Outlines of logic and of Encyclopædia of philosophy

Front matter

UBRARY OF CONGRil^,

UNITED STATES OF AMERICA.

M

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 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 successive, 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 coherence, 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, 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-cohering 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 separates 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 different 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 metaphysical principles. And, accordingly, a near relationship 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 determined 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 preliminary 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 different simple ideas. Wherever, then, some such * connection ' 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, becomes most distinctly apparent to us in the circumstance, 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 adjectively, as quality dependent and presupposing some other to which it adheres ; or verbally, as a movement 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 prismatic 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 significantly 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 accomplish 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 simple 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 presupposition 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 secondary 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 content, 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 belonging together is marked off from every other.

Expression in speech permits this act to be manifest in different classes of words with different degrees of distinctness. An adjective, as 'blue/ expresses least of this logical import. Verbs signify by means of their ending, that the content indicated by them is thought of as a unity in a definite 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 apprehends 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 example ; 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 phenomena 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 together, some reason for the latter is also thought.

§10. Now it is this principle of 'belonging together' 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.

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 principle 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 content 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 mental 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 precisely alike, we should arrive at a meaningless universal 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 comparison 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 universal one (notio generalis) by 'abstracting' from the unlike marks (notae) of the former, and retaining only the like ones. This theory adds the statement, therefore, that the content {materia complexus) 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 improved upon to this extent, that each universal has exactly so many marks, which it is indispensable should be thought together, as belong to the individuals 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 aforesaid 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 together 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 impression 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 separated 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 distinctions, 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 indivictual 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 together, the intuitions of time and space take the place of such strictly logical work. Through these intuitions we then know in what way, for instance, the distinctive marks of an animal — color, skin, head, swiftness, etc. — are to be brought together 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 speaking, 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 comparison 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 particular 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 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 universal concepts (notiones generates) in manifold gradations.

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 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 manner that there is in G no part, no mark and no combination 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. Besides, 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 concepts 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, according 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 terminate 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 relations of these two members we had, however, only expressions characteristic of like species. The universal served us only as a nucleus, as a normative principle, as a rule for the disposition and combination 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 impressions belong together, however, we have sought, not merely in somewhat universal which is common to the different impressions, but likewise in somewhat 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 possibility 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 follows : — 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 color), are apprehended as a whole whose distinguishable 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 coexistence 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 attribute 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