X, still S is not therefore a P. 
 
 § 30. If now we make prominent the fundamental 
 thought which the process of thinking has betrayed 
 through the elaboration of the hypothetical form of 
 judgment, we discover in it the second fundamental 
 law of logic : The principle of sufficient reason (Prin- 
 cipium rationis snfficie7ttis) . 
 
 The process of thought, as it were, says : You uni- 
 
PRINCIPLE OF SUFFICIENT REASON. 41 
 
 formly express a necessary truth when you put S = 
 S and P = P, in an identical judgment. You are 
 uniformly in error, when you put S = P, in a cate- 
 gorical judgment; that is, if you suppose it were 
 ever possible for an S to assume for itself alone a 
 property which does not belong to its concept, or 
 which it did not have previously ; or that, out of a 
 single principle, a single substance, a single power, a 
 single thought, it were ever possible for a multiplicity 
 of substances, developments, or ideas to emerge, — 
 in general anything manifold out of a unity. It 
 is, on the contrary, uniformly necessary, if, out of 
 one subject diverse new existences are to proceed, 
 that as many conditions differing from one another 
 should have to be brought to bear upon this sub- 
 ject as there are different results to be derived 
 from it. 
 
 The principle of sufficient reason therefore asserts 
 negatively (and in this respect is in agreement with 
 the law of identity) the impossibility of an immediate 
 connection of the two different contents of the idea, 
 $ and P ; affirmatively, on the other hand, it asserts 
 the possibility that, to a combination of two ideas, S 
 and X, which somehow determine each other, there 
 should be given a predicate P which is not given 
 either to the S alone, or to the X alone. The exist- 
 ing relation between S and X, whereby this becomes 
 
42 OUTLINES OF LOGIC. 
 
 possible, is the ratio sufficients of the connection of S 
 and P. 
 
 The universal logical meaning of this concept of 
 sufficient i reason ' (Grund) consists simply in the 
 supposition, that the manifold content of everything 
 thinkable is not a relationless and dispersed multi- 
 plicity ; but that there is a truth — that is, a sum of 
 such valid relations — through which a definite form 
 of uniting the single elements of the thinkable be- 
 comes of itself the equivalent of other elements. In 
 what, on the other hand, those relations consist, in 
 the particular instance or in single large domains of 
 the thinkable ; in what, therefore, the definite reason 
 for a definite combination of a certain S, or of a cer- 
 tain class of S, with a certain P, or a certain class 
 of P, — is not a matter of logic. 
 
 On this account, the principle of the 'ratio suffi- 
 cients' should not be confounded with that of the 
 causa efficients, the law of causation ; or with such 
 other general rules as relate to what is actual or to 
 particular classes of what is actual. A 'Cause' (Ur- 
 sache), for instance, is the power that produces some- 
 thing actual, which previously did not exist. A 
 'reason' {Grund) is always simply some valid truth 
 by virtue of which it happens, on the one hand, that 
 a definite effect is attributed to a certain cause ; and 
 by which also, on the other hand, in those provinces 
 
PRINCIPLE OF COHERENCE. 43 
 
 of thought, in which there is no 'happening/ — for 
 example, in mathematics — the combination of the 
 two contents of the concept depends, in respect to 
 its validity, upon the combination of two others, 
 regardless of time. How this comes to pass, and 
 what is, strictly speaking, involved in the fact, that 
 a condition can be the condition of that which is con- 
 ditioned by it, — of this no general logical explana- 
 tion is possible; — with the exception of a single 
 meaning of this question, in which meaning the 
 question is now indeed to be answered. 
 
 § 31. Although we do not ask in Logic to know 
 what consequences follow on what grounds, and by 
 what means the two cohere together, still, if the 
 process of thought is to be able to develop new 
 truths from given ones, we must possess some uni- 
 versal and purely logical principle, independent of 
 our knowledge of the thing to which it has merely to 
 be applied ; and according to this principle we must 
 be able to judge whether one proposition may be 
 rightly considered as the consequence of another. 
 
 Such a principle we do in fact possess. It con- 
 sists in this, that everything special must conform 
 to its general concept ; every individual case to the 
 rule of the general case. Had we not this formal 
 logical principle, then all special knowledge of in- 
 
44 OUTLINES OF LOGIC. 
 
 dividual conditionating relations which actually exist 
 between any of the elements of existence, would be 
 of no help to us. We should not be able to apply 
 them, and deduce any new truth from them. 
 
 § 32. This ^thought gains expression in the form 
 of the general judgment. Such form is to be dis- 
 tinguished from that of the universal judgment. 
 The latter, of the form 
 
 All S are P, 
 
 only asserts that, in fact, all instances of S have P, 
 — for example, 'All men are mortal/ — but does 
 not tell why. Perhaps it may be on account of a 
 combination of unfortunate accidents which have 
 no real connection with each other. 
 
 The general judgment substitutes the general con- 
 cept alone for the subject : i Man is mortal ' ; or it 
 indicates by the other form, * Every man is mortal/ 
 that the predicate is to be considered valid, not 
 merely of all actual but also of all thinkable exam- 
 ples of S ; and therefore is so by virtue of this 
 same general concept S, and not on other accidental 
 grounds. 
 
 More accurately considered, the general judgment 
 must besides be included in the hypothetical form. 
 For it is not the general concept S (the universal 
 man) which is to be considered as P (mortal) ; 
 
THE DISJUNCTIVE JUDGMENT. 45 
 
 but every individual, because he is man. Therefore, 
 the general form, strictly speaking, is : 'If any A 
 whatever is an example of the universal S, then 
 such A is necessarily P.* 
 
 § 33. The form of the general judgment is, never- 
 theless, still inexact in another way, — namely, in 
 this, that it attributes to the subject the predicate 
 of the general concept, although this subject is not 
 the general concept itself, but only the example sub- 
 ordinated to it ; for instance, the proposition, ' Every 
 material body has some color,' is untrue in so far as 
 the particular body never has color in general, but 
 is either red or green or blue, etc. 
 
 That is, the general judgment passes over into 
 the disjunctive or divisive, of the form, — ' Every S, 
 which is an example of the general concept M, re- 
 ceives from every general predicate P which is 
 attributed to M, one of its kinds, q, r, t, . . ., to the 
 exclusion of all others, as its own predicate. The 
 disjunctive judgment, therefore, furnishes S with no 
 definite predicate whatever, but only dictates to it, 
 as it were, the necessary choice between different 
 predicates ; and these, taken together, are individual 
 modifications of a general predicate P that is re- 
 quired by the higher concept of the genus M, to 
 which S is subordinated. 
 
46 OUTLINES OF LOGIC. 
 
 The next step forward would have to consist in 
 concluding this choice and making an actual selec- 
 tion between q, r, t, etc. But this cannot occur, in 
 so far as $ is a species of M, because this reason 
 leaves such choice wholly indeterminate ; but must 
 take place on account of the fact that S is S, — that 
 is to say, because it is such definite species of M 
 and none other. For making a decision, therefore, 
 two propositions will be employed ; the first of which 
 states what is true of S, so far as it is in general 
 one species of M, the second what is true of S, so 
 far as it is this species of M. These two proposi- 
 tions are obviously the so-called premises of a con- 
 clusion, to which new logical form we now pass 
 over. The series of judgments ends herewith, and 
 is not to be extended farther. 
 
 Remark. The ordinary abbreviated form of the disjunctive 
 judgment is as follows : 
 
 a) Affirmative : S is either q or r or t or . . . 
 
 b) Negative : S is neither q nor r nor t nor . . . 
 
 § 34. The interpretation of the disjunctive judg- 
 ment just adduced expresses two laws of thought 
 combined, w T hich have commonly been brought for- 
 ward as separate formulae : — 
 
 i. The 'Dictum de omni et nullo' 1 makes promi- 
 
 1 On the history of this, compare the Zeitschrift fur Philosophie u, 
 philos. Kritik, edited by Fichte, Ulrici, and Wirth, vol. lxxvi (Halle, 1880), 
 pp. 48 ff. 
 
PRINCIPLE OF EXCLUDED MIDDLE. 47 
 
 nent positively the dependence of the particular upon 
 its universal. The expressions which we frequently 
 hear, " What is true of the universal (or of the whole) 
 is also true of the particular (or of the part)/' are 
 evidently false. The scholastic formula, " Quidquid 
 de omnibus valet [negatur], valet [negatur] etiam de 
 quibusdam et de singulis," is indeed quite correct ; 
 yet it no longer expresses the relation as one of 
 dependence of the particular upon the universal to 
 which it belongs, but only as one of subordination of 
 the unity under the totality with which it is numeri- 
 cally included in the same conception ; in this way 
 the proposition becomes, fundamentally considered, a 
 tautology. 
 
 2. The second formula, the 'Principium exclusi 
 medii inter duo contradictoria,' is a special case of 
 the more general one which is expressed in the pre- 
 vious section. 
 
 That is to say ; if we presuppose, in the first place, 
 that the general predicate P has three or more spe- 
 cies q, r, t . . ., and that one subject S must, so far 
 as it is a species of M, make a choice among these 
 species of P, then the choice of one predicate q will 
 exclude all the rest, r, t . . . ; whereas the negation 
 of q does not involve the affirmation of a definite 
 one of the remaining r, t, etc. Of these predicates 
 q, r, t . . . it is said, that they stand in contrary oppo- 
 
48 OUTLINES OF LOGIC. 
 
 sition for an S, which is an M, to which M again P 
 belongs. 
 
 But furthermore, if P (gender) is separable into 
 only two species q and r (masculine and feminine), 
 then these two predicates stand in * contradictory- 
 opposition ' for every S which has any necessary re- 
 lation to P (for every living being) ; that is, not only 
 does the affirmation of the one deny the other, but 
 also the negation of the one affirms the other. 
 
 Finally, if we wish to avoid the condition, that the 
 S have a necessary relation to P dependent upon 
 its peculiar nature ; and if we therefore wish to 
 establish two predicates which are contradictory for 
 every S whatever ; then such relation can only con- 
 sist in some Q and non-Q, — whereby the latter com- 
 prehends all that is not Q. But 'precisely for that 
 reason non-Q is not an independent concept, which 
 can be attached as predicate to any S whatever; 
 and, strictly speaking, we no longer have a case of 
 an opposition between two concepts, but of an oppo- 
 sition between two judgments, one of which ascribes 
 a predicate Q to S, while the other totally denies 
 the same Q to it. 
 
 C. Immediate Inferences from Judgments. 
 
 § 35. According to an ancient mnemonic coup- 
 let, — Asserit A, negat E, verum generaliter ambo, 
 Asserit I, negat O, sed particulariter ambo, — 
 
SUBALTERNATION AND OPPOSITION. 49 
 
 we designate the universal affirmative judgment by 
 A, the universal negative by E, the particular affirm- 
 ative by I, and the particular negative by O. If we 
 conceive of these four forms as applied to one and 
 the same content S-P, the following relations occur 
 among them : — 
 
 A Oppositio Contraria E 
 
 * X X 1 
 
 I ^ X 1 
 
 I Oppositio Subcontraria O 
 
 I. Between A and I (All & are P — .sw^ S are 
 P), as well as between E and O (no S is P — some S 
 are not P) Subaltematio — that is, subordination of 
 the individual to the universal — takes place. The 
 validity of the general case always includes that of 
 the particular instance, the validity of the particular 
 not that of the general case. The invalidity of the 
 general case does not carry with it that of the par- 
 ticular ; the invalidity of the particular (which is 
 always understood as meaning that there is no partic- 
 ular instance whatever in which the content of the 
 judgment is valid) involves, on the contrary, the 
 
5<D OUTLINES OF LOGIC. 
 
 invalidity of the general case. Consequently, we 
 conclude ' ad subalternatam ' * from + A to + 1, from 
 + E to + O ; but not from — A to — I, not from — E 
 to — O. Further, we conclude 'ad subalternantem/ 
 from — I to — A, from — O to — E ; but not from 
 + 1 to + A, or from + O to + E. 
 
 Both of these prohibited conclusions — namely, 
 from the particular instance to the general case, and 
 from the invalidity of the general case to the like 
 invalidity of the particular — belong to the most 
 frequently occurring fallacies in logic. 
 
 2. From the contrary opposition between A and 
 E it follows, that the validity of the one excludes 
 that of the other ; the invalidity of the one, on the 
 contrary, does not involve the validity of the other. 
 We conclude therefore ' ad contrariam ' from + A to 
 — E, and from + E to — A ; but not from — A to 
 + E, or from — E to + A. 
 
 3. Between A and O and E and I there is contra- 
 dictory opposition. For if A is not valid, it is obvious 
 that there necessarily occur some cases, in which the 
 opposite is valid. So then the invalidity of a general 
 j udgment involves the validity of the opposite particu- 
 lar judgment ; and we conclude 'ad contradictoriam ' 
 from —A to +G, from — E to +1. In the same 
 
 1 The sign -f- stands for the validity, and — for the invalidity, of a judg- 
 ment. 
 
SUBCONTRARY OPPOSITION. 5 I 
 
 way it is self-evident, that when a particular judg- 
 ment is not valid, — that is, when there are no 
 individual instances in which it is valid, — then its 
 opposite is universally valid. We therefore likewise 
 conclude ' ad contradictoriam ' from — O to + A, 
 from — I to + E. Finally, it also is self-evident 
 that the validity of a universal proposition involves 
 the invalidity of opposite particular ones ; as well as 
 that the validity of a particular judgment involves 
 the invalidity of the opposite general judgment. 
 Therefore we also conclude 'ad contradictoriam ' 
 from + 1 to — E and conversely, and from +0 to 
 — A and conversely. 
 
 4. The subcontrary opposition between I and O, 
 if one of the two is valid, allows no conclusion to be 
 drawn. For if one particular judgment is correct, 
 it is possible that the opposite particular is also 
 valid ; but it is likewise possible that it is not valid, 
 and that the original proposition is only expressed 
 in particular form but is really universally valid. If, 
 on the contrary, a particular judgment is denied, then 
 the opposite general judgment is hereby affirmed 'ad 
 contradictoriam,' and as a consequence we have 'ad 
 subalternatam ' the validity of the subordinated (of 
 the previous opposite) particular judgment. We there- 
 fore conclude 'ad subcontrariam ' from —I to +O 
 and conversely, but not from + 1 to — O or conversely. 
 
52 OUTLINES OF LOGIC. 
 
 § 36. A judgment undergoes conversion (conversio) 
 when subject and predicate are exchanged. The natu- 
 ral interest of thought in this operation consists in this : 
 If a proposition 'S is P' gives to the S a predicate, 
 then we may desire to know whether this is an essen- 
 tial mark of S, whether therefore everywhere, where 
 P occurs, the subject with which it occurs is an S or 
 a species of S. That is, we wish essentially to know 
 whether the converted judgment, 'P is $,' is univer- 
 sally valid, or not. 
 
 Pure conversion {conversio purd) is the name given 
 to that in which the original and the converted prop- 
 osition have the same quantity. Impure (impura or 
 per accidens) conversion is that in which this is not 
 the case. 
 
 § 37. We may therefore have — 
 a) A universal affirmative judgment: 'All S are 
 P.' Three cases are here possible : 
 
 Fig. I. Fig. 2. Fig. 3. 
 
CONVERSION OF JUDGMENTS. 53 
 
 In Fig. i, S is subordinated to P: ' All metals are 
 bodies'; in Fig. 2, S is subsumed under P: 'All 
 gold is yellow/ In both cases it is self-evident that 
 the whole extension of P is not covered by S ; that 
 there are consequently many Ps which are not S ; 
 and that, accordingly, the conversion can only be 
 imperfect (impiird) and give nothing but the particu- 
 lar judgment : ' Some P are S ' (' Some bodies are 
 metals,' ' Some yellow bodies are gold '). — Fig. 3 is 
 therefore to be conceived of in such way, that two 
 equal circles $ and P completely cover each other ; 
 from which it follows that the conversion is pure 
 and gives the universal proposition : ' All P are S/ 
 Such judgments are called ' reciprocable/ But what 
 judgments belong to this class cannot be known on 
 logical grounds, but only from knowledge of actual 
 facts. To it, for example, belong all accurate defini- 
 tions, all correct equations, and many propositions 
 like this : ' All equilateral triangles are equiangular/ 
 
 The violation of this rule of conversion is one of 
 the most frequent of logical errors. 
 
 Fig. 4. 
 
54 OUTLINES OF LOGIC. 
 
 b) The universal negative judgment, * No S is P,' 
 obviously (Fig. 4) separates S and P completely, so 
 that it is self-evident that no P is an S ; that is, uni- 
 versal negative judgments by pure conversion give 
 universal negative judgments again. 
 
 c) The particular affirmative judgment, 'Some S 
 are P,' if S is subsumed under P, — for example, 
 i Some flowers are yellow ' (still more, like the analo- 
 gous universal judgment, according to Fig. 2) admits 
 only of the particular conversion, ' Some yellow ob- 
 jects are flowers ' ; if, on the other hand, P is subor- 
 dinated to S, and $ is therefore the higher generic 
 notion, — as for instance, 'Some dogs are pugs/ — 
 then conversion gives the universal judgment, 'All 
 P are S/ This case also we can know only from 
 knowledge of real things. 
 
 d) The particular negative judgment, 'Some S are 
 not P,' can in no rational way whatever be converted 
 into the negative ' Some P are not S ' ; for example, 
 from the statement that some monkeys have no tails 
 it does not follow that some things without tails are 
 not monkeys. For the tail might possibly occur only 
 in the case of monkeys, although they might not 
 all have it. Or in more general terms ; the negation 
 of a predicate to any subject does not justify any 
 affirmation as to what of such predicate otherwise 
 occurs or does not occur. All that can be done here 
 
CONTRAPOSITION OF JUDGMENTS. 55 
 
 is to join the negation to the predicate and convert it 
 into the particular affirmative. Therefore, ' Some S 
 are not P,' gives ' Some non-P are S.' 
 
 § 38. Furthermore, inquiry may be made as to the 
 relations which take place between a subject S which 
 has a predicate P, and another subject which has not 
 this P, — that is, a non-P. This leads to what is 
 called contraposition. According to this form, the 
 affirmative judgment is changed into a negative, in 
 which at the same time non-P is substituted for P, 
 the negative attaches its negation to the predicate, 
 and thereby becomes affirmative. Both then become 
 converted according to the customary rules. The 
 ' contraposited ' judgment has the opposite quality 
 from the original judgment. The quantity in the 
 particular judgment remains the same; the universal 
 affirmative becomes universal negative, and the uni- 
 versal negative becomes particular affirmative. 
 
 Examples : 
 
 All $ are P. 
 
 No S is non-P. 
 No non-P is S. 
 
 No S is P. 
 
 All S are non-P. 
 Some non-P are S. 
 
 The conclusions arrived at in this way are not 
 worthless ; but they can all be reached more con- 
 veniently and clearly without this apparatus of logi- 
 cal formalities. 
 
CHAPTER III. 
 
 OF SYLLOGISMS. 
 A. The Aristotelian Figures. 
 
 § 39. Before we further prosecute the problem 
 which the disjunctive judgment propounded as that 
 of the form of the conclusion, we have first to allude 
 to certain other forms of conclusion, which do not 
 indeed solve this problem, but only express as devel- 
 oped what was already contained in the form of the 
 general judgment. 
 
 In the former case a P was attributed to an S, in 
 so far as this S falls under the concept M. Such a 
 content is separable into two judgments, one of 
 which expresses a relation pf M to P, and the other 
 a relation of S to M ; whereupon the proposition it- 
 self asserts as a consequence a relation of S and P. 
 These are the elements of the ordinary conclusion : 
 M is the medius terminus, or ' middle concept/ by 
 means of which a relation is established between S 
 and P ; the propositions which express the relation, 
 in part of M to S, and in part of M to P, are the 
 premises ; the third proposition, which always com- 
 bines S and P, and in which M does not appear, is 
 
THE ARISTOTELIAN FIGURES. 57 
 
 the conclusion (Conclusio). According to the differ- 
 ent possible combinations of the three concepts in 
 the premises, the three so-called Aristotelian figures 
 of the conclusion are distinguished : — 
 
 I. Figure: M — P II. Figure: P — M III. Figure: M — P 
 S - 31 S -M M - S 
 
 S -P S -P S -P 
 
 It is only a matter of agreement, and yet one 
 universally accepted, that in the concluding proposi- 
 tion the concept shall always be the subject which 
 is combined with M in the second premise ; and the 
 other one, which stands in the first premise, the 
 predicate. Accordingly, the first premise may be 
 in general designated as the l major' premise (Propo- 
 siti major), the second as the ' minor' premise (Pro- 
 positi minor) ; although, according to the nature of 
 the thing, no inducement to this is found in the 
 second and third figures, since their premises are 
 constructed in a manner quite homogeneous. 
 
 For all three figures the universally valid condition 
 of the cogency of the conclusion consists in the com- 
 plete identity of the middle term in both premises. For 
 S and P would obviously not be connected together 
 through M, if the M with which P is connected were 
 another M from that with which S is connected. 
 
 § 40. If we consider the position of the premises 
 
58 OUTLINES OF LOGIC. 
 
 in the ' First Figure/ we discover that, according to 
 the very nature of the case, the same concept M can 
 be at one time subject and at another predicate, only 
 when it is a generic concept for which the major 
 premise furnishes a predicate, and under which the 
 minor premise subordinates some subject as a special 
 instance or example. 
 
 The force of the conclusion, therefore, depends 
 upon the subsumption of the particular under the uni- 
 versal. It will, accordingly, take place only when — 
 
 i) the major premise is universal (for the S in 
 the minor premise, which is an M, is with perfect 
 certainty subsumed under the M of the major pre- 
 mise, only in case this latter includes all M) ; and 
 when — 
 
 2) the minor premise is affirmative (for since the 
 conclusion depends upon subsumption, a negative 
 minor premise, which would deny any such subsump- 
 tion, would cut the nerve of the sequence). — On the 
 contrary — 
 
 3) the quality of the major premise is not essential 
 (for the same relation which it expresses between M 
 and P, whether it be affirmation or negation, should 
 and can be carried over in the conclusion to S and P). 
 Also — 
 
 4) the quantity of the minor premise is not essen- 
 tial (for it is just this relation of M and P that is not 
 
THE SECOND FIGURE. 59 
 
 altered by the number of the subjects to which it 
 applies). From this it follows, finally, — 
 
 5) that the conclusion always has the quality of 
 the major premise and the quantity of the minor 
 premise (for it borrows from the first the positive or 
 negative relation which it carries over ; and from the 
 second, the particular or universal subject to which 
 it carries the relation over). 
 
 If the vowels of the following words of three 
 syllables (following the mnemonic couplet of § 35) 
 designate, respectively, the quantity and quality of the 
 propositio major, of the propositio minor, and of the 
 conclusion of the syllogism, then there are four valid 
 so-called ' Modi ' of the first figure : Barbara, Cela- 
 rent, Darii, Ferio. 
 
 § 41. In the Second Figure, the premises estab- 
 lish a relation between two subjects P and S, and the 
 same predicate M. 
 
 If now, in the first place, we conceive of both as 
 1 possessing ' the M, then obviously nothing whatever 
 follows with reference to their reciprocal relation. 
 And the case would be exactly the same as if they 
 both did not have the M. Both premises, therefore, 
 should not be affirmative, nor both negative. If, on 
 the other hand, the one subject A — particular or 
 universal — either does or does not have the M, and 
 
60 OUTLINES OF LOGIC. 
 
 the other, B, is in the opposite relation with reference 
 to M, — not particular but universal, — and therefore 
 uniformly has not or has M ; then A cannot be a 
 species of B. 
 
 From this it would follow that one premise must 
 be affirmative, the other negative ; and that one must 
 be universal, and the other may be particular as well. 
 Still, since the A, which is to be the subject in 
 the conclusion, is always, according to conventional 
 usage, the subject of the minor premise (S), the 
 universal premise must be the first or major ; and its 
 rules are, accordingly, the following : — 
 
 i) The major premise in the second figure is uni- 
 formly universal, but its quality is either affirmative 
 or negative. 
 
 2) The minor premise is in quality uniformly the 
 opposite of the major premise ; but its quantity, on 
 the contrary, may be either universal or particular. 
 
 3) The conclusion is uniformly negative, and fol- 
 lows in quantity that of the minor premise. 
 
 The four modes (Modi) are : Camestres, BanSco, 
 Cesare, Festino. 
 
 § 42. In the Third Figure, the premises establish 
 a relation between one and the same subject and two 
 predicates. 
 
 Now if the subject has both predicates, — that is, 
 
THE THIRD FIGURE. 6l 
 
 if both predicates are affirmative, — then there fol- 
 lows, from this given example of an actual combina- 
 tion of S and P, the possibility of such combination 
 (the fact that S and P are 'unitable'); and, therefore, 
 the conclusion is : ' What is S may be P.'' This con- 
 clusion is customarily (and yet, strictly speaking, not 
 perfectly correctly) expressed in the particular form : 
 'Some S are P.' In order that the medius terminus 
 may both times signify exactly the same thing, and 
 therefore the M of the one premise may be certainly 
 contained in the M of the other also, one premise — 
 it makes no difference which — must be universal. 
 This gives three modes : Darapti, Datisi, Disamis. 
 
 If, on the other hand, the M has one predicate, but 
 not the other, — that is, if one premise is affirmative 
 and the other negative, — then it follows from this 
 that the two predicates are separable. Or (to express 
 the same thing more accurately) the predicate which 
 occurs is separable from that which does not occur 
 in this example (that is, is denied). But it does not 
 follow that the predicate here denied could occur 
 separate from that affirmed. From 
 
 All animals are living, 
 
 Some animals are not rational, 
 
 it does not follow that being rational could occur 
 without being alive (although the latter could very 
 
62 OUTLINES OF LOGIC. 
 
 well occur without the former). Now, since (§ 39, 
 last paragraph but one) the subject of the conclu- 
 sion must appear in the minor premise, it must be 
 affirmed ; and, besides, as in the previous figure, in 
 case of two affirmative premises, one must be uni- 
 versal. Strictly speaking, the conclusion merely 
 asserts : ' What S is, P need not be ' ; but this again, 
 expressed as a particular judgment (though strictly 
 speaking, not with accuracy) becomes : ' Some S are 
 not P.' This gives us the following three modes : 
 Felapton, Ferison, Bocardo. 
 
 Finally, if both premises are negative, then it is 
 customary to assert in treatises on logic that no con- 
 clusion is possible — ' ex mere negativis nihil sequi- 
 tur.' This is absolutely groundless and false. If 
 the same M is neither P nor S, then it follows from 
 this that P and S are not contradictorily opposed to 
 each other ; and that, consequently, what is not S 
 need not, on that account, be P. For example : The 
 just man is not recognized — The just man is not 
 unhappy ; — conclusion : Whoever is not recognized 
 is not on that account unhappy. Conclusions of this 
 kind are by no means to be esteemed as of small 
 value and importance ; since they assert, from affirm- 
 ative or mixed premises, the unitability or (respec- 
 tively) the separability of $ and P. And they, in 
 fact, are occurring every day, in order to refute some 
 
THE FIGURE OF GALEN. 63 
 
 false conclusion which has been drawn from the de- 
 ficiency of one predicate : " Because thou art not 
 that, thou needest not to be the other also.'' 
 
 § 43. A Fourth Figure, that of Galen, in which 
 the position of the premises is P — M, M — S, and 
 from which the conclusion S — P should follow, is 
 superfluous and faulty ; for example, — 
 
 All roses are plants. 
 All plants need air. 
 
 Some things needing air are roses. 
 
 The natural process of thought always draws from 
 the foregoing premises, when it converts them, the 
 following conclusion in accordance with the first 
 figure: 'AH P are $' — "All roses need air/ The 
 conclusion of Galen, — ' Some S are P ' — on the 
 contrary is not merely unnatural, but expresses less 
 than the other. For if it is converted, then we have 
 only the particular proposition : ' Some P are S ' — 
 'Some roses are things that need air.' But undoubt- 
 edly it is a logical fault, from given premises to con- 
 clude less than really follows from them. 
 
 And in similar manner, the conclusions possible 
 according to the fourth figure always admit of being 
 obtained more naturally and better by transposition 
 and transformation of the premises in accordance 
 with one of the first three, or Aristotelian figures. 
 
64 OUTLINES OF LOGIC. 
 
 The modes of the fourth figure are as follows : 
 Bamalip, Calemes, Dimatis, Fesapo, Fresiso. 
 
 § 44. Only the first figure appeared to the older 
 logic to be evidently conclusive and perfect. The 
 conclusions drawn according to the other figures, on 
 the contrary, were considered to be completely justi- 
 fied only when they could be referred (' reduced ') by 
 transformation, conversion, transposition, of the pre- 
 mises, etc., to the first figure ; and then the previous 
 conclusion drawn from them in accordance with this 
 figure. The operations necessary for this are signi- 
 fied by the consonants s p m c in the names of the 
 modes of the second, third, and fourth figures, in 
 accordance with the couplet, — 
 
 s vult simpliciter verti, p verti per accid. [accidens], 
 m vult transponi, c per impossibile duci. 
 
 That is to say, if m (metathesis) requires transposi- 
 tion of the premises (that the major premise be 
 made the minor premise, the minor premise the 
 major) ; s and p call for Conversio (more particularly, 
 s for pure conversion, simpliciter, p for impure, per 
 accidens) of that proposition behind whose character- 
 istic vowel they stand in the name of the modes. 
 For example ; in order to ' reduce ' Disamis to the first 
 figure, the major premise (on account of the s which 
 follows its vowel) must undergo pure conversion, — 
 
TRANSFORMATION OF PREMISES. 6$ 
 
 that is, in this case, conversion into a particular prop- 
 osition ; it is then to have its position exchanged (on 
 account of the ni after the a) with the minor pre- 
 mise. Now from these transformed premises a con- 
 clusion is drawn according to the first figure, which 
 is then in turn converted (on account of the last s) ; 
 and in that way, finally, the previous conclusion ac- 
 cording to Disamis is derived again. 
 Example : 
 
 Original in Disamis : 
 
 Some metals are magnetic. 
 All metals are fusible. 
 
 Some things fusible are magnetic. 
 
 Reduction to Darii of the first figure : 
 
 All metals are fusible. 
 
 Some magnetic substances are metals. 
 
 Some magnetic substances are fusible. 
 
 This conclusion converted : 
 
 Some things fusible are magnetic. 
 
 Finally, the letter c indicates a more circumstan- 
 tial operation (the Ductio per impossibile s per con- 
 tradictoriam propositionem), which amounts to the same 
 thing as that, for example, in Bocardo the conclusion 
 StfP 1 denies ; accordingly the proposition S#P affirms 
 
 1 S«P, SeP, S^P S<?P, are meant to designate, respectively, a universal 
 affirmative, particular affirmative, universal negative and particular nega- 
 tive judgment, with the subject S and the predicate P. Corresponding to 
 these, on the other hand, PaS would be a universal affirmative judgment 
 with the subject P and the predicate S, etc. 
 
66 OUTLINES OF LOGIC. 
 
 'ad contradictoriam,' and (the c stands in the name 
 of the modus behind the vowel which designates 
 the major premise) this contradictory opposite of 
 the conclusion is put in the place of the major pre- 
 mise of Bocardo. From it as major premise, and 
 from the second premise of Bocardo as minor pre- 
 mise, a conclusion then follows according to Barbara, 
 which is the contradictory opposite of the premise 
 given in fact as the first of Bocardo (and accordingly 
 is just as certainly false as that is correct) ; from 
 all of which it is clear that the negation of the 
 original conclusion in Bocardo is not permissible, 
 and that this other is therefore correct. 
 
 § 45. The distinguishing peculiarities of the three 
 Aristotelian figures are therefore the following : 
 
 i) Only the second figure can draw a conclusion 
 from a negative minor premise ; only the third 
 figure from a particular major premise. 
 
 2) Only the first figure can lead to a universal 
 affirmative conclusion. Only it has concluding 
 propositions of every kind : A, E, I, O ; on the 
 contrary, the second is only negative : E, O ; the 
 third is only particular : I, O. 
 
 This law holds good in the case of connected 
 series of syllogisms (syllogismi concatenati, catenae 
 syllogismorum) which originate from the fact that 
 
NATURE OF THE SORITES. 67 
 
 the conclusion of one syllogism — which is then 
 called ' prosyllogismus ' — is employed as a premise 
 for another, which then receives the name of 'epi- 
 syllogismus.' If the conclusion of the last epi- 
 syllogism, and therefore of the entire chain of 
 reasoning, is to be universal affirmative, then the 
 entire chain must be constructed according to the 
 mode Barbara of the first figure. If a particular 
 proposition at any place enters into it, then the 
 final conclusion can be only particular ; and only 
 negative, as soon as a negative conclusion has any- 
 where entered into it. 
 
 Finally, ' Sorites' (Kettenschluss) is the name for 
 certain chains of conclusions that are abbreviated 
 and simplified in expression (abbreviated and simpli- 
 fied by suppressing the concluding propositions of all 
 the prosyllogisms). It is customary to distinguish 
 the sorites of Aristotle and the sorites of Goclenius. 1 
 The structure and difference of the two are as follows : 
 
 Sorites of Aristotle. Sorites of Goclenius. 
 
 S-MO) MO) -P 
 
 MOO-M(J) MQO-MO) 
 
 M(£) - M(0 M(V) - M(y) 
 
 • • • • 
 
 • • • • 
 
 MO) -MOO MO)- MO) 
 
 M {y) -MO) M (a) - M (/) 
 
 MO) -P S-M(V) 
 
 S-P S-P 
 
 1 So called from Rudolph Goclenius (1547-1628), professor in Marburg, 
 
68 OUTLINES OF LOGIC. 
 
 § 46. Strictly speaking, all syllogisms simply carry 
 over unchanged (as their form of expression makes 
 perfectly clear in case we conceive of those which 
 follow the other figures as ' reduced ' to the first 
 figure, § 44) that relation which the major premise 
 states as between P and M, and apply it to the 
 subject S, which the minor premise somehow obvi- 
 ously includes in the conception of M. Accordingly, 
 the nature of the judgment which forms the major 
 premise, as well as of that which forms the minor pre- 
 mise, is unimportant for the form of the conclusion. 
 
 If the premises, therefore, are not categorical 
 judgments (as we have hitherto exclusively assumed 
 them to be), but if they are furnished to us in 
 hypothetical or disjunctive form, then these differ- 
 ences (which are, of course, important for the 
 judgments as such) require consideration ; but they 
 do not require any alteration of the rules for draw- 
 ing conclusions which are primarily established for 
 categorical premises. Nevertheless, in some sorts 
 of conclusions with hypothetical or disjunctive pre- 
 mises, the matter-of-fact interest has led to certain 
 artificial expressions to which allusion may be made. 
 
 author of the 'Lexicon philosophicum,' Francof. 1613, who in his ' Isagoge 
 in Organum Aristotelis,' Francof. 1598, was the first to require for the 
 sorites this (in the series of the traditional syllogistic-norms, comp. supra, 
 p. 57) transformation of the schema of the schools, which is, of course, 
 perfectly correct. 
 
NATURE OF THE SORITES. 69 
 
 In the first place, there is a series of cases in 
 which a hypothetical major premise, as a general 
 rule, attaches a sequence F in the following prop- 
 osition to a reason G that forms the content of 
 its preceding proposition ; but a categorical minor 
 premise either affirms or denies the validity either of 
 G or of F. 
 
 a) Now if the major premise asserts positively: 
 * If G is true, then F also is always true ' ; and the 
 minor premise just as positively: 'In all or some 
 cases of S, G is true ' ; then the conclusion is : 'In 
 all or some cases of S, F is also true.' This is called 
 the 'Modus ponendo ponens,' because by positing 
 the reason the consequent is established ; and it 
 corresponds to the modes Barbara and Darii. 
 
 b) If the major premise were the same, and the 
 minor premise, on the other hand, negative and also 
 assertory : ' F does not exist ' ; then the conclusion 
 would be: 'Consequently, G also does not exist.' 
 This is a 'modus tollendo tollens' that, by abolishing 
 the result, abolishes the reason which it would have 
 necessarily established in case it had been valid; as 
 for the rest, it is in appearance a type of Camestres 
 and Baroco. 
 
 c) If the major premise were negative : ' In case G 
 is true, F is never true ' ; and the minor premise 
 asserted positively : ' Now, however, F is true ; then 
 
yO OUTLINES OF LOGIC. 
 
 the conclusion would be : Therefore G is not true, 
 which would make F impossible, if it were/ etc. 
 This is a ' Modus ponendo tollens' (corresponding to 
 Cesare and Festino), which by positing a result 
 denies the reason which would have made it im- 
 possible. 
 
 And so forth : — we see that these consequences 
 admit of being referred without difficulty to the 
 course of thought in the Aristotelian figures. 
 
 Finally, 'Dilemma,' 'Trilemma' . . . 'Polylemma,' 
 are the names given to those conclusions with a 
 disjunctive major premise (having two, three ... or 
 many members, respectively) and with several minor 
 premises, whose number is the same as the number 
 of the disjoined members in the major premise ; and 
 which assert conjointly for each of these members 
 one and the same result T, or one and the same predi- 
 cate T. The name ' dilemma ' (and corresponding to 
 it, trilemma, etc.) is by preference originally given to 
 a conclusion of the form : 
 
 If Z is to be true, either U or W must be true, 
 Now neither U nor W is true, 
 
 Therefore Z is not true. 
 
 § 47. The Aristotelian figures admit of being 
 apprehended in yet another way. If we conclude 
 according to the first figure in Darii : 
 
DESIGN OF THE CONCLUSION. J I 
 
 All men are mortal, 
 Caius is a man, 
 
 Therefore Caius is mortal; — 
 
 it is indeed the design of the conclusion to deduce 
 the truth of the final proposition as something in 
 itself still questionable, from the truth of premises 
 regarded as already established. But our attention 
 is soon called to the fact, that i alV men are mortal 
 only in case Caius is, too ; and that Caius also is a 
 ' man ' only in case he has all the essential properties 
 of a man, and consequently that of being mortal. 
 That is to say, the conclusion suffers from a so-called 
 * double circle': major as well as minor premise, in 
 order themselves to be valid, presuppose the validity 
 of the conclusion which they ought to demonstrate. 
 
 Such a mode of drawing conclusions, therefore, 
 cannot be of direct service for the expansion of our 
 knowledge, but only for the purpose of bringing 
 truths already established into a relation of subordi- 
 nation that corresponds to the actual way things go. 
 
 i) It can expand knowledge only in case we are 
 warranted in asserting universal judgments, in order 
 to have independent major premises, before the 
 validity of every special instance subordinated to 
 them is proved ; — and in case we — 
 
 2) are warranted in subordinating a subject to a 
 general concept on account of certain marks, in order 
 
J2 OUTLINES OF LOGIC. 
 
 to have independent minor premises, before we know 
 whether it has all of its predicates. 
 
 § 48. Now the major premises can be constructed 
 in the second figure, if we expand them somewhat. 
 Its premises are formed quite alike: P — M, S— M. 
 In experience it often happens that several of them : 
 Q — M, R — M, T — M... are given. But from the 
 premises given just as many conclusions must be 
 drawn as follow from them. 
 
 If, therefore, the premises P — M, S — M, Q — M, 
 R — M . . . are given, — that is to say, if many other- 
 wise different subjects have the same predicate, — 
 then we conclude that not every single one of them 
 has M through some special accident, but that one 
 and the same common reason makes it necessary for 
 them all at the same time. 
 
 This reason is put forward in the form of a generic 
 concept, of which all the aforesaid subjects are 
 species ; and now the assertion is made that the M 
 belongs to this concept 2 as a rule, and that those 
 subjects possess the M only by means of their sub- 
 ordination under 2. The concluding proposition 
 therefore is : ' Every 2 is M,' — and this is the 
 simple conclusion of Induction, which has its position 
 in the system of thought at this place. 
 
 
KINDS OF INDUCTION. ^ 
 
 i Perfect ' and ' imperfect ' induction are distin- 
 guished. The first takes place if it is known that 
 the subjects enumerated in the premises, taken 
 together, exhaust all the species of 2. But then, 
 although the universal proposition, — ' All 2 are M/ 
 — taken strictly, can be asserted, since the same has 
 already been asserted in the premises of every single 
 species of 2, yet, on the other hand, this concluding 
 proposition is a bare summing-up, and not a real 
 expansion of our previous knowledge. For its 
 change into a general judgment — * Every 2 is M ' — ■ 
 is not, fundamentally considered, permissible ; since 
 from the mere fact that all species of 2 have one 
 predicate, it neither follows that they have it as 
 species of 2, nor that all species of 2 which are 
 perhaps still to be discovered will have it. 
 
 This last conclusion, if it is made, is nothing more 
 than the ' imperfect ' induction, which concludes from 
 the fact, that some species of 2 have a predicate, 
 to the appearance of the same predicate in all 
 species ; and which does this, indeed, in consequence 
 of its common generic concept. But such induction, 
 although not strictly conclusive as a consequence ad 
 subalternantem, does expand our knowledge ; in 
 applied logic, however, it requires certain rules to 
 restrict it. 
 
74 OUTLINES OF LOGIC. 
 
 § 49. In a similar way, the third figure can lead 
 to the formation of the minor premises required above. 
 
 If its premises that have a like construction are 
 increased, — M — S, M — P, M - Q, M — R . . ., they 
 present the frequently recurring case of manifold 
 properties being attached to the same subject. Here 
 also the conclusion is drawn that each one is not 
 present through some special accident, but that all 
 come from one and the same reason, — and this on 
 account of the fact that M is a species of the genus 
 2, in which the combination of the marks SPQR 
 . . . is prescribed. The conclusion therefore is: 'M 
 is a 55/ — which is the simplest form of conclusion 
 by Analogy. 
 
 This, too, would be ' perfect ' only in case it could 
 be shown that SPQR... are, taken together, the 
 entire collection of predicates which 2 requires. For, 
 of course, whatever has all the properties of a 2, 
 appears itself necessarily to be a 2. And yet this 
 consequence also is not quite strictly drawn. In 
 reality,, we can only sum up the premises, and say 
 in the concluding proposition, that in fact all the 
 predicates are found in M which belong to a 2. 
 That they are so, however, not merely in fact, but 
 by virtue of the truth that M is a 2, is never in per- 
 fect strictness a matter of demonstration; but such 
 a conclusion stands on an equality with the so-called 
 
FORMS OF CALCULATION. 75 
 
 ' imperfect analogy/ which draws a conclusion from 
 certain observed marks in M to the assumption that 
 M will also have the other marks which, together 
 with the foregoing, make out a 2 ; and that M will 
 therefore be a 2. 
 
 B. The Forms of Calculation. 
 
 § 50. The doctrine of judgment concluded with 
 the disjunctive form, which asserted that the one 
 or the other special modification of the general pred- 
 icate P must belong to the S, — which predicate 
 belongs to the higher generic concept of S, namely, 
 to the M. In order that this choice may be decided, 
 it was necessary that S be taken into consideration, 
 not merely as a species of M in general, but also with 
 reference to its specific nature, by which it is distin- 
 guished from other species of M. 
 
 The first Aristotelian figure, which depends upon 
 this relation of subsumption, does not do this. In 
 the minor premise it only subordinates the S in gen- 
 eral, as a species of M ; and can, therefore, also only 
 ascribe to it, in the conclusion, the universal P with- 
 out closer definition. This result is, in part, not cor- 
 rect, since the P in such indefiniteness cannot be a 
 predicate of S ; and, in part, it does not satisfy our 
 necessities. For in real life it is seldom enough to 
 conclude : ' All metals are fusible ' — ' iron is a metal ' 
 
j6 OUTLINES OF LOGIC. 
 
 — ' therefore iron is fusible' ; but we wish to know 
 how iron as iron, in distinction, for example, from 
 lead as lead (that is, perhaps, at what degree of tem- 
 perature), is fusible. 
 
 § 51. Still another consideration leads to the same 
 demand. Fixed and changeable (historical) predi- 
 cates of a subject may be distinguished. The man- 
 ner of drawing conclusions hitherto described referred 
 only to the former. For such properties as belong 
 to a subject by virtue of its subordination under its 
 higher genus, of course belong to it always and are 
 fixed predicates. 
 
 But in real life constantly, and very often in sci- 
 ence, we are far more interested in the changeable 
 predicates ; that is to say, in those which designate 
 some affection, some activity, some state, in brief, 
 something or other which happens to the S only so 
 far as certain conditions act on S, but which would 
 never flow from the mere fact that S is a species of 
 M (only so much is self-evident, however, that sub- 
 ordination of S under M must establish such a pred- 
 icate). 
 
 This necessity, too, which occurs — for example — 
 in the calculation of all future events, and in the 
 employment of means for our conduct, requires that 
 we should discover for S some quite definite predi- 
 
ARGUMENT FROM ANALOGY. JJ 
 
 cate which does not originate from the subsumption 
 of S under a general concept, but from one way of 
 regarding the special nature of the S and of all the 
 conditions acting upon it. 
 
 § 52. The conclusion of analogy, too, in case it is 
 to be of any use, requires that, from certain marks 
 which we observe in a subject, we should draw a con- 
 clusion directly to the presence of other marks also ; 
 and then from the sum of these marks form a con- 
 clusion secundo loco to the fact that the subject is one 
 species of a genus. The previous mode of procedure 
 was the reverse of this : in the first place, a subject 
 was subsumed as a species of a genus, and then se- 
 cundo loco a conclusion drawn from this to its pred- 
 icate. 
 
 The question now arises whether that which such 
 analogy could not strictly accomplish admits of being 
 thus strictly accomplished at all ; that is to say, 
 whether we can draw a conclusion from the pres- 
 ence of certain marks or conditions in a subject S, 
 directly and without taking our way around through 
 any general generic concept, to the necessary pres- 
 ence or absence, and to the definite value of other 
 marks of the S. 
 
?8 OUTLINES OF LOGIC. 
 
 § 53. The foregoing necessities would be satisfied 
 by any mode of conclusion, the major premise of which 
 breaks up a general concept, M, into the collective 
 number of its parts ; and substitutes for it, as hold- 
 ing equally valid, the developed combination of these 
 parts ; such a form, therefore, is 
 
 M = a + for +<^ 2 +••••, 
 
 in which all the mathematical signs are supposed 
 merely to represent the variety of the possible ways 
 of combining the marks. The minor premise would 
 assert of S, not merely that it is a species of M in 
 general, but that it is the definite species of M which 
 we get in case we let some further determining con- 
 dition act upon the universal M. This gives to the 
 minor premise (designated again by a mathematical 
 symbol) the form, — 
 
 S = <|> (M). 
 
 And now the concluding proposition has to ex- 
 press with complete definiteness what predicate must 
 belong to S ; because the combination of marks sub- 
 stituted for M in the major premise has, in the con- 
 clusion, experienced the special influence of the 
 conditions designated by + in the minor premise. 
 
 One needs no reminder to comprehend that this 
 way of drawing a conclusion is directly and strictly 
 applicable only in mathematics. In the case of other 
 objects of thought, — for example, concepts of nat- 
 
MATHEMATICAL ARGUMENT. 79 
 
 ural species and genera, — we cannot carry out the 
 substitution in the major premise ; because we never 
 perfectly know all the marks of any genus, and still 
 less accurately all its modes of combination. Fur- 
 ther : we can never perfectly show in the minor prem- 
 ise by what determination, <)>, the genus M passes 
 over into the species S. If we should be satisfied, 
 however, with making prominent some single mark 
 (as x) by which S is distinguished from other spe- 
 cies of M (without positively learning from x the 
 entire nature of $), then we should not be able in 
 the conclusion to demonstrate what transforming 
 influence this x must exercise upon all, or upon any 
 one, of the marks qualitatively different from it (to 
 which allusion is made in the major premise) or 
 upon the combination of such marks. 
 
 All this is possible only in the domain of mathe- 
 matics. Since every magnitude is comparable with 
 the rest, and all are resolvable into the same units, 
 and producible from them by different combinations ; 
 and, finally, since they are perfectly defined in their 
 content, — that is, in their value, and since there 
 are rules of calculation which determine accurately 
 the ' Facit ' that results in case a definite operation 
 is applied to a definite combination of magnitudes ; 
 it is, therefore, possible in this domain actually to 
 carry out the concluding proposition, and to fill out 
 
80 OUTLINES OF LOGIC. 
 
 in it the schema <|> (M) by assigning it a definite 
 value. For example : 
 
 S = M 2 
 
 S = a 2 + 2at>+P. 
 
 This limitation to mathematics, nevertheless, does 
 not rob such a conclusion of its place in Logic. 
 For calculation, too, is a process of thought, — and 
 that not the most unimportant. On the other hand, 
 it is to be considered that we succeed in an abso- 
 lutely certain expansion of knowledge only in so 
 far as we can refer the objects of our reflection to 
 relations of magnitude, and can make calculations 
 with them. 
 
 § 54. But if such an application of calculation to 
 concepts of qualitatively different content is to take 
 place, and if we are to be able to conclude from the 
 existence and value of one mark to the existence 
 and value of another, then the connection of the 
 two and the dependence of one on the other, al- 
 though it does not admit of being placed upon a 
 strictly logical basis, must be presupposed as a mat- 
 ter of fact ; and nothing further can be done than by 
 calculating according to a general law which holds 
 good for such a condition of dependency, to assign 
 to every given value of the one mark the value of 
 
EXPRESSION Of A PROPORTION. 8 1 
 
 the other belonging to it. This is done in the form 
 of a proportion : 
 
 The proportion does not refer the content of the 
 one mark back to the qualitatively different con- 
 tent of the other mark, but allows both to be what 
 they are. It also makes, in general, no comparison 
 whatever between the absolute magnitudes of the 
 changes which the two correspondingly experience. 
 For these two, — since they are measured by quite 
 different standards, — are frequently not comparable. 
 Strictly speaking, it only compares the number of 
 the units of change which both marks undergo (the 
 change in each one as measured according to its 
 own standard), and from the given number for the 
 one mark determines the corresponding number for 
 the other. 
 
 It is self-evident that almost all application of 
 mathematics to real objects depends upon this man- 
 ner of drawing conclusions ; further, that propor- 
 tions are possible exactly only where the marks of 
 the real object are determinable quantitatively; but 
 that they run into inexact comparisons with refer- 
 ence to other objects of thought. 
 
 § 55. The above-mentioned expression for a pro- 
 portion contains one further inaccuracy. If E be 
 
82 OUTLINES OF LOGIC. 
 
 the expansion and T the temperature, then the afore- 
 said expression leads to the idea that there are two 
 marks which, absolutely and without reference to 
 the subject in which they occur, stand in an unalter- 
 able relation to each other. But how much the ex- 
 pansion increases for every additional degree of 
 temperature, depends on the nature of the body 
 heated, and is different in the case of different 
 bodies. Indeed, the necessity that one mark should 
 exercise any influence on the other depends simply 
 on the fact that they are marks of one and the same 
 subject. This is true for every pair of marks. And 
 we are on this account obliged to apprehend the 
 nature of the subject as a law such that from it 
 flow the proportions of all its single pairs of marks. 
 
 Mathematics, and that in Analytical Geometry, 
 has, indeed, approximately discovered a formal ex- 
 pression for this logical demand in the comparison, 
 for example, of the different curves, in which it 
 defines the entire nature of a curved line, its shape 
 and its direction, etc., by means of a proportion 
 between the corresponding increments of the ab- 
 scissas and ordinates. 
 
 Such comparison also depends, of course, on the 
 fact that all the properties which can belong to a 
 spatial figure — for example, its curvature and the 
 like — after all depend simply upon different mag- 
 
CONCEPTS AND IDEAS. 83 
 
 nitudes of the same species ; and no qualitatively 
 incomparable properties occur. An extension of 
 this logical form to the treatment of real objects — 
 for example, the attempt to discover a formula for 
 the nature of man similar to that which we possess 
 for the nature of the ellipse — is a problem of in- 
 finite complexity and quite impracticable with any 
 exactness. But approximately the attempt has al- 
 ways been made to solve it, since there has been 
 an effort to discover a so-called i constitutive con- 
 cept' for every object. 
 
 That is to say : — a merely ' distinguishing ' con- 
 cept, such as barely suffices to render its object dis- 
 tinct from other objects but does not positively and 
 exhaustively tell in what it consists, is held to be 
 different from a 'descriptive' concept, which as far as 
 possible specifies completely the content of its object, 
 but makes no essential distinction in order of rank 
 between marks that are more original and Maw- 
 giving' (as it were) and such as are derived and 
 dependent. Finally, there are distinguished those 
 ' constitutive ' or 'speculative ' concepts (or the ' Ideas ') 
 which are limited to designating a certain primitive 
 content (Ur-Inhalt) of the object, from which all its 
 individual marks and their combinations are then 
 derived as its necessary consequences. 
 
84 OUTLINES OF LOGIC. 
 
 C. The Systematic Forms. 
 
 § 56. For the discovery of such a ' constitutive 
 concept,' we remind ourselves — as we have already 
 done in the doctrine of the concept, — of the fact, 
 that the isolated consideration of an object in itself 
 does not teach us how to distinguish the essential 
 and i law-giving ' marks in it from the unessential 
 and dependent. That in it which gives it its law 
 we find in the ' universal' which is common to it with 
 others of its species. By this means we are con- 
 ducted to the path of Classiftcatio7i ; and we suppose 
 that we know the ' essence' of an object just as soon 
 as we are able to assign to it its position in a * Sys- 
 tem,' which begins with some most general concept, 
 subordinates to.this many general concepts as spe- 
 cies, — and finally, to the latter a variety of partic- 
 ular concepts. 
 
 § 57. It is not quite this problem, but a more 
 superficial one, which is fulfilled by the so-called 
 ' artificial classification ' ; such as either develops all 
 its species or single instances from one general con- 
 cept M, or one general case M, — or else subordi- 
 nates these particulars to M as though they were 
 already well recognized. The following operations 
 are distinguished : 
 
MODES OF CLASSIFICATION. 85 
 
 1) The Partition of M into its different marks, 
 a, b, c . . . 
 
 2) The Disjunction of each of these marks into 
 its species ; of a into % a 2 . . . , of b into & /3 2 . . . 
 etc. 
 
 3) The Combination of every single species of 
 each predicate with every species of every other 
 predicate ; hence %&Yi, ai/?iy 2 ...» ^iAyi • • • $ 
 
 «2/8i7i ■ • • 
 
 4) The Arrangement of the species of M thus 
 
 deduced, either according to well-known lexical prin- 
 ciples, or according to some other that answers the 
 ends of use. 
 
 5) A Correction by which the non-valid or impos- 
 sible species are again removed ; — species which, 
 accordingly, originated from the fact that we have 
 had regard only to the presence and not to the mode 
 of the combination of the marks a b c in M. It is 
 possible that some modifications of these marks, — for 
 instance, <z 3 /3 2 y 2 , — do not admit of being combined 
 in this way at all (example : M — triangle, a = angle, 
 b = side, a Y = right, a 2 = obtuse, angle, & = equal, 
 /3 2 = unequal, sides. Hence a 1 /3 1 is impossible). 
 
 This whole mode of procedure is seldom used for 
 deducing its species from a concept M ; for the most 
 part, the species are previously known, and are only 
 arranged under the M. Much oftener it is of service 
 
86 OUTLINES OF LOGIC. 
 
 in developing, from a general case M (some judg- 
 ment), the special instances conceivable ; and, here* 
 just that which excites our interest is to know, which 
 of them are possible or impossible, and what standard 
 — for instance — is of real use, what absurd. 
 
 § 58. Artificial classifications, strictly speaking, 
 systematize the way which we must take for a survey 
 of the content, rather than this content itself. The 
 single species stand side by side, excluding each 
 other, — without any knowledge of their nature origi- 
 nating from such knowledge of their arrangement. 
 This particular problem of classification, — to wit, 
 the determining of the ' essence ' of each species by 
 its position in the system, — accordingly leads to the 
 fresh attempt to arrange the species of a concept M 
 in the so-called ' natural classification/ in a single 
 series or in series of series, in such manner that 
 they form a steady advance from the most imperfect 
 to the most perfect. 
 
 That two species may more or less adequately cor- 
 respond to their general concept, the marks of which 
 they must both possess collectively, is possible on 
 account of the fact that the marks combine in very 
 different magnitudes, and the relations between them 
 may be thought of in a variety of special forms and 
 different degrees of strictness. For example ; from 
 
MEANING OF THE UNIVERSAL. 87 
 
 general logical pre-judgments, that species is held to 
 be perfect which has all the marks uniformly elab- 
 orated ; and that to be imperfect in which some 
 marks disappear and others occur in excess. But 
 such pre-judgment constantly needs correction or 
 supplementing from a knowledge of the real thing ; 
 and only in the particular case does it admit of being 
 determined from this knowledge of the thing, whether 
 the aforesaid uniformity, rather than a definite ine- 
 quality of the marks, agrees more adequately with 
 the meaning of the universal. 
 
 But in order to be able to speak of any such ' mean- 
 ing,' it is further presupposed that the general con- 
 cept M is itself also a member of a higher series, and 
 has its position in this series side by side with N, O, 
 P, ... as other species of a yet higher universal ; so 
 that, by virtue of this position, a definite problem is 
 proposed to it, according to which it may be esti- 
 mated, which of its own species is the more perfect, 
 since it best answers this problem. 
 
 And so the series of these presuppositions pro- 
 ceeds. For a place in a series that is still higher, 
 and, finally, in the comprehensive series of the entire 
 coherent system of the universe, must be discovered 
 for the series M N O P, — a place which it assumes, 
 and from which some light is thrown upon the direc- 
 tion of that forward movement from the lower to the 
 
88 OUTLINES OF LOGIC. 
 
 higher which goes on in itself. Without such a com- 
 plete demonstration as matter of fact for the basis 
 of these valuations, all natural classifications, which 
 are limited to a single domain of objects, events, or 
 even concepts, remain incapable of logical proof. 
 Since they only lay at the foundation some general 
 concept, the direction of whose development they 
 suppose to be known, they are productive of asser- 
 tions that, although suggestive and not untrue, are 
 not so exclusively true as would be demanded in such 
 a case as this, where that ' constitutive concept ' is 
 required for every single concept, from which its 
 entire mode of behavior shall be deducible. 
 
 § 59. Besides these avoidable deficiencies, the nat- 
 ural classification has yet one other that is universal 
 and unavoidable. The 'constitutive concept,' for 
 which we are in search, ought above all to explain to 
 us, how its content must behave, react, or alter, in 
 case certain conditions act upon it. Of all this, clas- 
 sification teaches us nothing whatever. It simply 
 furnishes an indication of the 'meaning' which the 
 content of the concept — thought of as unchangeable 
 — has in the series of species, in connection with 
 which it expresses the nature of a general concept. 
 But it does not explain how it can originate, exist, 
 maintain itself, alter, or perish. 
 
EXPLANATORY SCIENCE. 89 
 
 It may be left undecided, which of two logical 
 forms satisfies a higher necessity. Certain it is that 
 the aforesaid ' indication ' alone is not enough ; that 
 it absolutely cannot be substituted in the place of 
 1 explanation ' ; and, finally, that the latter belongs to 
 those problems of life which are practically most 
 urgent. 
 
 § 60. Explanatory science, which undertakes the 
 latter problem, is distinguished from classification, 
 by its form, as follows : 
 
 It does not, like the latter, take its point of depart- 
 ure from a single concept ; and it does not develop 
 its conceivable species as though it were self-evident 
 that all which such concept postulates for its complete 
 manifestation is, on this account alone, also possible 
 or already actual. But rather since, as concerns this 
 latter point, — and as concerns the manner in which 
 the content of the concept behaves under any given 
 conditions, — it is of course, not the concept alone, 
 but only some rule which holds good for it and like- 
 wise for such external condition that can decide ; 
 explanatory science begins with one or more judg- 
 ments which are propounded as general laws. They 
 are therefore of such a kind that both their subject 
 and their predicate (or their major premise and their 
 minor premise) are universal and comprise under 
 
90 OUTLINES OF LOGIC. 
 
 them many particular instances; but it is the con- 
 tent of the judgment which determines the rule, ac- 
 cording to which one of the instances of the minor 
 premise depends on one of the instances of the major 
 premise. 
 
 Now since nothing results from general laws in 
 themselves, the second necessary, element is a series 
 of facts, expressed either singly or collectively, which 
 themselves then take the place of general cases, and 
 by which in each single case that definite modification 
 of the content contained in the major premise or in 
 the subject of the general law is designated, in 
 reference to which a determination of its minor prem- 
 ise or its consequent is sought. 
 
 Now new knowledge originates from the subordi- 
 nation of the fact under the law, on account of the 
 fact needing to be known only partially, — perhaps 
 on one of its sides, — in order to be capable of sub- 
 sumption under the law ; but, in consequence of such 
 subsumption, some one of its sides, previously not 
 recognized, becomes defined and recognized. The 
 most essential problem of explanatory theory, never- 
 theless, does not consist in this simple sequence of 
 the conclusion, but in demonstrating the reciprocal 
 influence which very many conditions, that are inde- 
 pendent of each other, exercise upon each other in 
 case they act on one and the same subject ; and in 
 
EXPLANATORY SCIENCE. 91 
 
 setting forth the entire nature of the subject as the 
 collective resultant of the complete circle of its con- 
 ditions (comp. the ' Applied Logic '). 
 
 § 61. The spirit of explanatory theory is at vari- 
 ance with that of classifications. 
 
 The latter think not merely to explain the indi- 
 vidual by the general concept, as a species of which 
 they apprehend it, or by its position in the series of 
 other species ; but also to legitimate it. That is to 
 say, only by means of the fact that it is a species of 
 a general concept which has its well-known place in 
 the total order of the world, does a justifiable exist- 
 ence, as it were, belong to the individual. It would 
 be untrue or obscure, if we could not answer the 
 question, — What is it ? — by pointing out its gen- 
 eral notion. 
 
 Explanatory science surrenders the thought above- 
 mentioned. It attaches no value, for example, to the 
 statement whether any particular object lying before 
 us is a ' plant' or an ' animal/ It bids us inves- 
 tigate, out of what elements, in what proportion and 
 form of combination, the object consists; and what 
 forces, according to what laws, are active between 
 these elements, and between them and the outside 
 world. If we are certain of this, then we know the 
 whole object and its whole present and future mode 
 
92 OUTLINES OF LOGIC. 
 
 of behavior. But the answer to the question, whether 
 it is an 'animal ' or a 'plant/ adds nothing whatever 
 to such knowledge. Complete cognition consists 
 therefore in this; — in apprehending every object as 
 the final resultant which proceeds from the action 
 and reaction of different conditions or forces ; which 
 forces not only act collectively for laying the basis 
 of this individual object, but also everywhere else act 
 according to general laws, and only produced this 
 object because they found themselves in this rather 
 than in some other one of many forms of combination 
 possible to them. 
 
 § 62. It is evident that explanatory science does 
 not furnish perfect satisfaction to our desires for 
 knowledge. It treats every phenomenon, every event, 
 only as an unimportant example of general laws, 
 and as a result of many conditions co-operative in 
 fact, but which it was not necessary should co-operate 
 at all, or in precisely such a manner. The objects 
 are, accordingly, deprived, by the very manner of 
 considering them, as well of their inner unity as of 
 the necessary character of their existence. It can 
 only be said hypothetically that, in case such or such 
 conditions prevail, then the object must be so or 
 otherwise. But it remains undecided what conditions 
 actually do prevail. 
 
THE IDEAL OF COGNITION. 93 
 
 Against the foregoing mode of apprehending the 
 truth, the fundamental thought of classification cer- 
 tainly presents a just consideration. It is necessary 
 to suppose that not merely do general laws hold good 
 in the world, while the arrangement of the facts on 
 account of which a definite form of actuality flows 
 from the laws is, on the contrary, given over to 
 chance, uncontrolled by any principle ; but rather 
 that in the arrangement of the aforesaid facts also, 
 a principle (that is to say, an ' Idea ') is effective, and 
 that this principle fixes beforehand the whole ar- 
 rangement of the final result, the whole system of 
 the future phenomena which are to be actualized by 
 means of the aforesaid facts in conformity to the 
 laws. 
 
 The Ideal of Cognition would therefore consist in 
 finding for the ' Things ' such i constitutive concepts ' 
 or i Ideas ' as not only determine their meaning and 
 significance, but also show how this meaning itself 
 reaches its own actualization, by bringing together 
 the necessary conditions and forces. This problem 
 leads us wholly beyond the limits of Logic, and can 
 only be taken up again in so-called real Philosophy 
 (comp. the ' Encyclopaedia of Philosophy '). 
 
Second Principal Division, 
 
 APPLIED LOGIC. 
 
Second Principal Division. 
 
 APPLIED LOGIC, 
 
 CHAPTER I. 
 
 APPLICATION OF THE FORMS OF THE CONCEPT. 
 
 § 63. All communication of an inner state, whether 
 it be feeling or thought, is an attempt so to direct 
 the inner activities peculiar to another as that this 
 other must himself have a vital experience of the 
 very content which is to be communicated. No 
 content can ever be carried over ready-made, as it 
 were, from one mind to another. 
 
 Now, much admits of being communicated only by 
 physically transposing the other person into the 
 state in which he must experience the matter in 
 question. We turn him toward the light or strike 
 him, in order that he may know what ' brightness ' 
 or c suffering ' is. In other cases, as in art, we pro- 
 duce a mental mood, since we indirectly, by means 
 of a series of changing ideas, conduct the mind 
 through a series of individual feelings. 
 
98 OUTLINES OF LOGIC. 
 
 Thoughts, on the contrary, are assumed to be capa- 
 ble of a logical communication, which consists in 
 this, that an accurately defined series of combina- 
 tions and separations of individual ideas, supposed 
 to be well known, is prescribed to the other person ; 
 and then exactly the conception which is to be com- 
 municated remains with him as their logical result- 
 ant. There are two opposite methods of doing this : 
 the explanation of a concept by abstraction, and its 
 explanation by construction. 
 
 § 64. We explain by ' abstraction ' in case we ab- 
 stract from single examples of the concept to be 
 explained that are better known to us than is the 
 concept itself, everything which is so special as not 
 to belong to it ; so that it alone remains for us to 
 contemplate. Necessarily, however, this occurs only 
 in the case of all such simple concepts as, for ex- 
 ample, * Being,' ' Becoming,' ' Unity,' etc., whose 
 content does not consist of a conjunction of other 
 ideas. 
 
 The second way, that of 'construction,' which en- 
 deavors to build up the concept from its constituent 
 parts, must, at least, be attempted in the case of all 
 composite concepts. For ' abstraction ' makes the 
 content of the concept intuitable only as a whole ; 
 but teaches us nothing concerning its interior struc- 
 
CONSTRUCTION AND DEFINITION. 99 
 
 ture. ' Construction ' is perfectly practicable only in 
 affairs of mathematics ; because here the meaning of 
 the individual ideas which are to be combined, and 
 of the forms in which they are to be combined, can 
 be fixed unequivocally. In the case of other con- 
 cepts, which combine marks qualitatively different 
 in manifold relations, neither of these things is pos- 
 sible. And on this account, wherever it is possible, 
 the intuitive image is included in the explanation. 
 
 Now, Definition is that kind of construction which 
 endeavors to build a concept up by means of merely 
 logical operations. Fundamentally considered, it 
 uniformly regards the greatest part of the work as 
 already achieved since it itself refers to some 
 higher general concept which is known, and which 
 already contains that entire mode of combining all the 
 marks which is so difficult of elucidation. To this, 
 definition adds a specific mark, which suffices to dis- 
 tinguish the concept in question from other species 
 of the same universal ; but it entrusts to the imagi- 
 nation, along with this, the task of conceiving the 
 other corresponding specific marks, which here take 
 the place of what is universal in the general concept, 
 and in connection with it form the entire nature of 
 the thing to be defined. Nevertheless, where the 
 attempt is made to enumerate them all, the defini- 
 tion becomes a description which, on account of its 
 
IOO OUTLINES OF LOGIC. 
 
 imperfectibility, is not valid as a proper logical 
 form. 
 
 § 65. It is essential for definition that the con- 
 cept of genus applied by it should be the one next 
 higher — the ' Genus proximum.' 
 
 Definitions that are too wide, and adapted not 
 merely to what is to be defined, but also to some- 
 thing else which we wish to distinguish from it, arise 
 in case we choose instead of this genus proximum> 
 some far higher general notion as our point of depar- 
 ture ; for in that case the ' Nota specifica ' does not 
 always admit of being included in such a way that 
 nothing else, too, falls under this definition. This 
 mistake is frequently met with in the practical 
 domain, in that it is customary to use a very high 
 and pre-eminent general concept for better recom- 
 mending some proposition. 
 
 Too narrow definitions adduce marks that are not 
 necessary to what is to be defined, and therefore 
 exclude some of its kinds. They easily originate 
 from the limited nature of our circle of experience, 
 which accustoms us to only a few of the more nearly 
 allied species of the universal. 
 
 Definition perpetrates a ' Circle,' in case it assumes 
 in the explanation that which is to be explained, 
 although under another form. This mistake always 
 
TASK OF DEFINITION. IOI 
 
 originates, in case we aim to define constructively 
 simple concepts — like ' Being/ ' Becoming/ and 
 others similar — which are to be made clear only 
 by means of abstraction. 
 
 Finally, the custom of apprehending substantively 
 all things that are to be defined, even when they are 
 by nature verbal or adjective, although not itself a 
 mistake, is one inducement to mistakes. It is more 
 natural and conformable to our purposes to define 
 thus: "A body is elastic, in case it, etc/'; or, "An 
 organism is alive (or is diseased), in case it, etc.," than 
 to define thus: "Elasticity is" . . . or, "Life (disease) 
 is, etc." The latter modes of expression are indeed 
 often quite harmless ; but they are also often produc- 
 tive of the habit of treating states, properties, and 
 events as though they were substantial and inde- 
 pendent beings. 
 
 § 66. The task of definition, which is not merely 
 to specify the content of the concept, but also to 
 limit it with respect to other concepts, can often be 
 accomplished only by arbitrarily fixing the usage of 
 speech. 
 
 In the first place, there are certain concepts which 
 have no secure point of departure for their validity, 
 like the collective ones, i throng/ 'heap/ 'bald- 
 headed ' ; then there are others contradictory to 
 
102 OUTLINES OF LOGIC. 
 
 each other, between which a point of indifference 
 exists, such as 'cold' and ( warm,' and the like. 
 In all the former cases a limit is wanting, at which 
 the concept begins to be valid ; in the latter, the 
 limit is also wanting at which they pass over into 
 the contradictory concept. We do not know where 
 'warm' ceases and 'cold' begins; we only know in 
 what direction of the series the cold diminishes and 
 the warmth increases, and the reverse. 
 
 Another great multitude of concepts has originated 
 in the living formation of speech, in such manner 
 that, when comparing what is particular, we, at one 
 and the same time hold to several points of view that 
 are independent of each other. Accordingly, those 
 species which fall under the concept attained, agree- 
 ably to all these points of view at once, indubitably 
 belong there ; on the contrary, other species, although 
 they appear to fall under it as judged in one respect, 
 in other respects, on the other hand, appear to be 
 excluded from it. In such a case nothing remains 
 to be done but to fix, for the exact use of science, 
 the extent of the concept, and accordingly the sig- 
 nificance of its name, in a way that agrees with 
 our purpose but is somewhat arbitrary ; and not to 
 take too much pains simply to remain in accord 
 with the usage of speech. The concept of 'dis- 
 ease,' for example, comprehends, on the one hand, 
 
LIMITATION OF CONCEPTS. IO3 
 
 every deviation from the normal condition ; on the 
 other, it signifies a condition which has a variable 
 course; in the third place, it signifies such an one 
 as is fraught with danger. Just so the conception 
 of ' crime' has respect, simultaneously, to the bad 
 will, to the execution of the deed, to the magnitude 
 of the harm done, etc. 
 
 § 67. With reference to the value which we ascribe 
 to the fixed limitation of concepts as set over against 
 each other, our ordinary process of thought controls, 
 sometimes by means of a principle of logical pedantry, 
 and sometimes by means of one of logical frivolity. 
 
 The former holds every distinction in concepts 
 insurmountable (the well-known mode of speaking : 
 " that is something quite different ") ; the other 
 regards every distinction as fluid, and teaches how 
 to change every concept by intermediate stages into 
 any other that is in any degree allied to it. This 
 change is accomplished by altering at pleasure the 
 magnitude of individual marks, — many (such as are 
 necessary to the new general concept, but wanting 
 in the given concept) being considered as present 
 but of no value, and others (such as are present but 
 do not belong to the new general concept) being 
 regarded as such that they must be inserted in these 
 examples also, and that they are wont to occur only 
 in certain of its kinds without being of any value. 
 
104 OUTLINES OF LOGIC. 
 
 All these logical transformations have their correct 
 use in art, where they are the servants of wit ; and in 
 ordinary life they are most frequently employed in 
 excuses, in cases where the intent is to deceive con- 
 cerning the real worth of some action by means of 
 approximating its content, piecemeal, as it were, as 
 much as possible toward something innocent. Even 
 in science they are of the greatest value in the right 
 place. But proof is always to be demanded that in 
 the nature of the realities with whose concepts we 
 are dealing, there lies the possibility or the actual 
 custom and the effort, of making such transitions. 
 
 § 68. Of every object a variety of concepts is pos- 
 sible, since it can be subordinated to each of its own 
 marks and to every possible combination of them. 
 Among these concepts one may be preferred, — 
 namely, that constitutive concept, which we previously 
 sought for, but found only approximately and in a 
 few domains, such as in the concepts of species be- 
 longing to the creations of nature. 
 
 Nevertheless, the interests of our thinking seldom 
 require this concept ; and every process of investiga- 
 tion is accustomed only to consider certain single 
 sides of an object from which it deduces conse- 
 quences in accordance with general laws. Accord- 
 ingly, it is for the most part only a prolixity, and 
 
SOURCES OF SOPHISTRY. 105 
 
 often a source of inaccuracy as well, when we forci- 
 bly aim to have an exhaustive speculative conception 
 for an object which we are treating ; and then, when 
 after all we cannot for the most part attain it, pursue 
 an inaccurate approximation thereto. It is more use- 
 ful to take our point of departure from ' partial defi- 
 nition,' which unites into one general concept only 
 the properties important for the shifting investigation ; 
 and then, of course, modifies the consequences that 
 flow from the subordination of the object under this 
 general concept, by having regard to the other peculi- 
 arities of the object. Thus, for example, medicine has 
 to bring 'man' under the concept of a mechanism 
 consisting of physical elements ; while national econ- 
 omy has to bring him under the concept of capital to 
 be produced. But both must limit the consequences 
 drawn therefrom by the reflection, that this ' mechan- 
 ism' and this ' capital' possesses likewise reason and 
 will. 
 
 One of the principal sources of sophistry will be 
 such partial definitions, in cases where we draw con- 
 sequences from them but neglect to introduce into 
 them the modifications which are requisite on ac- 
 count of the rest of the nature of the object, although 
 this is not included in the definition. Little as this 
 mode of procedure is scientifically permissible, yet 
 its application is justified in poetry and rhetoric. 
 
CHAPTER II. 
 
 CONCERNING THE ADDUCING OF PROOF. 
 
 § 69. In a judgment, what interests us practically 
 is its truth. Now the simpler case is this, that a 
 proposition with a definite content is given and its 
 proof is required ; the more difficult case is this, that 
 the discovery of a proposition still unknown is de- 
 manded. 
 
 All adducing of proof — to which we now turn our 
 attention — must begin with the demonstration of 
 the validity in fact of the given proposition. That is 
 to say, if it is discovered by means of a test which is 
 made of it either by experience or by single examples, 
 that it has no such validity whatever, then all pains 
 taken with adducing proof is wasted. This rule is 
 not always sufficiently observed, and numberless pro- 
 lixities arise in science as well as in ordinary life from 
 the attempt to explain facts — that is, to demonstrate 
 them as necessary — which have no existence at all. 
 
 Only after the validity of the proposition is estab- 
 lished, does the adducing of proof for its justification 
 begin, — that is, the demonstration that it has a right 
 to be held valid as a consequence of other truths and 
 facts. 
 
NATURE OF AXIOMS. IO7 
 
 § 70. The fact needs no explanation, that all ad- 
 ducing of proof whatever presupposes a number of 
 propositions which are not, in their turn, in need of 
 proof, and which are also not capable of such proof. 
 
 These propositions are ordinarily comprehended 
 under the name of axioms. Fundamentally consid- 
 ered, they fall into two classes : the one comprehends 
 ' assertory judgments' which express certain actual 
 facts, and which, taken collectively, are derived from 
 experience and admit only of the above-mentioned 
 proof of their validity. The other comprehends the 
 just as undemonstrable ' principles of reason and con- 
 sequent,' in accordance with which alone, from any 
 fact or truth a conclusion can be drawn to some 
 other. The latter, strictly speaking, are hypothetical 
 general judgments, which do not tell what is, but 
 merely what must be if something else is. 
 
 A criterion for affirming that any proposition is an 
 axiom of the latter kind lies only in the unconditioned 
 nature of the evidence with which it announces itself 
 in consciousness as necessarily valid. Nevertheless, 
 since erroneous prejudgments also can, from a variety 
 of reasons, unlawfully attain in our mind such evi- 
 dence, it is necessary to test the truth of any propo- 
 sition in question, not merely on its own evidence 
 but also on that of the impossibility of its contradic- 
 tory opposite. If the latter is not demonstrable, then 
 
I08 OUTLINES OF LOGIC. 
 
 the axiomatic and unconditional validity of the propo- 
 sition in question does not stand beyond doubt. 
 
 § 71. Proofs are distinguished, in accordance with 
 their proximate aim, as direct, which demonstrate 
 the given proposition immediately, and indirect ('apa- 
 gogic '), which primarily demonstrate the impossibil- 
 ity of its opposite. Only the first kind are able to 
 specify, in explanatory fashion, the grounds in right 
 for the truth of the proposition ; the second always 
 prove only its validity in fact. In convincing force, 
 however, the first is not always unqualifiedly to be 
 ranked as superior to the second. 
 
 The direct, as well as the apagogic, proof is uni- 
 formly either * a principio ad principiatum,' from rea- 
 sons to consequents (progressive, forward-moving) ; 
 or else it proceeds 'a principiato ad principium,' from 
 consequents to reasons (regressive, backward-moving). 
 
 The different forms of proof that spring out of the 
 foregoing fact have a very different value ; — partly 
 in general, and partly different according to the do- 
 mains of the content to which they are applied. 
 
 § 72. The ' direct ' proof can be progressively (and 
 therefore in such a manner that the process of think- 
 ing takes the same course, from reasons to conse- 
 quents, as the nature of the thing) carried on in two 
 forms. 
 
THE DIRECT PROOFS. IO9 
 
 1) The proposition in question is considered as the 
 terminal point of a conclusion ; we therefore take our 
 start from truths that are more general and already 
 established, and from them, by subordinating other 
 general or special sub-propositions, deduce the re- 
 quired thesis as a necessary conclusion. This form 
 is of all most to be preferred ; because it contains, 
 or may contain, the complete exposition of the thesis. 
 
 2) The thesis may be regarded as a point of start- 
 ing, and since it is considered valid, its consequences 
 developed. If these are at variance neither with 
 general truths nor with established facts, then the 
 validity of the thesis is — not indeed certain, but 
 probable. For since all the consequences can never 
 be developed, it remains possible that, in case we 
 were to proceed yet further, some contradiction 
 would still be revealed. As proof of the truth, ac- 
 cordingly, this form is not perfectly stringent. On 
 the other hand, it occurs in practical life, for recom- 
 mending certain proposals, as a proof of their con- 
 formity to an end. 
 
 Regressively also, ascending from consequents to 
 reasons, the direct proof may run its course in two 
 forms. That is to say — 
 
 1) The thesis in question serves as a point of starting, 
 and is, therefore, here regarded as a consequent from 
 which we ascend to its reasons. Now if the reasons 
 
IIO OUTLINES OF LOGIC. 
 
 which must hold good, in case the thesis is to hold 
 good, are in thorough accord with general truths, 
 then primarily only the conceivability or possibility 
 of the thesis is demonstrated thereby ; and only in 
 domains where (as in mathematics) all that is con- 
 ceivable has eo ipso the truth which appears in the 
 particular case, does such proof include the truth of 
 the thesis. In relation to everything actual, acces- 
 sory proof would be necessary, to the effect that the 
 causes are in existence which must actualize the 
 thesis, as yet in itself only possible. In practical 
 life, on the other hand, this form of proof is perfectly 
 sufficient — for example — to found or defend a legit- 
 imate claim. Finally — 
 
 2) The thesis can in turn be regarded as the ter- 
 minal point ; and therefore in this case as a reason. 
 We then take our start from certain other proposi- 
 tions or facts that are known to be valid, and show 
 that the sole ground of their possibility is to be found 
 in the validity of the thesis, which thereby is made 
 necessary. This proof is therefore conclusive, but 
 is difficult to adduce; and it often stands in need 
 of accessory proofs, in order to show that the thesis 
 is not merely an adequate reason for the aforesaid 
 facts, but is the exclusively possible and sole reason 
 for them. 
 
THE INDIRECT PROOFS. Ill 
 
 § 73. i Indirect ' proof cannot, strictly speaking, 
 immediately demonstrate that the opposite of the 
 given thesis — that is, the antithesis — is not valid 
 in fact ; or, in more general terms, the refutation of 
 a proposition can never be the immediate conclusion 
 of a proof. For never do anything but merely posi- 
 tive — that is to say — valid consequences (such as, for 
 the rest, can consist in affirmative and negative judg- 
 ments) follow from all such principles as could be 
 chosen for grounds of proof ; and only on account 
 of the fact that these consequences exclude the an- 
 tithesis, is the latter explained as not valid. 
 
 The first progressive form, which sets out from 
 general truths and shows the antithesis to be im- 
 possible, accordingly cannot occur. What appears 
 as this, is invariably a direct progressive proof, which 
 exhibits the necessity of some proposition by which 
 the antithesis is excluded. 
 
 On the contrary, the second progressive form, that 
 proceeds from the antithesis, which is assumed as 
 true, to its consequences, and the first regressive ', that 
 proceeds from the same to its presuppositions, are 
 both of great value as apagogic proofs (' Deductiones 
 ad absurdum '). They demonstrate the invalid nature 
 of the assumed proposition by showing that, either 
 the consequences which would flow from it, or the 
 reasons which must validate it if it is to be valid, are 
 
112 OUTLINES OF LOGIC. 
 
 not compatible with general truths or existing facts. 
 Now although they do not contain the grounds for 
 the validity of the thesis whose antithesis they dem- 
 onstrate to be impossible, still they are often to be 
 preferred to the tedious and involved direct proofs, 
 on account of the pictorial way in which they show 
 the absurdity of every proposition contradictory of 
 the thesis. 
 
 The second regressive form would draw a conclu- 
 sion from facts to the impossibility of explaining 
 them by the antithesis as their ground ; and this 
 obviously is practicable only in case the necessary 
 properties of such a ground are first positively de- 
 fined, and it is then shown that the antithesis is 
 thereby excluded. 
 
 § 74. Besides the distinctions already alluded to, 
 a further one is made which has to do with whether 
 a universal proposition (for example, one concerning 
 the triangle) is directly proved in its universality, or 
 in such manner that the demonstration first applies to 
 all individual instances (first for the right-angled tri- 
 angle, then for the acute-angled, and finally for the 
 obtuse-angled) and then the proofs are summarized. 
 Such collective proof requires that we should be in 
 a condition to enumerate all possible individual in- 
 stances which the general case can contain ; and 
 
PROOF BY EXCLUSION. II3 
 
 even when this is done, it always has the disadvan- 
 tage of simply establishing the validity in fact of the 
 proposition demonstrated for all examples of the 
 universal; but it neither proves nor explains how this 
 validity follows from the proper nature of the univer- 
 sal. Although it is often quite indispensable, since 
 the nature of a concept or of some general case is 
 often not so widely known, that we should be able 
 to recognize the grounds which it contains for the 
 universal validity of some assertion concerning it. 
 
 Related to the foregoing is the proof by exclusion. 
 This form, likewise, in case of a complete disjunc- 
 tion, enumerates all the conceivable individual in- 
 stances of a general case, and proves of all the rest, 
 except one, that they are impossible ; so that in case 
 it is established at all that some one species of the 
 universal must occur, then this one left remaining is 
 necessarily valid. 
 
 Finally, the limitation of a given value between 
 two limits — for example, the proof that a is neither 
 greater nor less than b, and accordingly equals b 
 — belongs in this connection. 
 
 § 75. In all the forms of proof alluded to, we 
 have assumed that the conclusion follows as to the 
 whole, according to the first figure, — that is, by sub- 
 sumption of one proposition under others. We 
 
114 OUTLINES OF LOGIC. 
 
 speak of the proofs by analogy and induction fur- 
 ther on. 
 
 This being presupposed, the question may arise, 
 how proofs are discovered, — by which we mean, 
 the superior propositions on which the validity of 
 the proposition in question depends ; as well as 
 how the inferior propositions or auxiliary construc- 
 tions are divined by whose mediation the latter 
 flow from the former. 
 
 On the whole, Logic cannot teach how to 'dis- 
 cover ' such proof ; but it can only admonish us 
 that in every science stereotyped methods of proof 
 for the single groups of related problems are de- 
 veloped, which put every one, who understands how 
 to bring a problem under its own group, upon the 
 right way. Besides this only one indication is 
 possible, — namely, that the ground for the truth of 
 a proposition, which expresses not merely a fact, but 
 some mode of procedure that is dependent on other 
 truths, must invariably be contained in the content 
 of the proposition itself, when the latter is perfectly 
 thought out. Synthetic judgments cannot be given 
 in such a way as to add to the subject S a predicate 
 P, which is neither contained, nor has its ground, 
 in the complete concept of S. Such a predicate 
 would be false. All correct judgments are as re- 
 spects their content, analytic ; or rather they are 
 
SERIES OF PROPOSITIONS. II5 
 
 'identical' and merely appear synthetic in form, 
 since one and the same content can be designated 
 in both subject and predicate, from points of view 
 that are very different and arbitrarily chosen. Ac- 
 cordingly, in order to find the proof on which the 
 correctness of a proposition is founded, one must 
 analyze subject and predicate and the combination 
 between the two, and add all the latent accessory 
 thoughts which are meant thereby ; in this way one 
 will see in this complete content of the proposition, 
 for the most part, its own proof of itself. 
 
 It frequently proves of advantage to consider as 
 not yet valid the subject of the thesis, or the prem- 
 ise to which this is attached as a consequent ; and 
 to let it originate from another subject or another 
 premise whose predicate or conclusion has already 
 been established. In this way it is more easily 
 shown how, by the changes of this other subject 
 into the one in question, the predicate in question 
 also originates from this other. If the different 
 instances of a universal proposition constitute a 
 series, — as often happens in mathematics, — this 
 proof takes the form of a f proof from n to (n + 1) ' ; 
 in such manner that the given thesis is first verified 
 for some special ' case or value of n, and then it is 
 shown that, in the formation of each next case 
 (n + 1) from the case n, the conditions, by virtue 
 
Il6 OUTLINES OF LOGIC. 
 
 of which the proposition of n holds good either are 
 maintained unchanged or are reproduced, or else 
 equivalent conditions take their place. 
 
 § 76. The Fallacies in proof, which logic, alas! 
 can only mention and not teach us to shun, are the 
 following : 
 
 'Petitio principii/ or 'the circle in proof' (Diallele) 
 is committed, in case what is only some other expres- 
 sion for it, or some consequence of the conclusion 
 which is first to be demonstrated, is employed as an 
 argument. 
 
 ' Fallacia falsi medii ' (Quaternio terminorum) con- 
 sists in the fallacy of taking, in one of the conclusions 
 that constitute the proof, the medius terminus in 
 both premises, in a different signification. The 
 inducement to this is not far to seek in the case 
 of abstract conceptions, whose signification has 
 equivocal elements ; and also in the case of such 
 empirical concepts (to which allusion has already 
 been made) as are likewise formed by abstraction 
 in accordance with different points of view. 
 
 In this connection the ' Fallacia de dicto simplici- 
 ter ad dictum secundum quid ' may be referred to ; 
 that is to say, the fallacy of applying a proposition, 
 which in itself holds true universally and absolutely, 
 to definite circumstances, without limiting and modi- 
 
KINDS OF FALLACY. 117 
 
 fying it in such a manner as these circumstances 
 require. This fallacy is in ordinary life the princi- 
 ple of Doctrinairism and unpractical Idealism, — of 
 i riding principles horseback/ Conversely, the 'Fal- 
 lacia de dicto secundum quid ad dictum simpliciter' 
 extends a principle, valid in a single instance, to 
 all instances, — even to such as are lacking in those 
 conditions that give grounds to or recommend its 
 validity. In practical life this is the principle of 
 pedantry and 'philistrosity/ 
 
 'Nimium probare,' and therefore i nihil probare/ 
 is the fallacy of demonstrating the validity of a 
 proposition, not merely for the subjects and cases 
 for which it holds good, but also for others for which 
 it does not in fact hold good, or should not hold 
 good. The fallacy comes from the choice of a false 
 argument, or from an otherwise correct argument 
 not being limited to those of its sub-species which 
 alone perfectly contain the ground for the validity 
 of the proposition. ' Parum probare ' is in itself only 
 a fallacy of method, because that which is proved 
 is correct. It becomes a logical fallacy only when 
 the validity of the proposition which is demonstrated 
 for a number of cases, is at the same time appre- 
 hended as a negation of its validity in the other 
 cases, in which it in fact also holds good. 
 
 'Hysteron-proteron ' (varepov irporepov), in dis- 
 
Il8 OUTLINES OF LOGIC. 
 
 tin ct ion from petitio principii, is the awkwardness 
 in method which from two propositions A and B, 
 that may be in turn deduced from each other, makes 
 that one the ground of the proof which would be 
 more fitly exhibited as the result of the other. 
 
 Finally, ' Heterozetesis ' (erepov Zqrrio-is), or ' Ig- 
 noratio elenchi,' is the complete aberration of the 
 proof, — arriving at a conclusion which was not to 
 be demonstrated at all. 
 
 § 77. Finally, we distinguish ' Paralogisms ' (' erro- 
 neous conclusions ') as undesigned fallacies in proof, 
 from ' Sophisms ' (' fraudulent conclusions'), — that 
 is to say, thoughts designedly so combined that from 
 them, in a way formally correct, either something 
 wholly absurd and false originates, or contradictory 
 assertions flow from them with equal correctness. 
 The first case, again, always depends upon designedly 
 committing some one of the customary fallacies in 
 argument. The others, the so-called 'Dilemmas' 
 that were specially celebrated under that title in 
 antiquity (the 'liar/ the i crocodile,' etc., — comp. 
 § 46 at the end) originate in this way ; the content 
 of a judgment A, which taken logically by itself 
 must be either correct or incorrect (without any 
 regard to the circumstances under which it is ut- 
 
KINDS OF FALLACY. 119 
 
 tered, or to facts not as yet established) is never- 
 theless apprehended as though it were conditioned 
 in its meaning or in its validity, by just those cir- 
 cumstances ('the liar') or by these not yet estab- 
 lished facts ('the crocodile'). 
 
CHAPTER III. 
 
 THE PROCESS OF THOUGHT IN DISCOVERY. 
 
 § 78. The second problem, to which allusion was 
 previously made (§ 69),- — namely, to discover some 
 general proposition — divides again into several, the 
 first of which is the discovery of a universal judg- 
 ment, that comprises a number of particular facts. 
 This may take place either in such manner that the 
 same content which a single fact expresses is demon- 
 strated as valid in general for all instances of its re- 
 currence ; or in such manner that a more general 
 proposition is sought for, which embraces within 
 itself as classes all the given facts. 
 
 § 79. The first case only furnishes us the occa- 
 sion to observe that the assertions — " Experience 
 teaches nothing universal" ; and "What is correct 
 in one case need not be so in another/' — are not 
 rightly made. Quite the contrary, it follows from 
 the law of Identity, that a truth which is valid once 
 cannot fail to be valid a second time ; accordingly, 
 that every individual experience is once for all valid, 
 — that is to say, the same predicate is again valid 
 at all times for all cases of the recurrence of the 
 same subject. 
 
THE IMPERFECT INDUCTION. 121 
 
 The difficult thing is simply to determine in praxi 
 whether a second instance does actually repeat pre- 
 cisely the subject observed in the first case. For this 
 the probabilities are different in different domains of 
 research. For example, it is enough for the chem- 
 ist, if he once knows that he has some element be- 
 fore him in a pure state, to observe its reaction 
 toward some other element a single time, in order 
 to establish it forever. The zoologist, on the con- 
 trary, will hold some peculiarity of a new animal, 
 only one example of which has been discovered, to 
 be 'normal/ that is, to be valid in general (since 
 disease and malformation are possible in such a 
 case), only when the analogies of other classes of 
 animals justify him in this assumption. 
 
 § 80. The second problem would be to deduce a 
 general judgment of the form — "All S are M" — 
 from individual perceptions, which (as previously 
 alluded to) bear the form : P is M, Q is M, R is M, 
 etc. This is the simple conclusion by imperfect In- 
 duction, to which allusion was previously made. 
 
 It was shown in the Pure Logic that this induc- 
 tive conclusion serves for the widening of our knowl- 
 edge only in case it is imperfect, — that is to say, 
 it follows, without strict conclusive force, from the 
 fact that some kinds of S have the predicate M, 
 
122 OUTLINES OF LOGIC. 
 
 that all kinds of S possess it. The precautionary 
 rules, which would be required to make the con- 
 clusion at least as probable as possible, are simply 
 as follows. 
 
 With the rising number of cases in which M oc- 
 curs among the species of S, the probability that it 
 belongs to all S increases of itself. Nevertheless, 
 every circle of human experience is limited, and we 
 can at least never be sure from that which we learn 
 to know only by experience, whether we are not 
 merely getting a view of certain particular species, 
 nearly allied, which do indeed all possess the predi- 
 cate M, and yet do not possess it by virtue of their 
 general concept, but on account of their other con- 
 cordant special marks. For this reason it is neces- 
 sary to show that the M, which we wish to ascribe 
 as universal to the concept S, occurs not merely 
 in the case of very manifold and very diverse species 
 of the S, but also occurs specifically in the case of 
 such pairs of them as are related to each other, 
 with reference to some mark which can be depended 
 on for having some influence on the establishment 
 of M, in the most contrary fashion possible. It can 
 then be concluded that the reason for M, or for the 
 subject to which M belongs, can only be some ge- 
 neric concept like S, which is common to all the 
 species. 
 
MORE COMPLEX PROBLEMS. 123 
 
 § 81. This same problem is much more important 
 for us in another form. That is to say, it is only 
 rarely of much use to us to show that a P is united 
 with a general generic concept S, and belongs to all 
 species of S. As a rule, we desire still further to 
 know on what ground P belongs to S. This, ex- 
 pressed in general form, leads to the problem of 
 searching for the conditions on which the occur- 
 rence of an event depends in all the otherwise di- 
 verse instances of its repetition. 
 
 In experience we almost uniformly meet with a 
 complex of diverse facts, a + J> + c + • • • = U, with 
 which another just as composite complex, a + ft + 7 
 + • • • = W, stands in combination. The problem is 
 to ascertain whether in general U is the condition of 
 W, and what particular part of U forms the condi- 
 tion of what particular part of W. 
 
 The means for such investigation are, either the 
 facts which observation yields spontaneously, or like- 
 wise such others as we add by experimentation. 
 
 Observation, for the most part, shows us effects 
 which depend on a large number of conditions at 
 the same time ; many of which, moreover, are wholly 
 withdrawn from observation. The main end of ex- 
 periment does not consist simply in multiplying facts, 
 but in permitting only a fixed and accurately known 
 number of conditions to be in every trial. Experi- 
 
124 OUTLINES OF LOGIC. 
 
 ment further consists in separating these conditions, 
 whenever it is possible, so that in every trial only one 
 is active, and yields an unmixed result, or, at least, so 
 that in every trial only a small number of conditions 
 co-operate, and, accordingly, the part of each single 
 condition in the collective result admits of being 
 determined by comparison of the different trials, in 
 the way of elimination. Finally (a matter concerning 
 which we shall speak later), experiment especially 
 seeks to secure the measureableness of the magni- 
 tudes of the conditions and of the results. 
 
 § 82. The following general cases serve simply as 
 examples of investigation : 
 
 i) If "W (the effect) uniformly follows upon U (the 
 cause), then it is possible that the reason for W lies 
 in U ; and it remains a matter for inquiry whether 
 the whole of U furnishes the reason for W, and 
 whether some other condition besides U, that is 
 uniformly connected with it but unobserved, is not 
 necessary in addition. But it is just as possible 
 that U and "W are ^-effects of a common cause, Z ; 
 and also possible, finally, that U and W occur to- 
 gether by a merely fictitious coincidence, without 
 any causal connection whatever. 
 
 2) After U has occurred, W is sometimes wanting. 
 Then U either is not the cause of W, or U and W 
 
CAUSES AND EFFECTS. 1 25 
 
 are £<?-effects of (Z ± Y) ; so that W occurs if Y is 
 positive, and not if it is negative ; or U is certainly 
 the adequate, and perhaps the only reason which can 
 produce W ; but there is in the cases that occur 
 some hindrance which prevents U from producing 
 its uniform result. 
 
 3) Suppose that W occurs before, or without, IT. 
 Then there is either no connection between the two, 
 or the two are again co-effects of (Z ± Y) ; or, finally, 
 U is not the only, although the quite sufficient, 
 reason for W, but there are other equivalent rea- 
 sons. 
 
 4) Suppose that U falls out or is experimentally 
 removed, and then W does not follow. In this case 
 it is either a mere coincidence, without real connec- 
 tion (which is, however, extremely improbable, and 
 is only to be assumed in observation, and not in 
 experimental treatment) ; or U is, or contains, the 
 condition of W (which is most probable) ; or, finally, 
 U and W are ^-effects of Z, and the same interfer- 
 ence which hindered Z from producing U, hinders 
 also the production of W. 
 
 5) If U vanishes or is removed (experimentally), 
 but W remains, then there is either no nexus be- 
 tween them, or they are again ^-effects of Z ; but 
 this time in such manner that the interference with 
 Z, which hinders U, permits W to exist ; or else U is 
 
126 OUTLINES OF LOGIC. 
 
 the cause of the origin of W, although not the cause 
 of its continuance. 
 
 The proposition " Cessante causa cessat effectus " 
 is false in this general form (indeed, if it were not 
 so, all our labor and action in the world would be 
 illusory). In general only those effects vanish with 
 the vanishing of the cause, which the cause would 
 further have had in case it had not vanished. Effects 
 already produced, on the contrary, continue after the 
 cessation of the cause, in so far as they consist in 
 states of things which are not in contradiction with 
 the proper nature of things and with the external 
 conditions in which they stand. Only in the opposite 
 case would they need a maintaining cause ; and this 
 is then, besides, not always the same as the produ- 
 cing cause. 
 
 6) Further, in case the part a disappears from U = 
 (a + h + c) and W is not altered, then one condition 
 of the continuance of W does not lie in a, although 
 perhaps the condition of its origin may. Conse- 
 quently, we have to investigate, where it is possible, 
 whether 1> + c alone produces W ; in which case a 
 would be a superfluous part of XJ. 
 
 On the other hand, if the whole of W disappears 
 with the vanishing of a, then a alone may be the 
 sufficing condition of W. Such condition, however, 
 may just as well lie in the entire sum (a + b + c), 
 
CAUSES AND EFFECTS. \2J 
 
 so that W always vanishes whatever part of U is 
 removed, but does not depend on any one of them 
 alone. This is often overlooked ; — for example, 
 when some one part of the brain, a, after the de- 
 struction of which a function W ceases, is physio- 
 logically considered as the sole organ of W. 
 
 7) If two different complexes of causes — U = (a 
 + b + c) and V = (m + n + c) — produce the same 
 effect W, then W will for the most part undoubtedly 
 depend on the c common to both. Still it is possible 
 that c is quite without any direct significance ; and 
 that, on the contrary, (a + b) and (m + n) furnish two 
 equivalent pairs of causes, in which one and the same 
 condition for W is only differently distributed to the 
 single elements. 
 
 8) Finally : if again (compare what is said under 6) 
 U = (a + b + c), and W also vanishes with the re- 
 moval of a, then a may be the sole cause of W ; but 
 it is also possible that such cause lies only in c, but 
 b is a hindrance to the efficiency of c, which was, on 
 its side, balanced by a. 
 
 The foregoing possibilities might be indefinitely 
 multiplied. 
 
 § 83. Now tne ascertainment of the fact that any 
 particular a is the condition of some a or other, does 
 not give us satisfying knowledge, as long as we are 
 
128 OUTLINES OF LOGIC. 
 
 unable to subsume under such a proposition certain 
 others, not wholly like it but only of similar kind ; — 
 that is to say, as long as we do not know according 
 to what general law a is changed by a fixed difference, 
 in case a is also changed by another fixed difference. 
 Now since determinations of number merely, and 
 not marks of quality, are deducible from each other 
 in thought according to general laws, the problem is 
 as follows ; — to seek for the law according to which 
 the values of the magnitude of the results depend 
 upon the magnitudes of the conditions belonging to 
 them. This is a problem which must be solved for 
 the most part experimentally. 
 
 § 84. If it is found that, when the magnitude of the 
 condition remains uniformly the same, or increases 
 uniformly or diminishes uniformly, the results de- 
 pendent on it do not alter their values in a perfectly 
 parallel way ; but — for example — when the value of 
 a increases, that of a for some time increases, and 
 then while a keeps on always increasing, assumes a 
 diminishing value : then this is a proof that a alone 
 does not contain the complete reason of a, but that 
 still other conditions co-operate ; and that these either 
 consist in accessory conditions which are independ- 
 ent of a, or in alterations which the object affected 
 by a experiences through the earlier influence of a, 
 
USE OF HYPOTHESES. 1 29 
 
 and which oppose resistance, sometimes uniformly 
 and sometimes periodically, to the further influence 
 of a. 
 
 In all such cases as the foregoing, there is a de- 
 mand for a further preliminary investigation. For 
 although we can often discover very simple general 
 laws for the course of such a composite effect, — as, 
 for example, the laws of Kepler show ; yet after all 
 we can only grasp perfectly the whole of it, in case 
 it can be demonstrated as the resultant of a combina- 
 tion of single effects, whose laws are such that a 
 constant increase in the result belonging to it always 
 corresponds to the constant increase of each single 
 condition. The place of such a preliminary investi- 
 gation is in part supplied by a further employment 
 of the previous artifices, and in part by hypotheses. 
 
 § 85. If we have discovered experimentally a series 
 of corresponding values for the conditions and the 
 results, then the intricate nature of the thing some- 
 times compels us (for example, in many problems of 
 statistics), inasmuch as many conditions that are 
 changing independently of each other always co- 
 operate, to confine ourselves to the collection in tab- 
 ular form of the appropriate material. 
 
 On the contrary, where it is possible to make the 
 transition to a general law which expresses the de- 
 
130 OUTLINES OF LOGIC. 
 
 pendence of every member in the series of results 
 upon the corresponding member in the series of con- 
 ditions, this transition always remains a kind of logi- 
 cal saltus. For no measuring, since it all invariably 
 depends upon nothing but the sharpness of our per- 
 ception by the senses, gives us absolutely accurate 
 numbers. Accordingly, if the series of values dis- 
 covered for the results accords accurately with that 
 calculated by a general formula from the values of 
 the conditions, it is only extremely probable but not 
 certain that such formula is the correct law. If it 
 does not agree with them, but must be corrected in 
 order to agree, then it is possible that another cor- 
 rection would make it explicable with equal facility 
 by another law. Nevertheless, if perfect certainty is 
 wanting, still a probability, which is to be estimated 
 as quite equal to it, may be attained for the correct- 
 ness of a law. This is principally done by measuring 
 the discovered series of values according to different 
 standards of measurement, and arranging the experi- 
 ments so that the dependence of the results on the 
 conditions is subject to observation from different 
 points of view. If the same formula fits in all such 
 altered expressions of the thing, then it will be the 
 correct one. 
 
 § 86. On this account, the discovery of a general 
 law is frequently called an ' Hypothesis.' 
 
CRITERION OF SIMPLICITY. I3I 
 
 We employ this word in a more limited meaning. 
 Hypotheses are conjectures by which we endeavor 
 to divine something real that is not given in percep- 
 tion, but of which we make the supposition that it 
 must be existent in actuality, in order that what is 
 given in perception may be possible ; — that is, may 
 be comprehensible in the light of those laws of the 
 connection of ' Things' which are recognized as 
 supreme. 
 
 Among the rules, by following which we endeavor 
 to give the greatest possible certainty to hypotheses, 
 it is incorrect to lay down the general one, that sim- 
 plicity is a criterion of truth. We must rather dis- 
 tinguish the nature of the cases. If we have to do 
 with establishing by hypothesis a relation which is 
 very general and which unites almost all that is 
 actual, then ' simplicity ' is most probably the correct 
 thing. On the other hand, to explain a fact which 
 manifestly depends on very many co-operating con- 
 ditions, a very simple hypothesis about it only awak- 
 ens the suspicion that all the difficulties of the matter 
 are not observed, and therefore not explained. 
 
 As for the rest, no rules can be given which assist 
 the intelligent process of discovery in the formation 
 of hypotheses, but only certain ones which limit it. 
 
 It is of use in the first place, to make it perfectly 
 obvious, what are the demands which some matter of 
 
132 OUTLINES OF LOGIC. 
 
 reality, when hypothetically assumed, must necessarily 
 fulfil, in order to satisfy the phenomenon that is to be 
 explained. This admits of being established with 
 a perfect cogency by concluding backwards from the 
 phenomenon itself. From these abstract but unques- 
 tionable parts of the hypothesis, a further special elab- 
 oration of it is to be distinguished, which endeavors 
 to divine the concrete matter of fact in which the 
 aforesaid demands are found to be actually fulfilled. 
 Very often several such matters of fact are possible. 
 The hypothesis should not blindly choose the one 
 which first falls in our way ; but it must previously 
 survey the entire domain of related phenomena, in 
 order to ascertain what kind of matter of fact is wont 
 to occur therein. 
 
 Now if a hypothesis has been framed with this ref- 
 erence to a rather large number of related phenom- 
 ena, then it very often happens that the progress of 
 experience contains new facts, for whose explanation 
 the previous hypothesis does not suffice. It must, 
 accordingly, be altered by new additions. This • build- 
 ing of hypothesis on hypothesis ' is not to be avoided 
 in the course of our scientific labors ; and, on this 
 account, it is incorrect to forbid it. Only it is cer- 
 tain that the investigation is not to be regarded as 
 ended until these hypotheses, composed piecemeal, 
 at last admit of being gathered together again into 
 
FICTIONS IN ARGUMENT. 1 33 
 
 one simple assumption corresponding to the sim- 
 plicity of the thing itself. 
 
 Finally, the rule — " not to frame any hypothesis 
 whose content lies beyond the borders of a possible 
 counter-proof" — is indeed an excellent one; but in 
 many domains of investigation, exactly where we are 
 most in need of hypotheses, it is not practicable. 
 
 § 87. Hypotheses are conjectures by means of 
 which we suppose that we are divining an actual 
 matter of fact. Fictions are assumptions which we 
 make with the consciousness of their incorrectness. 
 
 We are compelled to resort to fictions, when — for 
 example, in practical life — judgment must be passed 
 upon a case which does not exactly fall under any 
 single known rule ; we are then compelled to indicate 
 it in such a way that it can be subsumed under that 
 rule which is recognized as over some content most 
 nearly related to its own. 
 
 We are further compelled to adopt fictions, when 
 in science there are no modes of experience which 
 admit of a direct application to the data of some prob- 
 lem before us. In this way, for example, curved lines 
 are regarded as interrupted straight lines (which they 
 never are), and reckoned accordingly. 
 
 In both cases it is, of course, necessary to correct 
 the consequences which flow from the general ground 
 
134 OUTLINES OF LOGIC. 
 
 of judgment assumed by the fiction, with reference 
 to the fact, that the case in hand is not exactly sub- 
 ordinated thereto. And on this supposition, fictions 
 lead — for example, in mathematics — back again to 
 exact results and not merely to approximations. 
 
 Finally, fictions are very frequently, besides, em- 
 ployed as means of illustration, with the purpose of 
 bringing intricate relations, that obviously, as frequent 
 perception shows, belong to some case a, to apply to 
 a case h which possesses relations that, although not 
 wholly the same, are essentially similar. 
 
 § 88. Fictions of themselves lead to the procedure 
 called ' Analogy / which, although it does not propose 
 to extend a proposition to a subject that is certainly 
 not to be subsumed under it, still does transfer a 
 proposition from one subject to another, on account 
 of the similarity of the two. 
 
 This procedure depends upon the perfectly cogent 
 principle, that what is like must under like conditions 
 assume like predicates, and under unlike conditions 
 unlike predicates ; just as what is unlike must under 
 like conditions assume unlike predicates. 
 
 But the first half of this proposition avails nothing 
 for the extension of our knowledge; and the other 
 only slightly, because it yields no positive result, but 
 only teaches us that the predicates are not like. 
 
REASONING BY ANALOGY. 1 35 
 
 Accordingly, such principles, strictly speaking, are 
 productive only in mathematics, where it is possi- 
 ble to determine the degree of the unlikeness of the 
 subjects and that of the conditions, and consequently 
 also to reduce the unlikeness of the predicates to a 
 definite measure, and to give them a positive content. 
 
 Outside of mathematics, the principle that what 
 is similar assumes similar predicates under like con- 
 ditions, although always correct in abstractor is still 
 a very difficult one to apply ; and after all, every- 
 thing comes to this, that we gather from it what 
 group of marks (x+y) is present in A as a cause of 
 the predicate P being attributed to the A. For if 
 P is to be transferred from A to some B, on account 
 of the similarity of the two subjects, then B must 
 be like or similar to A in relation to (x + y) ; — that 
 is to say, must have this group of marks in common 
 with A; in which case, on the contrary, all other 
 similarity of A and B is of no avail whatever. 
 
 Now that (x + y) is the condition of P can be 
 demonstrated partially on other grounds ; and, in 
 case P is ascribed to the subject B, is no longer 
 a conclusion from analogy, but a direct sequence. 
 If such proof can not be adduced, then different 
 subjects must be compared as far as possible : and 
 it must be shown that all their other similarities 
 cannot produce the common predicate P, unless 
 
I36 OUTLINES OF LOGIC. 
 
 (x + y) is a common constituent of all the subjects; 
 and that, on the other hand, difference of the marks, 
 otherwise, does not destroy the common character 
 of P, as long as (x + y) remains common to all the 
 subjects. From this, finally, the conclusion is drawn 
 with a satisfactory degree of probability, that the 
 predicate P will belong to all subjects in which 
 (x + y) is found. 
 
 § 89. The other kind of problem (§ 78) is this, — 
 to demonstrate the reality of a single fact. 
 
 Three different points of starting may be discov- 
 ered for this purpose. That is to say, we have be- 
 fore us given facts which we can apprehend either 
 as causes, or as results, or as accompanying signs 
 of the fact in question. 
 
 In none of these ways is a strict demonstration 
 possible. For even if what is given always contains 
 the complete cause of what is to be proved, yet this 
 cause after all — since we are here not dealing with 
 valid truths, but with actual occurrences — may be 
 hindered by counter-forces from the production of 
 its effect. But if what is given can be explained 
 from what is to be proved, as its result, still it is 
 never demonstrable with such perfect cogency that 
 other equivalent causes could not also be assigned 
 for the same given fact. Finally, that the mere 
 
PROOF BY INDICIAE. 137 
 
 reciprocal companionship of two facts, because it 
 ordinarily occurs, does not establish any certain con- 
 clusion from one to the other, is self-evident. 
 
 § 90. The general principles, in pursuance of which 
 we try to give as much of probability as possible to 
 this 'proof from indiciaej depend upon the follow- 
 ing general views. 
 
 In reality a multitude of different causal nexuses, 
 which do not issue from one principle, constantly 
 run on side by side. Now it is not probable that 
 any one of them will, escaping all disturbance from 
 the others, produce the effect, abstractly belonging 
 to it, in its entirety and without abatement. On 
 this account, finely spun plans, which do not have 
 regard to 'accidents,' appear to us in practical life 
 convicted of folly ; and in art and history all repre- 
 sentations appear improbable which make an intrigue 
 succeed in all its results, or an important factor ac- 
 complish all its theoretically correct results for hun- 
 dreds of years together. 
 
 But, on the other hand, it is just as improbable 
 that an extraordinarily great multitude of causal 
 nexuses, independent of each other, should have in- 
 tersected each other in such a manner as to pro- 
 duce exactly one special matter of fact that, in the 
 form in which it exists, is comprehensible from some 
 
I38 OUTLINES OF LOGIC. 
 
 single other cause. Accordingly, we do not believe 
 in the efficiency of a thousand minute causes for the 
 production — for example, in history — of a result 
 which flows of itself from some one ' direction of 
 the Zeitgeist/ so-called. Nor in medicine do we 
 credit the view, that every symptom of a patient 
 has its separate harmless cause, as soon as the sum 
 of all the symptoms exhibit the unity of a ( disease/ 
 as arising from which they are all comprehensible. 
 Just so in jurisprudence we do believe in such a 
 diabolical concatenation of a thousand minutiae that 
 from them the appearance of single coherent ' crime ' 
 originated. 
 
 § 91. The importance of the single indicise is 
 estimated according to the same rules as in cases 
 of inductive proof ; consequently, the probability of 
 the instance to be proved is referred back to internal 
 grounds of actual fact. 
 
 Now there are instances enough where the proba- 
 bility of the occurrence of an event cannot be judged 
 at all from grounds of mere fact ; either because, as 
 in the case of future events, we do not by any means 
 know them all, or because it would take us into 
 details too much to estimate actually even the part of 
 them that is known. Here, however, it may not be 
 necessary to have an opinion about the occurrence 
 
GROUNDS OF PROBABILITY. 1 39 
 
 or non-occurrence of the event, in order to base upon 
 it some practical procedure. Nothing remains for 
 us in such a case but first to enumerate together, 
 as precisely alike possible, all the possible instances 
 for the occurrence of which wholly like reasons tes- 
 tify ; and then to ascribe to each of them a like 
 probability of its occurrence, or else (in case of prob- 
 lems where we are dealing with a manifold repeti- 
 tion of analogous events) the same frequency of ap- 
 pearance. Its probability is therefore measured by 
 a magnitude which divides the certainty that some 
 one case must occur (which is here put at unity) 
 by the number of all the cases alike possible with it. 
 
 This probability is distinguished from that pre- 
 viously discussed, which rested on grounds lying in 
 the very nature of the single case, as one which 
 occurs precisely where no such grounds exist. It is 
 in no respect a theoretical assertion about what will 
 actually occur in the future. For nothing prevents, 
 in spite of the calculation, the one case from always 
 occurring, and all the rest of the equally possible 
 cases, from not occurring. Such probability is rather, 
 in reality, a practical standard by which we endeavor 
 to determine the measure of the future confidence 
 that ought still to be cherished in the occurrence of 
 a definite single event among many that are alike 
 possible. 
 
I4O OUTLINES OF LOGIC. 
 
 § 92. The purely logical interest taken in choices, 
 votes, etc., does not consist merely in the attaining 
 of some result, but also in this, that each of the 
 single judgments from which it is to be attained 
 (that is, in this case, each opinion) should find oppor- 
 tunity for a complete and direct expression. Prac- 
 tical interests, on the contrary, and the considera- 
 tions which are had besides in both cases, are 
 opposed to this in many ways. 
 
 The logical interest is perfectly satisfied only when 
 a choice is direct, — that is, when it relates only to 
 one object of choice, is followed by 'aye' and 'no/ 
 and accordingly makes it possible to give an unmixed 
 expression to the negation. All other choices, which 
 are directed to several objects of choice at the same 
 time, which are followed merely with positive votes, 
 and therefore permit the negation of the one ob- 
 ject to be made only by affirmation of some other, 
 are logically deficient. They do indeed furnish a 
 result by means of the majority. But it remains pos- 
 sible that some other result would have satisfied in 
 like manner the collective will of those voting ; since, 
 although the result actually reached is somewhat 
 preferable to the majority, it is on the contrary de- 
 cidedly disagreeable to the minority ; while the other 
 result would have been scarcely less agreeable to the 
 majority and the only one agreeable to the minority. 
 
THE LOGIC OF VOTES. I4I 
 
 It depends upon the nature of the relation which the 
 choice induces, whether the more decided satisfaction 
 of the majority, or one less perfect but more equal- 
 ized among the entire collection of choices, is to be 
 preferred. 
 
 As a purely logical question it is taken for granted 
 that the constituency of voters all vote together on a 
 certain matter (that is, as united into one collection), 
 and form only a single decisive majority. On prac- 
 tical grounds, however, they are frequently divided 
 into a multitude of groups to be treated separately, 
 and the establishment of the definite result of the 
 choice follows on the ground of the majorities which 
 appear in the single groups ; so that, if the vote for 
 a candidate should be taken by aye and no, he 
 would be chosen as soon as — in case the whole were 
 divided into nine groups — he had for him five of 
 these groups (each one, according to its majority). 
 It can easily be understood that in this way the 
 decision may be reached by a minority of those 
 entitled to vote at all in the matter on hand. If 
 we divide ioo votes into 10 groups of 10 each, or 
 into 20 groups of 5 each ; then we have, in the first 
 case, 6 X 6 = 36, in the other 11X3 = 33, as the 
 number of votes necessary for a decision, — instead 
 of 51, which without this partition into groups, in 
 case the 100 voters gave their vote together, would 
 
142 OUTLINES OF LOGIC. 
 
 be required for a majority. It can be calculated that, 
 under such circumstances, the number of votes nec- 
 essary to a decision may perhaps fall as low as a 
 quarter of the whole number. And a still smaller 
 number is sufficient, in case the number of the votes 
 is not placed as equal (as we have done hitherto), 
 but different, in the single groups. 
 
 § 93. In voting on proposals for laws, which seek 
 to satisfy one and the same necessity by formulating 
 it in ways different and exclusive of each other, the 
 usage employed accords, strictly speaking, at only 
 one point with the logical interest. That is to say, 
 if the voting assembly wishes not to recognize in 
 principle the general thought which underlies all 
 these ways of formulating it, or the necessity itself ; 
 then this cannot be satisfactorily done by successive 
 negations of the single proposals, but only by a 
 'motion to fix the order of the day,' which must 
 always be established as soon as such a vote of the 
 whole body is expected. 
 
 From this point on, however, the logical procedure 
 must either be such that a decision must be reached 
 by an aye-and-no vote upon every proposal of the 
 kind, and that one of them all retained which gets 
 the majority of affirmative votes ; or else, at least, 
 one of the proposals must first be selected by merely 
 
THE LOGIC OF VOTES. I43 
 
 the votes in favor of it, without any further issue, 
 so as to make obvious what is the condition of opin- 
 ion thereupon. 
 
 The actual procedure is frequently much more 
 speculative as to its want of obvious significance, or 
 at least admits the existence of such speculation. 
 For whatever the order of questions may be, yet 
 custom hinders, by the affirmative of any question 
 of all those that follow being excluded from the 
 vote, as well the free expression of opinions as also 
 the attainment of a result that is wholly accommo- 
 dated to them. For every aye or no has in this 
 case a double significance ; either it means a choice 
 (or non-choice) of the individual proposal in itself 
 considered, or an affirmative (or negative) for it from 
 fear (or hope) of defeating (or carrying) by this 
 means some subsequent less (or more) agreeable 
 measure. Accordingly, the procedure passes out of 
 the purely logical domain into that of practical politi- 
 cal calculation and trickery. 
 
II. 
 ENCYCLOPEDIA OF PHILOSOPHY, 
 
 INTRODUCTION. 
 
 § 1. ' Philosophy ' should not be considered as an 
 employment of the thinking faculty, which attempts 
 to solve problems of its own, that are otherwise wholly 
 unknown, by means and methods just as peculiar and 
 otherwise unheard of ; and which, therefore, makes 
 its appearance as a kind of luxury superfluous to 
 our real life. The rather is it nothing else than the 
 strenuous effort of the human spirit, by a coherent 
 investigation, to find a solution, that is universally 
 valid and free from contradictions, for those riddles 
 by which our mind is oppressed in life, and about 
 which we are perforce compelled to hold some view 
 or other, in order to be able really to live at all. 
 
 Life itself involves, in that which we are wont to 
 call 'education/ numerous attempts at such a solu- 
 tion. As well concerning the nature of things and 
 their connection under law, as concerning the grounds 
 of beauty in phenomena, and, finally, concerning the 
 
I46 ENCYCLOPEDIA OF PHILOSOPHY. 
 
 rules obligatory for human conduct, education is 
 accustomed to establish a number of trains of thought 
 that excite a great interest on account of the liveli- 
 ness and warmth which they possess as witnesses, 
 not for unprejudiced reflection but for life's immedi- 
 ate experience. Their disadvantage, however, con- 
 sists in this, that they are not connected systemati- 
 cally together, are often contradictory of each other, 
 and are as a rule interrupted before they have at- 
 tained the ultimate ground of certainty. Aroused 
 by certain events, which happen to one man in one 
 way and to another in a different way, all these reflec- 
 tions retreat in a lively manner some steps backward, 
 in order to discover the reasons that will explain such 
 experiences. They then ordinarily come to a halt, 
 and regard as sufficiently ultimate principles certain 
 points of view, which themselves include what is yet 
 more of a riddle. It is natural that many such trains 
 of thought, setting out as they do from different 
 points of view, should not coincide in one whole but 
 leave gaps and contradictions between them. 
 
 The same relation maintains itself with the indi- 
 vidual sciences. They attach themselves to single 
 domains of actuality, and are satisfied when they 
 discover principles which are constantly valid within 
 such a domain, but which at once become doubtful 
 in their application on being carried over to any other 
 
EXISTENCE OF TRUTH. I47 
 
 domain. Thus the conception of a cause that acts 
 according to law is undoubtedly valid in physics. 
 But the consideration of organic life, as well as ethi- 
 cal speculations, frequently oppose to it the concep- 
 tion of a cause that is determined only by its ends 
 and not by laws, or of one that acts with a complete 
 freedom. It is the problem of philosophy to deter- 
 mine the claims of these different principles and the 
 circuit within which they are valid. Accordingly it 
 admits, for the present, of being defined as the en- 
 deavor, by means of an investigation which has for 
 its object that which is the principle of investigation 
 in education and in the particular sciences, to estab- 
 lish a view of the world that is certain, coherent, and 
 of universal validity. 
 
 § 2. To this entire undertaking two presupposi- 
 tions are necessary. 
 
 The first is this, that there exists in the world at 
 large a 'truth' which affords a sure object for cog- 
 nition. This assumption has seldom been called in 
 doubt. To its denial there stands opposed, princi- 
 pally, the moral conviction that without such truth 
 the world would be absurd ; and that the world can- 
 not after all be this. 
 
 The other presupposition is, that we are in a con- 
 dition to apprehend this truth, — although by no 
 
I48 ENCYCLOPAEDIA OF PHILOSOPHY. 
 
 means necessarily the whole of it ; and yet some 
 part which shall serve us as a firm basis for an in- 
 vestigation that is not perfectible in particulars. 
 In opposition to this assumption, doubt arises in 
 three forms : 
 
 a) A Scepticism that is without motif raises the 
 question whether, at last, all may not be quite dif- 
 ferent from what we are necessarily compelled to 
 think it. This doubt we pass by. For since it does 
 not arise out of the content of what is necessary to 
 thought, but only demands in a general way some 
 pledge for the truth of our thinking, that lies out- 
 side of all our thought, no satisfaction can ever -be 
 given it, but it can only be overcome by a conviction 
 of the absurdity of its own content. 
 
 b) A second kind of Scepticism, with a motif, 
 endeavors to show that the thoughts which we are 
 compelled to think according to the necessary rules 
 of our cognition are frequently impossible according 
 to rules just as necessary; and, therefore, that what 
 is a necessity to our thought does not lead us to any 
 true knowledge. Such doubts are not to be refuted 
 or confirmed, without investigation. We derive from 
 them simply the rule of circumspection, accurately 
 to test the most general conceptions and principles 
 which appear to us as necessities of thought ; to sep- 
 arate what they in truth mean and prescribe from 
 
SCEPTICISM AND CRITICISM. I49 
 
 the more special and not necessary adjunct thoughts, 
 such as have attached themselves to the former dur- 
 ing their application to limited circles of objects ; 
 and then to see whether, in this way, the contradic- 
 tions are made to vanish. 
 
 c) As related to scepticism and derived from it, 
 Criticism endeavors to establish cognition more 
 securely, since it premises an investigation of the 
 nature of the faculty of cognition, and thereby seeks 
 to determine the limits of the validity of our forms 
 of cognition, previous to their application to their 
 objects. Nevertheless, although a preliminary ori- 
 entating of ourselves concerning the origin and 
 connection of our knowledge may guard us against 
 many vain undertakings, yet we cannot regard the 
 undertaking of criticism as anything more than a 
 petitio principii. That is to say, previous to the 
 application of knowledge to things, we cannot do 
 anything but become conscious of those grounds 
 of judgment which our reason contributes to the 
 consideration of things as necessities of its thought. 
 Whether these principles are applicable to 'things 
 themselves,' does not .admit of being decided in a 
 preliminary way from the history of the genesis of 
 our cognition ; because, in order to have such a his- 
 tory at all, one must necessarily already have taken 
 one's point of departure from actual presuppositions 
 
I50 ENCYCLOPEDIA OF PHILOSOPHY. 
 
 concerning the nature of things cognizable, concern- 
 ing the nature of the cognizing spirit, and concern- 
 ing the kind of reciprocal action that takes place 
 between them. 
 
 § 3. We therefore enter upon our philosophizing 
 with the confidence which reason has toward itself, — 
 that is to say, with the principle that all propositions 
 which remain, after the correction of all accidental 
 and changeable errors, as always and universally 
 necessary to thought, are put by us at the founda- 
 tion of everything as confessedly true ; and that 
 according to them must our views concerning the 
 nature of things be determined, and from them alone 
 must a theory of our cognition be obtained. 
 
 But as concerns the way which we are to take 
 in our philosophizing, two views are distinguished. 
 Both are at one so far as this, that the world itself 
 must be a unity ; and consequently the perfected 
 cognition of it must be, as it were, a closed system, 
 which can contain no parts that are not united, or 
 that stand toward each other without any ordering 
 whatever. 
 
 One view, however, believes that it is both able 
 and obligated to divine at the beginning the One 
 Real Principle, on which the world actually depends, 
 and from it to deduce or construe the entire actuality 
 
INVESTIGATION OF TRUTH. I 5 I 
 
 as the sum of its consequences. Such a beginning 
 for cognition would be the best if we were gods. 
 On the contrary, as finite beings, we do not ourselves 
 stand in the creative centre of the world, but eccen- 
 trically in the hurly-burly of its individual sequences. 
 It is not at all probable and is never certain, that we 
 should perfectly divine the one true Principle of the 
 world in any one fundamental thought, however 
 noble and important, to which some sudden intui- 
 tion might lead us ; still more uncertain that we 
 should formally apprehend it so accurately that the 
 series of its true consequences should obviously pro- 
 ceed from it. It is rather altogether probable that 
 the first expression of the principle will be defective, 
 and that mistakes will always multiply in the course 
 of the deduction ; since one has regard to no inde- 
 pendent point of view from which they might be 
 corrected. 
 
 The second view — of which we fully approve — 
 distinguishes the investigation from the exhibition 
 of truth. The mere search for the truth is by no 
 means under the necessity of taking its point of 
 departure from one principle, but is justified in set- 
 ting forth from many points of attachment that lie 
 near each other. It is only bound to the laws of 
 thought, — beyond that, to no so-called ' method ' 
 whatever. All direct and indirect means of getting 
 
152 ENCYCLOPAEDIA OF PHILOSOPHY/ 
 
 behind the truth must be applied by it in the freest 
 manner possible. The. latter, however, — the exhibi- 
 tion of truths already gained — has only to satisfy 
 the need for unity and systematic coherency. But 
 for it, too, this is a problem of which we do not 
 know beforehand in how far it is solvable. 
 
 § 4. A preliminary division of Philosophy may be 
 attempted simply with the design of separating the 
 different groups of the problems, each one of which 
 appears to be self-coherent and to require an inves- 
 tigation of a specific kind. We attribute little value 
 to the reciprocal arrangement of these single groups 
 under each other. In the history of science, too, 
 names for these single groups are customary before 
 any definite usage as to their systematic arrange- 
 ment. 
 
 Two domains are now, in the first place, distin- 
 guished. We require, on the one hand, certain in- 
 vestigations concerning that which exists; and, on 
 the other hand, concerning the value which we attach 
 to what is actual or to what ought to be. We now 
 see that nothing in relation to its value follows im- 
 mediately from insight into the origin and continued 
 existence of anything actual whatever ; and nothing 
 in relation to the possibility of its being actual fol- 
 lows from insight into its value. Accordingly, al- 
 
DIVISIONS OF PHILOSOPHY. I53 
 
 though we assume that at the end of the investiga- 
 tion a close connection will be shown between that 
 which exists and that which is of some value, still, 
 at the beginning we separate the two investigations, 
 — the one concerning the actuality and the one con- 
 cerning the value of things. 
 
 § 5. Of the further organization of the subject, 
 what follows may be presupposed : 
 
 Inducements to questions that concern the expla- 
 nation of actuality come to us in part from external 
 nature and in part from the life of the soul. The two 
 domains do not immediately exhibit the appearance 
 of complete similarity ; but the consideration of both 
 leads to a series of quite similar inquiries, — for ex- 
 ample, concerning the possibility of the alteration of 
 one and the same Being, concerning the possibility 
 of the influence of one Thing upon another, etc. 
 Such inquiries may be separated from others and 
 combined into a universal preliminary investigation, 
 Metaphysic, upon which the Philosophy of Nature 
 and Psychology should then follow, as applications of 
 the results reached in it to special cases. 
 
 The second main division finds two obviously re- 
 lated subjects in the kinds of value which we ascribe 
 to the existent, and in those which we ascribe to 
 such actions or sentiments as ought to be ; these are, 
 
1 54 ENCYCLOPEDIA OF PHILOSOPHY. 
 
 however, primarily distinguished by the fact that 
 only the latter directly include an obligation. On 
 this account, the investigation of the two divides 
 into ^Esthetics and Ethics ; and for these two inves- 
 tigations a third, common to both, may be conceived, 
 but has hitherto never been carried out, — namely, 
 an investigation concerning the nature of all deter- 
 minations of value (corresponding to Metaphysic). 
 
SECTION FIRST. 
 
 THEORETICAL PHILOSOPHY. 
 
 § 6. In life and in the particular sciences we are 
 constantly employed with the explanation of phenom- 
 ena which, in the form in which they are presented 
 to us, are full of riddles through their contradictions, 
 gaps, and lack of coherence, — a fact to which allu- 
 sion has already been made. In doing this we nec- 
 essarily start from certain general presuppositions 
 to which nature and the coherency of things must 
 correspond in order to be true. These presupposi- 
 tions are ordinarily employed only in an uncritical 
 way and without any clear consciousness of their 
 meaning ; but Metaphysic endeavors to make a col- 
 lection of them, to explain their true meaning, and 
 to remove the prejudgments which have become at- 
 tached to them from being accustomed to a limited 
 circle of experience. Three great groups of inves- 
 tigations appear at this point : 
 
 i) one, concerning the most general conceptions 
 and propositions which we apply in judging of every 
 actuality ; 
 
 2) a second, concerning the most general forms 
 
I56 ENCYCLOPAEDIA OF PHILOSOPHY. 
 
 in which this actuality appears in the existences of 
 nature (Space, Time, Motion) ; 
 
 3) a third, concerning the possibility of the ' recip- 
 rocal being (Fureinandersein) of things/ by which the 
 one becomes a perceivable object, and the other a 
 perceiving subject. 
 
 These three groups appear under different titles, with 
 somewhat of deviating limitations and, of course, very 
 differently treated, in most systems of Metaphysic. 
 
 In the Metaphysic of the older school the first 
 part appears as Ontology ; the second as Cosmology, 
 having the problem of showing how the individual 
 things are connected together into an orderly world- 
 whole, — a problem which, although it is related to 
 the second of those mentioned above, is still not 
 identical with it. Rational Psychology corresponds 
 to the third group. On the contrary, the fourth 
 part of such Metaphysic, rational theology, must be 
 distinguished as a constituent of a foreign kind and 
 not strictly belonging to Metaphysic. 
 
 Just so in Herbart's Metaphysic, if we count out 
 the first part, the ' Methodology', then the others 
 correspond perfectly to the above-mentioned divis- 
 ion : Ontology, Synechology, as the doctrine of 
 what is permanent, and Eidolology, or the doctrine 
 of images (el'SwXa), which arise in one being as com- 
 ing from the others. 
 
QUESTIONS OF ONTOLOGY. 1 57 
 
 In the same way does Hegel's ' Logic/ by its par- 
 tition into the doctrines of Being, of Phenomenon 
 (from which, of course, though to its disadvantage, 
 space and time remain excluded), and of Idea, ex- 
 hibit the plainest analogies to the foregoing division 
 of such problems. 
 
 § 7. Ontology, from its being employed with expe- 
 rience, is led to the following principal inquiries : 
 
 i) What, exactly, is the absolute Subject, which 
 is not a predicate of another ; that is to say, in what 
 does that consist which is the truly existent in all 
 ' Things/ whose nature we ordinarily believe our- 
 selves able to specify by a number of so-called prop- 
 erties ; and which is the support (Trager) of these 
 properties and not itself in turn a property of any 
 other ? 
 
 2) How is the possibility of a variety of simulta- 
 neous and successive properties belonging to one 
 and the same subject to be comprehended? 
 
 3) How can such a unity exist among a variety of 
 Things that the states of one become causes for alter- 
 ations in the states of another ? 
 
 § 8. Before we consider the different answers 
 which have been given to these inquiries, we make 
 prominent some very general kinds of error. 
 
I58 ENCYCLOPEDIA OF PHILOSOPHY. 
 
 The first is the confounding of the logical analysis 
 of our mental representations and the metaphysical 
 explanation of the things to which the mental repre- 
 sentations relate. It is in general quite obvious that 
 there cannot be, in the matter of fact itself and as 
 developments of its own nature, as many movements 
 and turnings as would correspond to the various 
 steps, the separations and combinations, and in gen- 
 eral to all the turnings which we must make in 
 thought, in order from our point of view to appre- 
 hend the nature of such matters of fact. This is 
 perfectly clear to every one, in case one has to do, 
 for example, with the more intricate artifices of inves- 
 tigation through which we endeavor to discover any 
 secret fact. Here the whole expenditure of the oper- 
 ations of thought is quite obviously nothing but our 
 subjective exertion, as it were, to get behind the in 
 itself simple thing. On the contrary, all this be- 
 comes obscure, in case one has to do with the simplest 
 logical operations. And at this point we very gen- 
 erally fall into the error of regarding our logical sep- 
 arations and combinations of the mental images and 
 their parts as events which happen also in the nature 
 of the things themselves. 
 
 For example ; in definition we premise for the 
 individual a general conception, and elaborate this 
 by added modifications up to the point of likeness 
 
JUDGMENT AND REALITY. 1 59 
 
 with the individual in question. Hence the frequent 
 error, as though in reality some ' primitive animal/ 
 some 'primitive matter,' some 'primitive substance/ 
 must precede as a substratum in fact, from which, as 
 something secondary, the individual subordinate spe- 
 cies might originate through the influence of modify- 
 ing conditions. The logical dependence of the sepa- 
 rate members of a classification is, therefore, con- 
 founded with a real, matter-of-fact derivation of one 
 from the other. 
 
 In judgment we divide the object of a perception 
 into a subject, from which we as yet exclude a pred- 
 icate ; then into such predicate ; and, finally, into the 
 third mental representation, that of the copula by 
 which the predicate is united again with the subject. 
 These operations are necessary in order to secure 
 clearness to the process of thinking. But it is an 
 error to assume that, in general, any like transaction 
 corresponds to them as a matter of fact, so that 
 there can really be, in the last analysis, a somewhat 
 that is without all predicates, and only just a some- 
 what, but not any definite somewhat ; and, further, 
 that there can be predicates which were somewhat 
 previous to their being actualized in some subject ; 
 and, finally, that there is in rerum natitra some 
 'cement/ as it were, similar to the logical copula 
 by means of which the predicates are brought to 
 
l6o ENCYCLOPEDIA OF PHILOSOPHY. 
 
 ' inhere ' — as the customary expression goes — in 
 the subject. 
 
 One of the most frequent inducements to such 
 errors as the foregoing lies in the comparisons 
 which we are able at will to establish in the pro- 
 cess of thinking between the contents of any 
 two ideas we please. We are very much inclined 
 to regard the predicates — for example, 'greater/ 
 'smaller/ 'different/ 'opposed/ and the like — which 
 belong ' to the content compared, only after the com- 
 parison is made, as essential, integrating properties 
 of the content itself. 
 
 From these mistakes there originate, in part, a 
 multitude of artificial difficulties, inasmuch as we 
 begin to seek for an explanation of matter-of-fact 
 properties of things which we have previously cre- 
 ated for them (as, for example, when the question 
 is raised, how an x can be at the same time ' greater ' 
 and 'smaller/ — that is, greater than y and smaller 
 than z) : and, in part, many actual difficulties are 
 met with and no solution for them found, because 
 we imagine that we have succeeded in exhibiting 
 the development of a matter of fact, when we have 
 in truth merely depicted the development of our 
 conceptions of the matter of fact. To this latter 
 case belongs, for example, the application of the 
 conceptions of 'potentia' and 'actus/ or of 'dynamis' 
 
EXPLANATION OF PRINCIPLES. l6l 
 
 and 'entelechy,' or of 'power' and 'expression/ — 
 faults of a kind which is especially frequent in 
 ancient philosophy (compare ' Microcosmus,' vol. II, 
 pp. 321 ff.). 
 
 § 9. A second very general mistake, the exact 
 opposite of the previous one, consists in the effort to 
 make clear the supreme principles by explanations 
 that have no meaning except in the case of individual 
 phenomena dependent on the principles ; and that 
 even here have their meaning only in virtue of the 
 principles themselves. The simplest way of making 
 this obvious is, in brief, the following. 
 
 Our cognition is accustomed to the investigation 
 of individual events. These have their definite con- 
 ditions, under which they are produced and main- 
 tained. On this account, w r e can often show step 
 by step in a pictorial manner, how the phenomenon 
 arises from the co-operation of its conditions ; that 
 is to say, we know the mechanism of its coming 
 to be, the way in which it is produced. Now this 
 same inquiry may also very easily be raised with 
 reference to the general principles, which are the 
 very foundation of the possibility of the aforesaid 
 mechanism, or of every way in which any thing 
 whatever can be produced. For example, the ques- 
 tion is asked, how does it happen that in all 
 
1 62 ENCYCLOPEDIA OF PHILOSOPHY. 
 
 ' becoming ' one state follows upon the others ; or 
 how does a ' cause ' begin to produce its appropriate 
 effect. This is as though one should wish to inves- 
 tigate some internal mechanism, by which the points 
 of relation existing between these two most general 
 conceptions were held together; although — just the 
 other way — every possible mechanism presupposes 
 the validity of these two conceptions. 
 
 It is just so in many other cases. This fault is the 
 opposite of the foregoing, inasmuch as in the case of 
 objects of thought that are absolutely incomprehen- 
 sible except in the form of abstract concepts and are 
 definable only as to their essential meaning, it is not 
 satisfied with such apprehension as belongs to the 
 concept, but demands for them a kind of intuitive 
 knowledge such as in this case is quite impossible. 
 
 § 10. The difference in different treatises on Met- 
 aphysic admits of being referred to two antithetic 
 principles which are dependent on fundamental pre- 
 suppositions that are together introduced to consid- 
 eration. 
 
 One view, which is realistic, finds the inducement 
 to investigation exclusively in the ' contradictions ' 
 of experience. If there were none of these, then 
 Realism would take no offence at letting the world 
 pass in the form in which it exists as bare matter 
 
METAPHYSIC OF REALISM. 163 
 
 of fact ; and would raise no further inquiries. Ac- 
 cordingly, if it succeeds in placing underneath this 
 world of experience, a world of what is existent truly 
 and devoid of contradictions, out of which the former 
 becomes comprehensible ; then it regards its problems 
 as solved. 
 
 The other and idealistic view sees in every fact, 
 even although it include no contradiction, some rid- 
 dle ; and it believes that we ought to recognize as 
 truly existent only such matter-of-fact as, by virtue 
 of its meaning and significance, admits of being 
 demonstrated to be an essential member of the 
 rational world-whole. 
 
 § 11. The Metaphysic of Realism is more inclined 
 to the pursuit of special investigations which are at- 
 tached to single groups of problems ; and it is only 
 afterward that it endeavors to combine the results it 
 has attained into one whole. The Metaphysic of 
 Idealism, on the contrary, prefers to apprehend as 
 its single main problem the meaning of the world 
 as a whole ; and it believes that the solution of this 
 problem includes that of all the special problems, 
 and that thereby a coherent, uninterrupted develop- 
 ment can best be obtained. The methods of both 
 partake of this distinction. 
 
 Realism takes its point of departure from the abso- 
 
164 ENCYCLOPEDIA OF PHILOSOPHY. 
 
 lute certainty of the law of identity. Accordingly, 
 it sees so-called ' contradictions ' everywhere that 
 ordinary experience shows us a ' unity of the one 
 and the many ' (for example, the ' many properties ' 
 of .a 'Thing' and their 'alteration'). It further 
 tries to find a general solution for the contradiction 
 in the assertion that the unity is here only appar- 
 ent ; and that what corresponds as subject to the 
 many properties (whether simultaneous or succes- 
 sive) is not one Being that remains the same with 
 itself and yet undergoes change, but is a complex 
 of many beings which, in themselves always simple 
 and always self-identical, only appear to us as one 
 i Thing ' through their relations to each other and 
 through their changes — as one Thing with many 
 properties, as one changeable thing. 
 
 § 12. The Metaphysic of Idealism sets itself a 
 single main problem, which is as follows ; to dis- 
 cover the nature of the truly Existent, against the 
 recognition of which as absolute, independent, and 
 supreme Ground of actuality, none of those presup- 
 positions which our reason is compelled to make 
 concerning such a principle, any longer protests. 
 
 Such a problem leads to a method of its own. 
 That is to say, the aforesaid 'truly Existent,' which 
 we wish to discover, hovers before us, at the begin- 
 
METAPHYSIC OF IDEALISM. 1 65 
 
 ning of philosophy, in the form of a very obscure 
 although very lifelike presentiment. Positively, we 
 are not able exhaustively to express what we mean 
 by it. But yet, in case some thought not identical 
 with it is mentioned to us, we are able very definitely 
 to deny that it is this which we mean. If we there- 
 fore assume that we have first established for this 
 obscure content X some definition a, which contains 
 those features of X that are relatively most clear to 
 us ; then we can next compare a with X, and there- 
 upon observe not merely in general that a does not 
 perfectly represent what we mean by X, but also 
 why or wherein a is unlike X, and consequently 
 stands in need of improvement. Thus there origi- 
 nates a second definition a — X, with which the 
 same procedure is instituted as with a : and so on, 
 until we finally discover a definition A = X in which 
 we see all that we obscurely meant under X trans- 
 formed into clear conceptions. 
 
 Thus regarded, this method is nothing but a series 
 of subjective operations of thought by which we in- 
 tend to transform a knowledge of our object which 
 is at first unsatisfactory into one more adequate ; — 
 that is, of operations executed, with an altogether defi- 
 nite purpose in view, £y us as interpreting subjects. 
 
 If the object X still remains as obscure as are those 
 high-flying thoughts called 'the truly Existent/ 'the 
 
l66 ENCYCLOPAEDIA OF PHILOSOPHY. 
 
 Absolute/ etc., then, as a rule, it becomes very diffi- 
 cult to get any altogether accurate consciousness of 
 the precise reasons why a first definition a is not sat- 
 isfactory. We indeed feel its unsatisfactoriness in a 
 general way, and this of itself urges us toward a sec- 
 ond definition a which much better corresponds to 
 the X. But the logical motives for this transition 
 remain obscure. It merely follows with a certain 
 poetic justice ; and now it appears to us, since we 
 have lost hold of the reins that are to guide the 
 process of thought, as an inner development pecu- 
 liar to X itself, of which we as thinking subjects 
 are simply spectators. 
 
 On the other hand, Idealism took its point of 
 departure from the matter-of-fact supposition of a 
 single Ground of the world, of an ' Absolute/ which 
 ' develops ' into the variety of phenomena. If it 
 had been known what this Absolute is, then we 
 should have been able to deduce from its nature a 
 mode of development corresponding to it. But this 
 was not known ; on the contrary, the name ' Abso- 
 lute ' merely designated the value of a Supreme Prin- 
 ciple to which a content as yet unknown was, so to 
 speak, to be elevated. No definite mode of devel- 
 opment could therefore be divined, but it could sim- 
 ply be asserted what mode may possibly be attrib- 
 uted to the Absolute ; and so in any case it must 
 
BEING IN ITSELF. 167 
 
 at least correspond to the general conception of 
 'development.' 
 
 Now the following thoughts are involved in the 
 foregoing conception, — namely, that the self-devel- 
 oping being is not yet that which it is to become, 
 but that at the same time the possibility of its be- 
 coming this lies in it alone. It therefore appears 
 as a ' germ ' which is not yet fully unfolded, but 
 which is ' in itself ' what it will later become. Fur- 
 ther, the germ must not remain germ, but must 
 develop into a variety of actual phenomena ; none 
 of which, although they all correspond perfectly to 
 its essence, is exclusively correspondent thereto, with- 
 out having others beside itself. Therefore that which 
 is 'in itself {das An Sick) is at the same time realized 
 and brought to an end in this development, which is 
 the ' being other than itself ' ; since it assumes a defi- 
 nite form, and thus excludes other possible forms 
 which it might have assumed. This incongruity 
 between that which the Being is ' in itself ' and the 
 ' being other than itself ' of the phenomenon must 
 be in turn removed : and it is a further step neces- 
 sary to the development, by which the one-sidedness 
 of the phenomenon is negated and the Being re- 
 turns into its own infiniteness ; although since it 
 has this definite development behind it, it does 
 not return to the simplicity of Being ' in itself/ 
 
l68 ENCYCLOPEDIA OF PHILOSOPHY. 
 
 but to the higher state of ' Being for self ' (Filr- 
 sichseiu). 
 
 These three steps deduced from the conception of 
 development in abstracto have been established, be- 
 sides, by many significant examples taken from expe- 
 rience, — as, for example, from vegetable, animal, and 
 spiritual life ; and so it came about that the afore- 
 said primary and subjective method of explaining 
 obscure conceptions blended with this objective 
 'rhythmus' of development; and philosophy came 
 to believe that it possesses herein a method at once 
 subjective and objective, according to which things 
 have unfolded themselves before our consciousness 
 (compare ' Geschichte der Aesthetik in Deutschland] 
 Miinchen, 1868, pp. 176-183). 
 
 § 13. It is obvious that, from the foregoing method, 
 there is to be expected only a development in which 
 a certain poetic justice more or less clearly rules; 
 but not such an one as that every step in it can 
 be made good by definite proofs as necessary or as 
 alone possible to the exclusion of others. 
 
 In fact, the use of the same method by different 
 philosophers of this school has led to wholly diver- 
 gent results. 
 
 Only the fundamental thought of their Ontology 
 remains; and it is this, that ' Being' is never simple, 
 
RESULTS OF REALISM. 169 
 
 unchangeable ' Position,' but is constant movement 
 through the three ' Moments ' above alluded to, — 
 namely, ' Being-in-itself/ i Being-other-than-self,' and 
 ' Being-for-self.' It is further agreed that there is 
 only one i Existent,' whose finite and limited mani- 
 festation is the individual things ; and, finally (a fact 
 which may be observed here in a preliminary way), 
 that this one Absolute does not remain a wholly 
 empty name for an obscure point, but has essen- 
 tially the nature of the Spirit, and its development 
 is the advance from the 'being-in-itself of uncon- 
 scious existence to the ' being-f or-self ' of self-con- 
 sciousness. 
 
 § 14. The results of Realism are different. Di- 
 rected primarily toward the explanation of the pos- 
 sibility of phenomena, it naturally required, in oppo- 
 sition to the change which would include a contra- 
 diction, that Being should be considered as a simple, 
 irremovable 'position.' It further required, that the 
 primary elements, from whose changeable combina- 
 tion the phenomena proceed, should be seen in a 
 variety of ultimate subjects or real beings. The 
 original nature of these beings it believed cannot 
 be recognized ; but it simply concluded, from the 
 facts that 'appear, back to relations which must 
 take place between them in order to make this 
 appearance possible. 
 
I/O ENCYCLOPEDIA OF PHILOSOPHY. 
 
 Both views, Idealism and Realism, come from dif- 
 ferent sides on one and the same difficulty. The 
 former can perchance develop, in a general way, 
 from the one Idea which it presupposes, those prob- 
 lems which reality must solve in order to correspond 
 to this Idea. Only it is not able to explain the spe- 
 cial actions and reactions which take place between 
 the individual examples of those species of Being that 
 are derived from it ; but for this it needs the ' plural- 
 istic ' assumption that the aforesaid Idea, in a manner 
 that requires additional demonstration, has previously 
 divided into a variety of elements which are in the 
 future to act independently. 
 
 Realism, on the contrary, in order to comprehend 
 an action and reaction between its many elements, 
 must assume a unity of general laws to which they 
 are all subjected. The explanation of how this sub- 
 ordination of the many under this unity is possible, 
 is the counterpart of the before-mentioned problem 
 of Idealism. We may therefore consider as the final 
 problem of Ontology — a problem not yet satisfac- 
 torily solved — this inquiry after the connection 
 between the necessary unity and the alike neces- 
 sary manifoldness of the Existent. 
 
 § 15. After Ontology has established certain gen- 
 eral conceptions of Being, of the Existent, of Hap- 
 
COSMOLOGICAL PROBLEMS. 171 
 
 pening and Acting, cosmological investigations raise 
 the inquiry after the relation of this Being and Act- 
 ing to Space and Time. Under this head the prin- 
 cipal problems are the following three : 
 
 1) The problem whether 'space' exists in itself, 
 and things are in it, so that the latter are partially 
 distinguished by their place in space ; or whether 
 space is in things only as a form of intuiting them, 
 and the latter are accordingly distinguished only 
 qualitatively, and appear at different points in one 
 space intuited of them, in consequence of their 
 qualitative differences toward each other. 
 
 Connected with this inquiry after the * reality ' or 
 ' ideal character ' of space stands — 
 
 2) The inquiry after the nature of ( matter/ 
 although the two do not coincide. The question 
 is : Should the spatial volume of any body of matter 
 be held to be a continuous volume full of what is 
 real ? Or is it only a space-volume within which 
 many active elements exist that are distinguished by 
 their place but are in themselves unextended ? This 
 is the question in dispute between the dynamic filling 
 of space and Atomism, — the meaning of which, how- 
 ever, it appears must be apprehended in a way the 
 very reverse of what customarily happens. The 
 conception of matter as continuous asserts that what 
 is real accomplishes an actual achievement by filling 
 
172 ENCYCLOPAEDIA OF PHILOSOPHY. 
 
 up space ; and, indeed, by filling it up with its pres- 
 ence. The other view allows space to be simply 
 controlled and not ' crammed ' full, as it were, by 
 real existence. It alone, besides, would be compati- 
 ble with the correct view concerning the ideal char- 
 acter of space. 
 
 3) A third question in dispute arises from the 
 consideration of what happens in the physical realm. 
 On the one hand, we are necessitated to recognize 
 the origin of phenomena from the co-operation of 
 many previously unconnected elements, and at the 
 same time the validity of general laws according 
 to which these elements act in every case ; so that 
 they are dependent for their effect only upon these 
 laws, upon their own permanent nature, and upon 
 the momentary disposition of circumstances, and 
 not at all upon a result which, according to hypoth- 
 esis, has not as yet been attained. Over against this 
 so-called ' mechanical view' of forces working blindly 
 according to general laws, there stands the idealistic 
 view, which regards only 'active Ideas' as truly effec- 
 tive in the world of things. Such Ideas are ever 
 striving to realize themselves, and on this account 
 are not bound to constantly uniform laws of their 
 action, but modify their mode of behavior at every 
 moment with a teleological reference to the result 
 for which they strive. Now it needs no explanation 
 
VALIDITY OF COGNITION. 1 73 
 
 to see that, as long as the l Ideas' use means for their 
 actualization, this actualization cannot follow without 
 certain general laws being valid, in accordance with 
 which these means act. But just so, on the other 
 hand, would the world be absurd if there existed in 
 it mere i mechanism ' without any power of Ideas or 
 final purposes. The ultimate object of Cosmology 
 will therefore be the inquiry, how Ideas and final 
 purposes can be effective within a world whose 
 events are subject to the laws of a mechanism. 
 
 § 16. After we have, in Ontology and Cosmology, 
 formed a view concerning the nature of Things and 
 their reciprocal actions, we should in the last part of 
 Metaphysic investigate Cognition itself as a single but 
 important case of the reciprocal action between two 
 elements, — to wit, the case in which the one being 
 is capable of apprehending as conscious ideas the 
 impressions which it receives from the others. 
 
 In the first place, we should in realistic fashion 
 discover from the consideration of this reciprocal 
 action, that the image of the one being A cannot 
 be formed like A within the other being B ; be- 
 cause, although it always on the one side depends 
 upon the impression from A, it likewise on the 
 other side depends on the nature of B. This, 
 therefore, is the same as saying that, by virtue of 
 
174 ENCYCLOPEDIA OF PHILOSOPHY. 
 
 this unavoidable ' subjectivity of all ideation/ cog- 
 nition cannot be ' true ' in the sense that it copies 
 the essence of objects in form similar to the objects 
 themselves ; but at most in the sense that it repeats 
 the relations between things in the form of relations 
 of their mental images. 
 
 The foregoing result, however, causes us to raise 
 the inquiry of Idealism after the significance of this 
 entire mode of procedure. The Realism of common 
 opinion is wont to regard the world, apart from cog- 
 nition, as a ready-made matter-of-fact that subsists 
 entirely complete in itself ; and cognition as only a 
 kind of appendage by means of which this subsist- 
 ing matter-of-fact is simply recapitulated for the 
 best good of the cognizing being, but without in 
 this way experiencing any increment of reality. 
 Now Idealism establishes the truth that the pro- 
 cess of ideation itself is one of the most essen- 
 tial constituents of the world's ongoing course ; 
 that objectivity is not a goal the attainment and 
 further shaping of which is a task set before idea- 
 tion ; but that ideation or, rather, the whole spir- 
 itual life is a goal, to the attainment of which is 
 summoned the entire world of objects that do not 
 share in the process, and the entire ordering of 
 relations between them. 
 
PHILOSOPHY OF NATURE. 175 
 
 § 17. The design in dividing theoretical Philoso- 
 phy into Metaphysic and its applications, the Phi- 
 losophy of Nature and Psychology, is that the first 
 shall answer the question : How must all that be 
 which is really to be at all ? or, If anything what- 
 ever really is, to what necessary laws of all thought 
 is it subjected? Over against this abstract science 
 are the two other concrete ones. That is to say, 
 they must consider the actuality which, although it 
 obeys the laws of Metaphysic, still does so in a spe- 
 cial form that might be otherwise, and that therefore 
 is provisionally regarded as only an example, empi- 
 rically given, of the aforesaid necessary laws of 
 thought. But the design of this distinction is neither 
 accurately carried out, nor does it possess any great 
 value. 
 
 The problem of the Philosophy of Nature would 
 accordingly be the following; not so much to describe 
 the elements which are in existence, as rather to 
 show what general habitudes of action and reaction 
 occur in this definite ' Nature ' so-called ; and, there- 
 fore, what ones among the different forces conceivable 
 in abstracto actually occur and what ones among the 
 many possible dispositions of them actually subsist 
 from the beginning and maintain themselves amid 
 manifold forms of change. For example, that the 
 mass of matter in the world is separated into indi- 
 
I76 ENCYCLOPAEDIA OF PHILOSOPHY. 
 
 vidual material bodies ; that these are distinguished 
 among themselves into cohering and -reciprocally 
 exclusive systems ; that on our planet the three dif- 
 ferent forms of inorganic, vegetable, and animal 
 existence occur ; that what exists in these three 
 kingdoms is — or how far it is — divided into spe- 
 cies, kinds, etc. ; that a systematic action and reac- 
 tion, which is necessary for their continued exist- 
 " ence, takes place between everything living and the 
 inorganic material, — all this constitutes the prob- 
 lems of the concrete Philosophy of Nature. From 
 the realistic point of view, we take an interest in 
 investigating the effective conditions upon which 
 all these facts concerning the ordering of nature de- 
 pend ; from the idealistic, in showing that it is an 
 ordering in which, if one knows it once for all, the 
 striving after the fulfilment of those universal prob- 
 lems that are unavoidable in every conceivable rational 
 world may be recognized again and again. But Ideal- 
 ism claims far too much when it, as in Schilling's 
 philosophy of nature, aims to ' deduce ' all these con- 
 crete forms of existence, as consequences necessary 
 to thought, from one Supreme Idea. 
 
 § 18. In Psychology, too, the same principal views 
 stand in contrast with one other. The realistic aims 
 by investigations in causality to discover the condi- 
 
PROBLEMS OF PSYCHOLOGY. 1 77 
 
 tions under which every single phenomenon of the 
 life of the Soul occurs, endures, or changes, and by- 
 reciprocal action with other phenomena lays the 
 foundation for new states. Such investigations 
 may either be founded, in a manner quite like that 
 of natural science, upon experience and experiment, 
 or philosophically upon metaphysical presuppositions. 
 The larger gain with reference to the explanation of 
 the individual comes in the former way ; but a more 
 secure apprehension for the whole of a theory is only 
 to be gained in the second way. But the entire real- 
 istic investigation is indispensable, because it is only 
 the knowledge of the working forces in the life of the 
 Soul which admits of practical applications, — in Paed- 
 agogics, Psychiatry, etc. 
 
 Idealism also upon this point investigates, in the 
 first place, the constitutive conception of the Soul, 
 — that is to say, the special Idea for the realization 
 of which the Soul is summoned to a definite place 
 in the whole coherent system of the world ; and it 
 then aims at demonstrating the individual activities 
 of the Soul as a cohering series of steps of develop- 
 ment, which gradually construct for this conception an 
 ever more adequate realization. The previous attempts 
 (Schelling, Hegel, etc.) suffer, in part, from inaccu- 
 racies to which the previous article alludes, and, in 
 part, from an over-estimate (that is without sufficient 
 
I78 ENCYCLOPAEDIA OF PHILOSOPHY. 
 
 motif) of mere intelligence in comparison with the 
 whole spiritual life. They look upon mere self-knowl- 
 edge, the most perfect self-consciousness, as the final 
 goal of the Soul and of the World ; while in our view 
 all intelligence is only the conditio sine qua non y under 
 which alone the final purposes that are really supreme 
 — personal love and hate, the moral culture of char- 
 acter — and, in general, the whole content of life so 
 far as it has value appears possible at all. 
 
SECTION SECOND. 
 
 PRACTICAL PHILOSOPHY. 
 
 § 19. Realism takes up those claims, of the con- 
 science that obligates us to a definite form of con- 
 duct, which urge themselves upon our interior life, 
 as though they were mere problems of fact, — 
 problems on this account because, in spite of the 
 clearness with which the claims of conscience fol- 
 low in many individual cases, still in other cases 
 we feel ourselves obligated in a contradictory fash- 
 ion to irreconcilable modes of conduct. 
 
 Investigation, accordingly, proceeds in the first 
 place to the confirming of the matter of fact, — 
 that is to say, to establishing certain fundamental 
 moral principles in which, since they refer to the 
 most simple relations of several personal wills 
 toward one another, a uniformly similar and un- 
 changeable judgment of approbation or disappro- 
 bation is expressed concerning a definite mode of 
 the will's behavior. Whence these judgments of 
 conscience originate within us ; in what connection 
 they stand with the laws that govern what happens 
 in reality ; whether, finally, they admit of being de- 
 
l8o ENCYCLOPEDIA OF PHILOSOPHY. 
 
 duced from one supreme command or not, — all 
 these are allied questions, the answer to which, 
 however it may turn out, neither heightens nor 
 diminishes the obligatory force of the aforesaid 
 moral principles. 
 
 Realism pronounces it to be a capital fault to sur- 
 render this independence of the moral principles, and 
 to be willing to deduce the supreme rules, according 
 to which our conduct has to be directed, from any 
 theoretical insight whatever into the nature of real- 
 ity. In * Being ' alone no significance with respect 
 to what ' ought ' to be is involved. From that which 
 is and happens, prudential maxims for conduct 
 which will shun the dangers of this reality admit 
 of being developed ; but not the obligations which, 
 apart from any consequences, make any kind of 
 conduct appear in itself valuable, honorable, and 
 praiseworthy. 
 
 The investigations of Idealism have, for the most 
 part, justified these observations. Since it takes its 
 point of starting from a supreme fact, — to wit, the 
 development of the absolute ' Ground ' of the world, 
 — it has not discovered, strictly speaking, any place 
 for the conception of such an obligatory ' ought ' ; 
 but it substitutes for the conceptions of the morally 
 'Good/ and the morally 'Bad/ simply certain theo- 
 retical conceptions of the harmonizing or not-har- 
 
ETHICS AND PRACTICAL PHILOSOPHY. l8l 
 
 monizing of any mode of conduct with the tendency 
 of the self-development of the Absolute. 
 
 § 20. The formal distinction between the two 
 modes of treatment consists in this, that the realis- 
 tic proceeds from general laws of conduct, from 
 which the special maxims of conduct that are 
 necessary in consideration of the circumstances 
 can be deduced for each particular case of an oc- 
 casion for conduct ; and from which, besides, since 
 it brings into consideration the empirical nature of 
 man and the ever recurring social relations, science 
 is also able to develop a series of permanent life- 
 aims that hold good both for the individual and for 
 society. This last problem may be called that of 
 'Practical Philosophy ' in special; while the doctrine 
 of the culture of character according to general ethi- 
 cal principles is called ' Moral Science ' or ' Ethics.' 
 
 Idealism, as a rule, does not reach any special dis- 
 tinction in these two forms of ' discipline/ To it the 
 'Good' appears, not as that which merely ought to 
 be, but likewise as that which eternally is. As well 
 the individual man as society and the history of soci- 
 ety are, in its view, ' factors in the development of 
 the Absolute/ To it that appears as 'good/ which 
 adapts itself to the meaning of this development. 
 
SECTION THIRD. 
 
 PHILOSOPHY OF RELIGION. 
 
 § 21. A common conclusion for both theoretical 
 and practical investigations in philosophy is sought 
 for in the Philosophy of Religion. 
 
 We designate this part of philosophy by this name, 
 because the human mind has uniformly sought in 
 religion for such a conclusion to its view of the world ; 
 that is to say, for certainty concerning the final and 
 supreme Cause of that reality, of which every indi- 
 vidual investigation, since it proceeds from limited 
 points of view, gives only a one-sided explanation. 
 More particularly, however, this certainty has refer- 
 ence to the inquiry, how it is that what appears in 
 our conscience as the only thing that has real value, 
 — how the Good and the Beautiful possess a validity 
 corresponding to their value in the totality of the 
 world. Finally, we employ the term, because the 
 human mind has sought for a supplement to our 
 experience of the world, that shall follow from the 
 results of such painstaking endeavors, by means of 
 some intuition of a supersensible extension of the 
 world into realms withdrawn from experience. 
 
PHILOSOPHY OF RELIGION. 1 83 
 
 It is in ' Religion ' that the human mind has either 
 solved all these problems by a lively phantasy, or 
 some revelation has furnished the solution. In the 
 first case, philosophy has to explain, to test, and to 
 correct, the impulses by which the phantasy would 
 be directed. In the second case, it has to demon- 
 strate, to what demands of the mind, that are in 
 themselves justifiable, the revelation vouchsafes a 
 satisfaction which is not discoverable by the reason, 
 but which is intelligible as soon as it exists. 
 
 But even apart from this relation to religion as a 
 fact actually met with, philosophy carries within 
 itself the very greatest demand for reflection upon 
 the connection between its theoretical and its ethi- 
 cal view of the world. 
 
 § 22. Should the before-mentioned problem be 
 completely solved, then the ' Philosophy of Relig- 
 ion ' would be in a position to make the transition 
 from the way of investigation to the way of a con- 
 tinuous, systematic exhibition of philosophical truth ; 
 since it would indeed have fused all the results of 
 investigation into a single unity. 
 
 But at this point philosophy concludes with an 
 unattainable ideal : — that is to say, with the con- 
 viction that the universal and necessary laws of 
 thought, in accordance with which we judge of all 
 
184 ENCYCLOPEDIA OF PHILOSOPHY. 
 
 reality ; second, that the primitive facts of this 
 reality; third, that the supreme Ideas of the Good 
 and the Beautiful, which hover before us as the 
 final purposes of the world, — are all perfectly 
 coherent factors of one and the same Supreme 
 Principle, of the nature of God, although we are 
 unable strictly to demonstrate this fact of their 
 coherency. From the fact that such general laws 
 hold good in mathematics, it does not follow that 
 this system of nature which is empirically given 
 is necessary, and any other is impossible. Both 
 the laws and the facts appear to us possible and 
 valid, even although no Idea of the Good were 
 ruling the world. In brief, laws, facts, and final 
 purposes (Ideas) are for its three principles, dis- 
 tinct from each other, and not deducible from each 
 other. 
 
 For this reason Philosophy can never be such an 
 unchanging science, as to be able to deduce from 
 one Supreme Principle all its results in uniform 
 sequence ; but its investigations will always be sep- 
 arated into (1) those of Metaphysic, which con- 
 cern the possibility of the world's course ; (2) into 
 those of the Philosophy of Nature, which concern 
 the connection, in fact, of its reality ; and (3) into 
 those of the Philosophy of Religion, which concern 
 its ideal significance and final purposes. 
 
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