Chapter 5

(H. T. A.)

1Apost. Constit.viii. 2.2Canon 42.

1Apost. Constit.viii. 2.

2Canon 42.

CATEGORY(Gr.:κατηγορία, “accusation”), a term used both in ordinary language and in philosophy with the general significance of “class” or “group.” In popular language it is used for any large group of similar things, and still more generally as a mere synonym for the word “class.” The word was introduced into philosophy as a technical term by Aristotle, who, however, several times used it in its original sense of “accusation.” He also used the verbκατηγορεῖν, to accuse, in the specific logical sense, to predicate;τὸ κατηγορούμενονbecomes the predicate; andκατηγορικὴ πρότασιςmay be translated as affirmative proposition. But though the word thus received a new signification from Aristotle, it is not on that account certain that the thing it was taken to signify was equally a novelty in philosophy. In fact we find in the records of Oriental and early Greek thought something corresponding to the Aristotelian classification.

Our knowledge of Hindu philosophy, and of the relations in which it may have stood to Greek speculation, scarcely enables us to give decisive answers to various questions that naturally arise on observation of their many resemblances (seeHindu philosophy.an article by Richard Garbe inMonist, iv. 176-193). Yet the similarity between the two is so striking that, if not historically connected, they must at least be regarded as expressions of similar philosophic needs. The Hindu classification to which we specially refer is that of Kanada, who lays down six categories, or classes of existence, a seventh being generally added by the commentators. The term employed isPadārtha, meaning “signification of a word.” This is in entire harmony with the Aristotelian doctrine, the categories of which may with truth be described as significations of simple terms,τὰ κατὰ μηδεμίαν συηπλοκὴν λεγόμενα. The six categories of Kanada are Substance, Quality, Action, Genus, Individuality, and Concretion or Co-inherence. To these is added Non-Existence, Privation or Negation.Substanceis the permanent substance in whichQualitiesexist.Action, belonging to or inhering in substances, is that which produces change,Genusbelongs to substance, qualities and actions; there are higher and lower genera.Individuality, found only in substance, is that by which a thing is self-existent and marked off from others.Concretionor Co-inherence denotes inseparable or necessary connection, such as that between substance and quality. Under these six classes,γένη τοῦ ὄντος, Kanada then proceeds to range the facts of the universe.1Within Greek philosophy itself there were foreshadowings of the Aristotelian doctrine, but nothing so important as to warrant the conclusion that Aristotle was directly influenced by it. Doubtless the One and Many, Being and Non-Being, of theGreek philosophyEleatic dialectic, with their subordinate oppositions, may be called categories, but they are not so in the Aristotelian sense, and have little or nothing in common with the later system. Theirstarting-point and results are wholly diverse. Nor does it appear necessary to do more than mention the Pythagorean table of principles, the number of which is supposed to have given rise to the decuple arrangement adopted by Aristotle. The two classifications have nothing in common; no term in the one list appears in the other; and there is absolutely nothing in the Pythagorean principles which could have led to the theory of the categories.2One naturally turns to Plato when endeavouring to discover the genesis of any Aristotelian doctrine, and undoubtedly there are in the Platonic writings many detached discussions in which the matter of the categories is touched upon. SpecialPlato.terms also are anticipated at various times,e.g.ποιότηςin theTheaetetus,ποιεῖνandπάσχεινin theGorgias, andπρός τιin theSophist.3But there does not seem to be anything in Plato which one could say gave occasion directly and of itself to the Aristotelian doctrine; and even when we take a more comprehensive view of the Platonic system and inquire what in it corresponds to the widest definition of categories, say as ultimate elements of thought and existence, we receive no very definite answer. The Platonic dialectic never worked out into system, and only in two dialogues do we get anything like a list of ultimate or root-notions. In theSophist, Being, Rest and Motion (τὸ ὄν αύτὸ καὶ στάσις καὶ κίνησις) are laid down asμέγιστα τῶν γενῶν.4To these are presently added the Same and the Other (ταὐτὁν καὶ θάτερον), and out of the consideration of all five some light is cast upon the obscure notion of Non-Being (το μὴ ὄν). In the same dialogue (262 seq.) is found the important distinction ofὄνομαandῥῆμα, noun and verb. ThePhilebuspresents us with a totally distinct classification into four elements—the Infinite, the Finite, the Mixture or Unity of both and the Cause of this unity (τὸ ἄπειρον, τὸ πέρας, ἡ σύμμιξις, ἡ αίτία). It is at once apparent that, however these classifications are related to one another and to the Platonic system, they lie in a different field from that occupied by the Aristotelian categories, and can hardly be said to have anything in common with them.The Aristotelian doctrine is most distinctly formulated in the short treatiseΚατηγορίαι, which generally occupies the first place among the books of theOrganon. The authenticity of the treatise was doubted in early times by some of theAristotle.commentators, and the doubts have been revived by such scholars as L. Spengel and Carl Prantl. On the other hand, C.A. Brandis, H. Bonitz, and Ed. Zeller are of opinion that the tract is substantially Aristotle’s. The matter is hardly one that can be decided eitherproorconwith anything like certainty; but this is of little moment, for the doctrine of the categories, even of thetencategories, does not stand or fall with only one portion of Aristotle’s works.It is surprising that there should yet be so much uncertainty as to the real significance of the categories, and that we should be in nearly complete ignorance as to the process of thought by which, Aristotle was led to the doctrine. On both points It is difficult to extract from the matter before us anything approaching a satisfactory solution. The terms employed to denote the categories have been scrutinized with the utmost care, but they give little help. The most important—κ. τοῦ ὄντοςorτῆς οὐσίας, γένη τοῦ ὄντοςorτῶν ὄντων, γένηsimply,τὰ πρῶταorτὰ κοινὰ πρῶτα, αἱ πτῶσεις, orαἱ διαιρέσεις—only indicate that the categories are general classes into which Being as such may be divided, that they aresumma genera. The expressionsγένη τῶν κατηγορίωνandσχήματα τῶν κ., which are used frequently, seem to lead to another and somewhat different view.κατηγορίαbeing taken to mean that which is predicated,γένη τῶν κ.would signify the most general classes of predicates, the framework into the divisions of which all predicates must come. To this interpretation there are objections. The categories must be carefully distinguished from predicables; in the scholastic phraseology the former refer tofirst intentions, the latter tosecond intentions,i.e.the one denote real, the other logical connexion. Further, the categories cannot without careful explanation be defined as predicates; they are this and something more. The most important category,οὐσία, in one of its aspects cannot be predicate at all.In theΚατηγορίαιAristotle prefixes to his enumeration a grammatico-logical disquisition on homonyms and synonyms, and on the elements of the proposition,i.e.subject and predicate. He draws attention to the fact that things are spoken of either in the connexion known as the proposition,e.g.“a man runs,” or apart from such connexion,e.g.“man” and “runs.” He then proceeds, “Of things spoken of apart from their connexion in a proposition (τῶν κατὰ μηδεμίαν συμπλοκὴν λεγομένων), each signifies either Substance (οὐσία), or Quantity (ποσόν), or Quality (ποιόν), or Relation (πρός τι,) or Where (i.e.Place,ποῦ), or When (i.e.Time,ποτέ), or Position (κεῖσθαι), or Possession (ἔχειν), or Action (ποιεῖν), or Passion (πάσχειν).οὐσία, the first category, is subdivided intoπρώτη οὐσίαor primary substance, which is defined to beτόδε τι, the singular thing in which properties inhere, and to which predicates are attached, andδεύτεραι οὐσίαι, genera or species which can be predicated of primary substances, and are thereforeοὐσία. only in a secondary sense. Nevertheless, they too, after a certain fashion, signify the singular thing,τόδε τι” (K. p. 3 b 12, 13). It is this doctrine ofπρώτη οὐσίαthat has raised doubts with regard to the authenticity of theΚατηγορίαιBut the tenfold classification, which has also been captiously objected to, is given in an acknowledged writing of Aristotle’s (seeTopica, i. 9, p. 103 b 20).5At the same time it is at least remarkable that in two places where the enumeration seems intended to be complete (Met.p. 1017 a 25;An. Pos.i. 22, p. 83 a 21), only eight are mentioned,ἔχεινandκεῖσθαιbeing omitted. In other passages6six, five, four, and three are given, frequently with some addition, such asκαὶ αἱ ἄλλαι κ. It is also to be observed that, despite of this wavering, distinct intimations are given by Aristotle that he regarded his list as complete, and he uses phrases which would seem to indicate that the division had been exhaustively carried out. He admits certainly that some predicates which come under one category might be referred to another, but he declines to deduce all from one highest class, or to recognize any relation of subordination among the several classes.The full import of the categories will never be adequately reached from the point of view taken up in theΚατηγορίαι, which bears all the marks of an early and preliminary study. For true understanding we must turn to theMetaphysics, where the doctrine is handled at large. The discussion of Being in that work starts with a distinction that at once gives us a clue.τὸ ὄνis spoken of in many ways; of these four are classified—τὸ ὄν κατὰ συμβεβηκός, τὸ ὄν ὼς ὰληθές, τὸ ὄν δυνάμει καὶ ἑνεργείᾳ, andτὸ ὄν κατὰ τὰ σχήματα τῶν κατηγορίων. It is evident from this that the categories can be regarded neither as purely logical nor as purely metaphysical elements. They indicate the general forms or ways in which Being can be predicated; they are determinations of Being regarded as an object of thought, and consequently as matter of speech. It becomes apparent also why the analysis of the categories starts from the singular thing, for it is the primary form under which all that is becomes object of knowledge, and the other categories modify or qualify this real individual.Πάντα δὲ τὰ γιγνόμενα ὑπό τέ τινος γίγνεται καὶ ἔκ τινος καὶ τὶ. Τὸ δὲ τὶ λέγω καθ᾽ ἑκάστην κατηγορίαν᾽ ἢ γὰρ τόδε ἢ ποσὸν ἢ ποιὸν ἢ ποῦ(Met.p. 1032 a 13-15).... The categories, therefore, are not logical forms, but real predicates; they are the general modes in which Being may be expressed. The definite thing, that which comes forward in the process from potentiality to full actuality, can only appear and be spoken of under forms of individuality, quality, quantity and so on. The nine later categories all denote entity in a certain imperfect fashion.The categories then are not to be regarded as heads of predicates, the framework into which predicates can be thrown. They are real determinations of Being—allgemeine Bestimmtheiten, as Hegel calls them. They are notsumma generaof existences, still less are they to be explained as a classification of namable things in general. The objections Mill has taken to the list are entirely irrelevant, and would only have significance if the categories were really—what they are not—an exhaustive division of concrete existences. Grote’s view (Aristotle, i. 108) that Aristotle drew up his list by examining Various popular propositions, and throwing the different predicates into genera, “according as they stood in different logical relation to the subject,” has no foundation. The relation of the predicate category to the subject is not entirely a logical one; it is a relation of real existence, and wants the essential marks of the prepositional form. The logical relations ofτὸ ὂνare provided for otherwise than by the categories.Aristotle has given no intimation of the course of thought by which he was led to his tenfold arrangement, and it seems hopeless to discover it. Trendelenburg in various essays has worked out the idea that the root of the matter is to be found in grammatical considerations, that the categories originated from investigations into grammatical functions, and that a correspondence will be found to obtain between categories and parts of speech. Thus, Substance corresponds to noun substantive, Quantity and Quality to the adjective, Relation partly to the comparative degree and perhaps to the preposition, When and Where to the adverbs of time and place. Action to the active, Passion to the passive of the verb, Position (κεῖσθαι) to the intransitive verb,ἔχεινto the peculiar Greek perfect. That there should be a very close correspondence between the categories and grammatical elements is by no means surprising; that the one were deduced from the other is both philosophically and historically improbable. Reference to the detailed criticisms of Trendelenburg by Ritter, Bonitz, and Zeller will be sufficient.Aristotle has also left us in doubt on another point. Why should there be onlytencategories? and why should these be the ten? Kant and Hegel, it is well known, signalize as the great defect in the Aristotelian categories the want of a principle, and yet some of Aristotle’s expressions would warrant the inference that hehada principle, and that he thought his arrangement exhaustive. The leading idea of all later attempts at reduction to unity of principle,the division into substance and accident, was undoubtedly not overlooked by Aristotle, and Fr. Brentano7has collected with great diligence passages which indicate how the complete list might have been deduced from this primary distinction. His tabular arrangements (pp. 175, 177) are particularly deserving of attention. The results, however, are hardly beyond the reach of doubt.There was no fundamental change in the doctrine of the categories from the time of Aristotle to that of Kant, and only two proposed reclassifications are of such importance as to require notice. The Stoics adopted a fivefold arrangement ofLater Greek.highest classes,γενικώτατα.τὸ ὄνorτὶ, Being, or somewhat in general, was subdivided intoὑποκείμεναor subjects,ποιάor qualities in general, which give definiteness to the blank subject,πὼς ἔχοντα, modes which further determine the subject, andπὼς ἔχοντα, definite relative modes. These categories are so related that each involves the existence of one higher than itself, thus there cannot be aπρός τι πὼς ἔχονwhich does not rest upon or imply aπὼς ἔχον, butπὼς ἔχονis impossible withoutποιόν, which only exists inὑποκείμενον, a form or phase ofτὸ ὄν.8Plotinus, after a lengthy critique of Aristotle’s categories, sets out a twofold list.τὸ ἔν, κίνησις, στάσις, ταὐτότης, ἑτερότηςare the primitive categories (πρῶτα γένη) of the intelligible sphere.οὐσία, πρός τι, ποιά, ποσόν, κίνησιςare the categories of the sensible world. The return to the Platonic classification will not escape notice.Modern philosophy, neglecting altogether the dry and tasteless treatment of the Aristotelian doctrine by scholastic writers, gave a new, a wider and deeper meaning to the categories. They now appear as ultimate or root notions, the metaphysicalModern philosophy.or thought elements, which give coherence and consistency to the material of knowledge, the necessary and universal relations which obtain among the particulars of experience. There was thus to some extent a return to Platonism, but in reality, as might easily be shown, the new interpretation was, with due allowance for difference in point of view, in strict harmony with the true doctrine of Aristotle. The modern theory dates in particular from the time of Kant, who may be said to have reintroduced the term into philosophy. Naturally there are some anticipations in earlier thinkers. The Substance, Attribute and Mode of Cartesianism can hardly be classed among the categories; nor does Leibnitz’s chance suggestion of a fivefold arrangement into Substance, Quantity, Quality, Action and Passion, and Relations, demand any particular notice. Locke, too, has a classification into Substances, Modes and Relations, but in it he has manifestly no intention of drawing up a table of categories. What in his system corresponds most nearly to the modern view of these elements is the division of kinds of real predication. In all judgments of knowledge we predicate either (1) Identity or Diversity, (2) Relation, (3) Co-existence, or necessary connexion, or (4) Real existence. From this the transition was easy to Hume’s important classification ofphilosophical relationsinto those of Resemblance, Identity, Time and Place, Quantity or Number, Quality, Contrariety, Cause and Effect.These attempts at an exhaustive distribution of the necessary relations of all objects of knowledge indicate the direction taken by modern thought, before it received its complete expression from Kant.The doctrine of the categories is the very kernel of the Kantian system, and, through it, of later German philosophy. To explain it fully would be to write the history of that philosophy. The categories are called by Kant Root-notions of theKant.Understanding (Stammbegriffe des Verstandes), and are briefly the specific forms of the a priori or formal element in rational cognition. It is this distinction of matter and form in knowledge that marks off the Kantian from the Aristotelian doctrine. To Kant knowledge was only possible as the synthesis of the material or a posteriori with the formal or a priori. The material to which a priori forms of the understanding were applied was the sensuous content of the pure intuitions, Time and Space. This content could not beknownby sense, but only by intellectual function. But the understanding in the process of knowledge makes use of the universal form of synthesis, the judgment; intellectual function is essentially of the nature of judgment or the reduction of a manifold to unity through a conception. The specific or type forms of such function will, therefore, be expressed in judgments; and a complete classification of the forms of judgments is the key by which one may hope to discover the system of categories. Such a list of judgments Kant thought he found in ordinary logic, and from it he drew up his well-known scheme of the twelve categories. These forms are the determinations of all objects of experience, for it is only through them that the manifold of sense can be reduced to the unity of consciousness, and thereby constituted experience. They are a priori conditions, subjective in one sense, but objective as being universal, necessary and constitutive of experience.The table of logical judgments with corresponding categories is as follows:—Judgments.Categories.UniversalParticularSingularI.Of QuantityUnity.Plurality.Totality.AffirmativeNegativeInfiniteII.Of QualityReality.Negation.Limitation.CategoricalHypotheticalDisjunctiveIII.Of RelationInherence and Subsistence (Substance and Accident).Causality and Dependence (Cause and Effect).Community (Reciprocity).ProblematicalAssertoricApodicticIV.Of ModalityPossibility and Impossibility.Existence and Non-Existence.Necessity and Contingency.Kant, it is well known, criticizes Aristotle severely for having drawn up his categories without a principle, and claims to have disclosed the only possible method by which an exhaustive classification might be obtained. What he criticized in Aristotle is brought against his own procedure by the later German thinkers, particularly Fichte and Hegel. And in point of fact it cannot be denied that Kant has allowed too much completeness to the ordinary logical distribution of propositions; he has given no proof that in these forms are contained all species of synthesis, and in consequence he has failed to show that in the categories, or pure conceptions, are contained all the modes of a priori synthesis. Further, his principle has so far the unity he claimed for it, the unity of a single function, but the specific forms in which such unity manifests itself are not themselves accounted for by this principle. Kant himself hints more than once at the possibility of a completely rational system of the categories, at an evolution from one single movement of thought, and in hisRemarks on the Table of the Categoriesgave a pregnant hint as to the method to be employed. From any complete realization of this suggestion Kant, however, was precluded by one portion of his theory. The categories, although the necessary conditions under which alone an object of experience can be thrown, are merely forms of the mind’s own activity; they apply only to sensuous and consequently subjective material. Outside of and beyond them lies the thing-in-itself, which to Kant represented the ultimately real. This subjectivism was a distinct hiatus in the Kantian system, and against it principally Fichte and Hegel directed criticism. It was manifest that at the root of the wholeFichte.system of categories there lay the synthetizing unity of self-consciousness, and it was upon this unity that Fichte fixed as giving the possibility of a more complete and rigorous deduction of the pure notions of the understanding. Without the act of the Ego, whereby it is self-conscious, there could be no knowledge, and this primitive act or function must be, he saw, thepositionor affirmation of itself by the Ego. The first principle then must be that the Ego posits itself as the Ego, that Ego = Ego, a principle which is unconditioned both in form and matter, and therefore capable of standing absolutely first, of being thepriusin a system. Metaphysically regarded this act of self-position yields the categories of Reality. But, so far as matter is concerned, there cannot be affirmation without negation,omnis determinatio est negatio. The determination of the Ego presupposes or involves the Non-Ego. The form of the proposition in which this second act takes to itself expression, the Ego is not = Not-Ego, is unconditioned, not derivable from the first. It is the absolute antithesis to the primitive thesis. The category of Negation is the result of this second act. From these two propositions, involving absolutely opposed and mutually destructive elements, there results a third which reconciles both in a higher synthesis. The notion in this third is determination or limitation; the Ego and Non-Ego limit, and are opposed to one another. From these three positions Fichte proceeds to evolve the categories by a series of thesis, antithesis and synthesis.In thus seizing upon the unity of self-consciousness as the origin for systematic development, Fichte has clearly taken a step in advance of, and yet in strict harmony with, the Kantian doctrine. For, after all that can be said as to the demonstrated character of formal logic, Kant’s procedure was empirical, and only after the list of categories had been drawn out, did he bring forward into prominence what gave them coherence and reality. The peculiar method of Fichte, also, was nothing but a consistent application of Kant’s own Remark on the Table of the Categories. Fichte’s doctrine, however, is open to some of the objections advanced against Kant. His method is too abstract and external, and wants the unity of a single principle. The first two of his fundamental propositions stand isolated from one another, not to be resolved into a primitive unity. With him, too, the whole stands yet on the plane of subjectivity. He speaks, indeed, of the universal Ego as distinct from the empirical self-consciousness; but the universal does not rise with him to concrete spirit. Nevertheless theWissenschaftslehrecontains the only real advance in the treatment of the categories from the time of Kant to that of Hegel.9This, ofcourse, does not imply that there were not certain elements in Schelling, particularly in theTranscendental Idealism, that are of value in the transition to the later system; but on the whole it is only in Hegel that the whole matter of the Kantian categories has been assimilated and carried to a higher stage. The Hegelian philosophy, in brief, is a system of the categories; and, as it is not intended here to expound that philosophy, it is impossible to give more than a few general and quite external observations as to the Hegelian mode of viewing these elements of thought. With Kant, as has been seen, the categories were still subjective, not as being forms of the individual subject, but as having over against them the world ofnoumenato which they were inapplicable. Self-consciousness, which was, even with Kant, thenodusor kernel whence the categories sprang, was nothing but a logical centre,—the reality was concealed. There was thus a dualism, to overcome which is the first step in the Hegelian system. The principle, if there is to be one, must be universally applicable, all-comprehensive. Self-consciousness is precisely the principle wanted; it is a unity, an identity, containing in itself a multiplicity. The universal in absolute self-consciousness is just pure thinking, which in systematic evolution is the categories; the particular is the natural or multiform, the external as such; the concrete of both is spirit, or self-consciousness come to itself. The same law that obtains among the categories is found adequate to an explanation of the external thing which had so sadly troubled Kant. The categories themselves are moments of the universal of thought, type forms, or definite aspects which thought assumes; determinations,Bestimmungen, as Hegel most frequently calls them. They evolve by the same law that was found to be the essence of ultimate reality—i.e.of self-consciousness. The complete system is pure thought, the Universalpar excellence.After the Hegelian there can hardly be said to have been a philosophical treatment of the categories in Germany which is not more or less a criticism of that system. It does not seem necessary to mention the unimportant modifications introduced by Kuno Fischer, J.E. Erdmann, or others belonging to the school. In the strongly-opposed philosophy of J.F. Herbart the categories can hardly be said to hold a prominent place. They are, with him, the most general notions which are psychologically formed, and he classifies them as follows:—(1) Thing, either as product of thought or as given in experience; (2) Property, either qualitative or quantitative; (3) Relation; (4) The Negated. Along with these he posits as categories of inner process—(1) Sensation, (2) Cognition, (3) Will, (4) Action. Joh. Fr. L. George (1811-1873),10who in the main follows Schleiermacher, draws out a table of categories which shows, in some points, traces of Herbartian influence. His arrangement by enneads, or series of nine, is fanciful, and wanting in inner principle.The most imposing of more recent attempts at a reconstruction of the categories is that of F.A. Trendelenburg. To him the first principle, or primitive reality, is Motion, which is both real as external movement, and ideal as inner construction.Trendelenburg.The necessary conditions of Motion are Time and Space, which are both subjective and objective. From this point onwards are developed the mathematical (point, line, &c.) and real (causality, substance, quantity, quality, &c.) categories which appear as involved in the notion of motion. Matter cannot be regarded as a product of motion; it is the condition of motion, we must think something moved. All these categories, “under the presupposition of motion as the first energy of thought, are ideal and subjective relations; as also, under the presupposition of motion as the first energy of Being, real and objective relations.”11A serious difficulty presents itself in the next category, that of End (Zweck), which can easily be thought for inner activity, but can hardly be reconciled with real motion. Trendelenburg solves the difficulty only empirically, by pointing to the insufficiency of the merely mechanical to account for the organic. The consideration of Modality effects the transition to the forms of logical thought. On the whole, Trendelenburg’s unique fact of motion seems rather a blunder. There is much more involved than he is willing to allow, and motionper seis by no means adequate to self-consciousness. His theory has found little favour.Hermann Ulrici works out a system of the categories from a psychological or logical point of view. To him the fundamental fact of philosophy is the distinguishing activity (unterscheidende Tätigkeit) of thought. Thought is only possibleUlrici.by distinction, difference. The fixed points in the relations of objects upon which this activity turns are the categories, which may be called the forms or laws of thought. They are the aspects of things, notions under which things must be brought, in order to become objects of thought. They are thus the most general predicates or heads of predicates. The categories cannot be completely gathered from experience, nor can they be evolved a priori; but, by attending to the general relations of thought and its purely indefinite matter, and examining what we must predicate in order to know Being, we may attain to a satisfactory list. Such a list is given in great detail in theSystem der Logik(1852), and in briefer, preciser form in theCompendium der Logik(2nd ed., 1872); it is in many points well deserving of attention.The definition of the categories by the able French logician Charles Bernard Renouvier in some respects resembles that of Ulrici. To him the primitive fact is Relation, of which all the categories are but forms. “The categories,” he says, “are theRenouvier, Cousin, Hamilton, Mill.primary and irreducible laws of knowledge, the fundamental relations which determine its form and regulate its movements.” His table and his criticism of the Kantian theory are both of interest.12The criticism of Kant’s categories by Cousin and his own attempted classification are of no importance. Of little more value is the elaborate table drawn out by Sir W. Hamilton.13The generalized category of theConditionedhas but little meaning, and the subordinate categories evolve themselves by no principle, but are arranged after a formal and quite arbitrary manner. They are never brought into connexion with thought itself, nor could they be shown to spring from its nature and relations. J.S. Mill presented, “as a substitute for the abortive classification of Existences, termed the categories of Aristotle,” the following as an enumeration of all nameable things:—(1) Feelings, or states of consciousness; (2) The minds which experience these feelings; (3) Bodies, or external objects which excite certain of those feelings; (4) Successions and co-existences, likenesses and unlikenesses, between feelings or states of consciousness.14This classification proceeds on a quite peculiar view of the categories, and is here presented only for the sake of completeness.By modern psychologists the subject has been closely investigated. Professor G.F. Stout (Manual of Psychology, vol. ii. pp. 312 foll.) defines categories as “forms of cognitive consciousness, universal principles or relations presupposed either in allModern psychologists.cognition or in all cognition of a certain kind.” He then treats External (or Physical) Reality, Space, Time, Causality and “Thinghood” from the standpoint of the perceptual consciousness; showing in what sense the categories of causality, substance and the rest exist in the sphere of perception. As contrasted with the ideational, the perceptual consciousness is concerned with practice. Perception tells the child of things as separate entities, not in their ultimate relations as parts of a coherent whole. G.T. Ladd (Psychology Descriptive and Explanatory, ch. xxi., on “Space, Time and Causality”) defines the categories from the psychological standpoint as “those highly abstract conceptions which the mind frames by reflection upon its own most general modes of behaviour. They are our own notions resulting from co-operation of imagination and judgment, concerning the ultimate and unanalyzable forms of our own existence and development.” In other words, the categories are highly abstract, have no content, and are realized as a kind of thinking which has for its object all the other mental processes.Authorities.—Besides those quoted above, see Eduard v. Hartmann,Kategorienlehre(Leipzig, 1896), and “Begriff der Kategorialfunktion”, inZeitschr. f. Philos. und phil. Krit.cxv. (1899), pp. 9-19; E. König in the same periodical cxiii. (1889), pp. 232-279, and cxiv. (1899), pp. 78-105; F.A. Trendelenburg,Geschichte der Kategorienlehre(1846); P. RagniscoStoria critica delle categorie(2 vols., Florence, 1871); W. WindelbandVom System der Kategorien(Tübingen, 1900); R. Eisler,Wörterbuch der philospphischen Begriffe(Berlin, 1899), pp. 400-409; S. Joda,Studio critico su le categorie(Naples, 1881); H. Vaihinger,Die transcendentale Deduktion der Kategorien(Halle, 1902); H.W.B. Joseph,Introduction to Logic(Oxford, 1906), ch. iii.; F.H. Bradley,Principles of Logic(1883); B. Bosanquet’sKnowledge and Reality(1885, 2nd ed. 1892); histories of philosophy. For further authorities see works quoted underAristotleandKant, and in J.M. Baldwin’sDict. Philos. Psych.vol. iii. pt. 2, p. 685.

Within Greek philosophy itself there were foreshadowings of the Aristotelian doctrine, but nothing so important as to warrant the conclusion that Aristotle was directly influenced by it. Doubtless the One and Many, Being and Non-Being, of theGreek philosophyEleatic dialectic, with their subordinate oppositions, may be called categories, but they are not so in the Aristotelian sense, and have little or nothing in common with the later system. Theirstarting-point and results are wholly diverse. Nor does it appear necessary to do more than mention the Pythagorean table of principles, the number of which is supposed to have given rise to the decuple arrangement adopted by Aristotle. The two classifications have nothing in common; no term in the one list appears in the other; and there is absolutely nothing in the Pythagorean principles which could have led to the theory of the categories.2

One naturally turns to Plato when endeavouring to discover the genesis of any Aristotelian doctrine, and undoubtedly there are in the Platonic writings many detached discussions in which the matter of the categories is touched upon. SpecialPlato.terms also are anticipated at various times,e.g.ποιότηςin theTheaetetus,ποιεῖνandπάσχεινin theGorgias, andπρός τιin theSophist.3But there does not seem to be anything in Plato which one could say gave occasion directly and of itself to the Aristotelian doctrine; and even when we take a more comprehensive view of the Platonic system and inquire what in it corresponds to the widest definition of categories, say as ultimate elements of thought and existence, we receive no very definite answer. The Platonic dialectic never worked out into system, and only in two dialogues do we get anything like a list of ultimate or root-notions. In theSophist, Being, Rest and Motion (τὸ ὄν αύτὸ καὶ στάσις καὶ κίνησις) are laid down asμέγιστα τῶν γενῶν.4To these are presently added the Same and the Other (ταὐτὁν καὶ θάτερον), and out of the consideration of all five some light is cast upon the obscure notion of Non-Being (το μὴ ὄν). In the same dialogue (262 seq.) is found the important distinction ofὄνομαandῥῆμα, noun and verb. ThePhilebuspresents us with a totally distinct classification into four elements—the Infinite, the Finite, the Mixture or Unity of both and the Cause of this unity (τὸ ἄπειρον, τὸ πέρας, ἡ σύμμιξις, ἡ αίτία). It is at once apparent that, however these classifications are related to one another and to the Platonic system, they lie in a different field from that occupied by the Aristotelian categories, and can hardly be said to have anything in common with them.

The Aristotelian doctrine is most distinctly formulated in the short treatiseΚατηγορίαι, which generally occupies the first place among the books of theOrganon. The authenticity of the treatise was doubted in early times by some of theAristotle.commentators, and the doubts have been revived by such scholars as L. Spengel and Carl Prantl. On the other hand, C.A. Brandis, H. Bonitz, and Ed. Zeller are of opinion that the tract is substantially Aristotle’s. The matter is hardly one that can be decided eitherproorconwith anything like certainty; but this is of little moment, for the doctrine of the categories, even of thetencategories, does not stand or fall with only one portion of Aristotle’s works.

It is surprising that there should yet be so much uncertainty as to the real significance of the categories, and that we should be in nearly complete ignorance as to the process of thought by which, Aristotle was led to the doctrine. On both points It is difficult to extract from the matter before us anything approaching a satisfactory solution. The terms employed to denote the categories have been scrutinized with the utmost care, but they give little help. The most important—κ. τοῦ ὄντοςorτῆς οὐσίας, γένη τοῦ ὄντοςorτῶν ὄντων, γένηsimply,τὰ πρῶταorτὰ κοινὰ πρῶτα, αἱ πτῶσεις, orαἱ διαιρέσεις—only indicate that the categories are general classes into which Being as such may be divided, that they aresumma genera. The expressionsγένη τῶν κατηγορίωνandσχήματα τῶν κ., which are used frequently, seem to lead to another and somewhat different view.κατηγορίαbeing taken to mean that which is predicated,γένη τῶν κ.would signify the most general classes of predicates, the framework into the divisions of which all predicates must come. To this interpretation there are objections. The categories must be carefully distinguished from predicables; in the scholastic phraseology the former refer tofirst intentions, the latter tosecond intentions,i.e.the one denote real, the other logical connexion. Further, the categories cannot without careful explanation be defined as predicates; they are this and something more. The most important category,οὐσία, in one of its aspects cannot be predicate at all.

In theΚατηγορίαιAristotle prefixes to his enumeration a grammatico-logical disquisition on homonyms and synonyms, and on the elements of the proposition,i.e.subject and predicate. He draws attention to the fact that things are spoken of either in the connexion known as the proposition,e.g.“a man runs,” or apart from such connexion,e.g.“man” and “runs.” He then proceeds, “Of things spoken of apart from their connexion in a proposition (τῶν κατὰ μηδεμίαν συμπλοκὴν λεγομένων), each signifies either Substance (οὐσία), or Quantity (ποσόν), or Quality (ποιόν), or Relation (πρός τι,) or Where (i.e.Place,ποῦ), or When (i.e.Time,ποτέ), or Position (κεῖσθαι), or Possession (ἔχειν), or Action (ποιεῖν), or Passion (πάσχειν).οὐσία, the first category, is subdivided intoπρώτη οὐσίαor primary substance, which is defined to beτόδε τι, the singular thing in which properties inhere, and to which predicates are attached, andδεύτεραι οὐσίαι, genera or species which can be predicated of primary substances, and are thereforeοὐσία. only in a secondary sense. Nevertheless, they too, after a certain fashion, signify the singular thing,τόδε τι” (K. p. 3 b 12, 13). It is this doctrine ofπρώτη οὐσίαthat has raised doubts with regard to the authenticity of theΚατηγορίαιBut the tenfold classification, which has also been captiously objected to, is given in an acknowledged writing of Aristotle’s (seeTopica, i. 9, p. 103 b 20).5At the same time it is at least remarkable that in two places where the enumeration seems intended to be complete (Met.p. 1017 a 25;An. Pos.i. 22, p. 83 a 21), only eight are mentioned,ἔχεινandκεῖσθαιbeing omitted. In other passages6six, five, four, and three are given, frequently with some addition, such asκαὶ αἱ ἄλλαι κ. It is also to be observed that, despite of this wavering, distinct intimations are given by Aristotle that he regarded his list as complete, and he uses phrases which would seem to indicate that the division had been exhaustively carried out. He admits certainly that some predicates which come under one category might be referred to another, but he declines to deduce all from one highest class, or to recognize any relation of subordination among the several classes.

The full import of the categories will never be adequately reached from the point of view taken up in theΚατηγορίαι, which bears all the marks of an early and preliminary study. For true understanding we must turn to theMetaphysics, where the doctrine is handled at large. The discussion of Being in that work starts with a distinction that at once gives us a clue.τὸ ὄνis spoken of in many ways; of these four are classified—τὸ ὄν κατὰ συμβεβηκός, τὸ ὄν ὼς ὰληθές, τὸ ὄν δυνάμει καὶ ἑνεργείᾳ, andτὸ ὄν κατὰ τὰ σχήματα τῶν κατηγορίων. It is evident from this that the categories can be regarded neither as purely logical nor as purely metaphysical elements. They indicate the general forms or ways in which Being can be predicated; they are determinations of Being regarded as an object of thought, and consequently as matter of speech. It becomes apparent also why the analysis of the categories starts from the singular thing, for it is the primary form under which all that is becomes object of knowledge, and the other categories modify or qualify this real individual.Πάντα δὲ τὰ γιγνόμενα ὑπό τέ τινος γίγνεται καὶ ἔκ τινος καὶ τὶ. Τὸ δὲ τὶ λέγω καθ᾽ ἑκάστην κατηγορίαν᾽ ἢ γὰρ τόδε ἢ ποσὸν ἢ ποιὸν ἢ ποῦ(Met.p. 1032 a 13-15).... The categories, therefore, are not logical forms, but real predicates; they are the general modes in which Being may be expressed. The definite thing, that which comes forward in the process from potentiality to full actuality, can only appear and be spoken of under forms of individuality, quality, quantity and so on. The nine later categories all denote entity in a certain imperfect fashion.

The categories then are not to be regarded as heads of predicates, the framework into which predicates can be thrown. They are real determinations of Being—allgemeine Bestimmtheiten, as Hegel calls them. They are notsumma generaof existences, still less are they to be explained as a classification of namable things in general. The objections Mill has taken to the list are entirely irrelevant, and would only have significance if the categories were really—what they are not—an exhaustive division of concrete existences. Grote’s view (Aristotle, i. 108) that Aristotle drew up his list by examining Various popular propositions, and throwing the different predicates into genera, “according as they stood in different logical relation to the subject,” has no foundation. The relation of the predicate category to the subject is not entirely a logical one; it is a relation of real existence, and wants the essential marks of the prepositional form. The logical relations ofτὸ ὂνare provided for otherwise than by the categories.

Aristotle has given no intimation of the course of thought by which he was led to his tenfold arrangement, and it seems hopeless to discover it. Trendelenburg in various essays has worked out the idea that the root of the matter is to be found in grammatical considerations, that the categories originated from investigations into grammatical functions, and that a correspondence will be found to obtain between categories and parts of speech. Thus, Substance corresponds to noun substantive, Quantity and Quality to the adjective, Relation partly to the comparative degree and perhaps to the preposition, When and Where to the adverbs of time and place. Action to the active, Passion to the passive of the verb, Position (κεῖσθαι) to the intransitive verb,ἔχεινto the peculiar Greek perfect. That there should be a very close correspondence between the categories and grammatical elements is by no means surprising; that the one were deduced from the other is both philosophically and historically improbable. Reference to the detailed criticisms of Trendelenburg by Ritter, Bonitz, and Zeller will be sufficient.

Aristotle has also left us in doubt on another point. Why should there be onlytencategories? and why should these be the ten? Kant and Hegel, it is well known, signalize as the great defect in the Aristotelian categories the want of a principle, and yet some of Aristotle’s expressions would warrant the inference that hehada principle, and that he thought his arrangement exhaustive. The leading idea of all later attempts at reduction to unity of principle,the division into substance and accident, was undoubtedly not overlooked by Aristotle, and Fr. Brentano7has collected with great diligence passages which indicate how the complete list might have been deduced from this primary distinction. His tabular arrangements (pp. 175, 177) are particularly deserving of attention. The results, however, are hardly beyond the reach of doubt.

There was no fundamental change in the doctrine of the categories from the time of Aristotle to that of Kant, and only two proposed reclassifications are of such importance as to require notice. The Stoics adopted a fivefold arrangement ofLater Greek.highest classes,γενικώτατα.τὸ ὄνorτὶ, Being, or somewhat in general, was subdivided intoὑποκείμεναor subjects,ποιάor qualities in general, which give definiteness to the blank subject,πὼς ἔχοντα, modes which further determine the subject, andπὼς ἔχοντα, definite relative modes. These categories are so related that each involves the existence of one higher than itself, thus there cannot be aπρός τι πὼς ἔχονwhich does not rest upon or imply aπὼς ἔχον, butπὼς ἔχονis impossible withoutποιόν, which only exists inὑποκείμενον, a form or phase ofτὸ ὄν.8

Plotinus, after a lengthy critique of Aristotle’s categories, sets out a twofold list.τὸ ἔν, κίνησις, στάσις, ταὐτότης, ἑτερότηςare the primitive categories (πρῶτα γένη) of the intelligible sphere.οὐσία, πρός τι, ποιά, ποσόν, κίνησιςare the categories of the sensible world. The return to the Platonic classification will not escape notice.

Modern philosophy, neglecting altogether the dry and tasteless treatment of the Aristotelian doctrine by scholastic writers, gave a new, a wider and deeper meaning to the categories. They now appear as ultimate or root notions, the metaphysicalModern philosophy.or thought elements, which give coherence and consistency to the material of knowledge, the necessary and universal relations which obtain among the particulars of experience. There was thus to some extent a return to Platonism, but in reality, as might easily be shown, the new interpretation was, with due allowance for difference in point of view, in strict harmony with the true doctrine of Aristotle. The modern theory dates in particular from the time of Kant, who may be said to have reintroduced the term into philosophy. Naturally there are some anticipations in earlier thinkers. The Substance, Attribute and Mode of Cartesianism can hardly be classed among the categories; nor does Leibnitz’s chance suggestion of a fivefold arrangement into Substance, Quantity, Quality, Action and Passion, and Relations, demand any particular notice. Locke, too, has a classification into Substances, Modes and Relations, but in it he has manifestly no intention of drawing up a table of categories. What in his system corresponds most nearly to the modern view of these elements is the division of kinds of real predication. In all judgments of knowledge we predicate either (1) Identity or Diversity, (2) Relation, (3) Co-existence, or necessary connexion, or (4) Real existence. From this the transition was easy to Hume’s important classification ofphilosophical relationsinto those of Resemblance, Identity, Time and Place, Quantity or Number, Quality, Contrariety, Cause and Effect.

These attempts at an exhaustive distribution of the necessary relations of all objects of knowledge indicate the direction taken by modern thought, before it received its complete expression from Kant.

The doctrine of the categories is the very kernel of the Kantian system, and, through it, of later German philosophy. To explain it fully would be to write the history of that philosophy. The categories are called by Kant Root-notions of theKant.Understanding (Stammbegriffe des Verstandes), and are briefly the specific forms of the a priori or formal element in rational cognition. It is this distinction of matter and form in knowledge that marks off the Kantian from the Aristotelian doctrine. To Kant knowledge was only possible as the synthesis of the material or a posteriori with the formal or a priori. The material to which a priori forms of the understanding were applied was the sensuous content of the pure intuitions, Time and Space. This content could not beknownby sense, but only by intellectual function. But the understanding in the process of knowledge makes use of the universal form of synthesis, the judgment; intellectual function is essentially of the nature of judgment or the reduction of a manifold to unity through a conception. The specific or type forms of such function will, therefore, be expressed in judgments; and a complete classification of the forms of judgments is the key by which one may hope to discover the system of categories. Such a list of judgments Kant thought he found in ordinary logic, and from it he drew up his well-known scheme of the twelve categories. These forms are the determinations of all objects of experience, for it is only through them that the manifold of sense can be reduced to the unity of consciousness, and thereby constituted experience. They are a priori conditions, subjective in one sense, but objective as being universal, necessary and constitutive of experience.

The table of logical judgments with corresponding categories is as follows:—

Kant, it is well known, criticizes Aristotle severely for having drawn up his categories without a principle, and claims to have disclosed the only possible method by which an exhaustive classification might be obtained. What he criticized in Aristotle is brought against his own procedure by the later German thinkers, particularly Fichte and Hegel. And in point of fact it cannot be denied that Kant has allowed too much completeness to the ordinary logical distribution of propositions; he has given no proof that in these forms are contained all species of synthesis, and in consequence he has failed to show that in the categories, or pure conceptions, are contained all the modes of a priori synthesis. Further, his principle has so far the unity he claimed for it, the unity of a single function, but the specific forms in which such unity manifests itself are not themselves accounted for by this principle. Kant himself hints more than once at the possibility of a completely rational system of the categories, at an evolution from one single movement of thought, and in hisRemarks on the Table of the Categoriesgave a pregnant hint as to the method to be employed. From any complete realization of this suggestion Kant, however, was precluded by one portion of his theory. The categories, although the necessary conditions under which alone an object of experience can be thrown, are merely forms of the mind’s own activity; they apply only to sensuous and consequently subjective material. Outside of and beyond them lies the thing-in-itself, which to Kant represented the ultimately real. This subjectivism was a distinct hiatus in the Kantian system, and against it principally Fichte and Hegel directed criticism. It was manifest that at the root of the wholeFichte.system of categories there lay the synthetizing unity of self-consciousness, and it was upon this unity that Fichte fixed as giving the possibility of a more complete and rigorous deduction of the pure notions of the understanding. Without the act of the Ego, whereby it is self-conscious, there could be no knowledge, and this primitive act or function must be, he saw, thepositionor affirmation of itself by the Ego. The first principle then must be that the Ego posits itself as the Ego, that Ego = Ego, a principle which is unconditioned both in form and matter, and therefore capable of standing absolutely first, of being thepriusin a system. Metaphysically regarded this act of self-position yields the categories of Reality. But, so far as matter is concerned, there cannot be affirmation without negation,omnis determinatio est negatio. The determination of the Ego presupposes or involves the Non-Ego. The form of the proposition in which this second act takes to itself expression, the Ego is not = Not-Ego, is unconditioned, not derivable from the first. It is the absolute antithesis to the primitive thesis. The category of Negation is the result of this second act. From these two propositions, involving absolutely opposed and mutually destructive elements, there results a third which reconciles both in a higher synthesis. The notion in this third is determination or limitation; the Ego and Non-Ego limit, and are opposed to one another. From these three positions Fichte proceeds to evolve the categories by a series of thesis, antithesis and synthesis.

In thus seizing upon the unity of self-consciousness as the origin for systematic development, Fichte has clearly taken a step in advance of, and yet in strict harmony with, the Kantian doctrine. For, after all that can be said as to the demonstrated character of formal logic, Kant’s procedure was empirical, and only after the list of categories had been drawn out, did he bring forward into prominence what gave them coherence and reality. The peculiar method of Fichte, also, was nothing but a consistent application of Kant’s own Remark on the Table of the Categories. Fichte’s doctrine, however, is open to some of the objections advanced against Kant. His method is too abstract and external, and wants the unity of a single principle. The first two of his fundamental propositions stand isolated from one another, not to be resolved into a primitive unity. With him, too, the whole stands yet on the plane of subjectivity. He speaks, indeed, of the universal Ego as distinct from the empirical self-consciousness; but the universal does not rise with him to concrete spirit. Nevertheless theWissenschaftslehrecontains the only real advance in the treatment of the categories from the time of Kant to that of Hegel.9This, ofcourse, does not imply that there were not certain elements in Schelling, particularly in theTranscendental Idealism, that are of value in the transition to the later system; but on the whole it is only in Hegel that the whole matter of the Kantian categories has been assimilated and carried to a higher stage. The Hegelian philosophy, in brief, is a system of the categories; and, as it is not intended here to expound that philosophy, it is impossible to give more than a few general and quite external observations as to the Hegelian mode of viewing these elements of thought. With Kant, as has been seen, the categories were still subjective, not as being forms of the individual subject, but as having over against them the world ofnoumenato which they were inapplicable. Self-consciousness, which was, even with Kant, thenodusor kernel whence the categories sprang, was nothing but a logical centre,—the reality was concealed. There was thus a dualism, to overcome which is the first step in the Hegelian system. The principle, if there is to be one, must be universally applicable, all-comprehensive. Self-consciousness is precisely the principle wanted; it is a unity, an identity, containing in itself a multiplicity. The universal in absolute self-consciousness is just pure thinking, which in systematic evolution is the categories; the particular is the natural or multiform, the external as such; the concrete of both is spirit, or self-consciousness come to itself. The same law that obtains among the categories is found adequate to an explanation of the external thing which had so sadly troubled Kant. The categories themselves are moments of the universal of thought, type forms, or definite aspects which thought assumes; determinations,Bestimmungen, as Hegel most frequently calls them. They evolve by the same law that was found to be the essence of ultimate reality—i.e.of self-consciousness. The complete system is pure thought, the Universalpar excellence.

After the Hegelian there can hardly be said to have been a philosophical treatment of the categories in Germany which is not more or less a criticism of that system. It does not seem necessary to mention the unimportant modifications introduced by Kuno Fischer, J.E. Erdmann, or others belonging to the school. In the strongly-opposed philosophy of J.F. Herbart the categories can hardly be said to hold a prominent place. They are, with him, the most general notions which are psychologically formed, and he classifies them as follows:—(1) Thing, either as product of thought or as given in experience; (2) Property, either qualitative or quantitative; (3) Relation; (4) The Negated. Along with these he posits as categories of inner process—(1) Sensation, (2) Cognition, (3) Will, (4) Action. Joh. Fr. L. George (1811-1873),10who in the main follows Schleiermacher, draws out a table of categories which shows, in some points, traces of Herbartian influence. His arrangement by enneads, or series of nine, is fanciful, and wanting in inner principle.

The most imposing of more recent attempts at a reconstruction of the categories is that of F.A. Trendelenburg. To him the first principle, or primitive reality, is Motion, which is both real as external movement, and ideal as inner construction.Trendelenburg.The necessary conditions of Motion are Time and Space, which are both subjective and objective. From this point onwards are developed the mathematical (point, line, &c.) and real (causality, substance, quantity, quality, &c.) categories which appear as involved in the notion of motion. Matter cannot be regarded as a product of motion; it is the condition of motion, we must think something moved. All these categories, “under the presupposition of motion as the first energy of thought, are ideal and subjective relations; as also, under the presupposition of motion as the first energy of Being, real and objective relations.”11A serious difficulty presents itself in the next category, that of End (Zweck), which can easily be thought for inner activity, but can hardly be reconciled with real motion. Trendelenburg solves the difficulty only empirically, by pointing to the insufficiency of the merely mechanical to account for the organic. The consideration of Modality effects the transition to the forms of logical thought. On the whole, Trendelenburg’s unique fact of motion seems rather a blunder. There is much more involved than he is willing to allow, and motionper seis by no means adequate to self-consciousness. His theory has found little favour.

Hermann Ulrici works out a system of the categories from a psychological or logical point of view. To him the fundamental fact of philosophy is the distinguishing activity (unterscheidende Tätigkeit) of thought. Thought is only possibleUlrici.by distinction, difference. The fixed points in the relations of objects upon which this activity turns are the categories, which may be called the forms or laws of thought. They are the aspects of things, notions under which things must be brought, in order to become objects of thought. They are thus the most general predicates or heads of predicates. The categories cannot be completely gathered from experience, nor can they be evolved a priori; but, by attending to the general relations of thought and its purely indefinite matter, and examining what we must predicate in order to know Being, we may attain to a satisfactory list. Such a list is given in great detail in theSystem der Logik(1852), and in briefer, preciser form in theCompendium der Logik(2nd ed., 1872); it is in many points well deserving of attention.

The definition of the categories by the able French logician Charles Bernard Renouvier in some respects resembles that of Ulrici. To him the primitive fact is Relation, of which all the categories are but forms. “The categories,” he says, “are theRenouvier, Cousin, Hamilton, Mill.primary and irreducible laws of knowledge, the fundamental relations which determine its form and regulate its movements.” His table and his criticism of the Kantian theory are both of interest.12The criticism of Kant’s categories by Cousin and his own attempted classification are of no importance. Of little more value is the elaborate table drawn out by Sir W. Hamilton.13The generalized category of theConditionedhas but little meaning, and the subordinate categories evolve themselves by no principle, but are arranged after a formal and quite arbitrary manner. They are never brought into connexion with thought itself, nor could they be shown to spring from its nature and relations. J.S. Mill presented, “as a substitute for the abortive classification of Existences, termed the categories of Aristotle,” the following as an enumeration of all nameable things:—(1) Feelings, or states of consciousness; (2) The minds which experience these feelings; (3) Bodies, or external objects which excite certain of those feelings; (4) Successions and co-existences, likenesses and unlikenesses, between feelings or states of consciousness.14This classification proceeds on a quite peculiar view of the categories, and is here presented only for the sake of completeness.

By modern psychologists the subject has been closely investigated. Professor G.F. Stout (Manual of Psychology, vol. ii. pp. 312 foll.) defines categories as “forms of cognitive consciousness, universal principles or relations presupposed either in allModern psychologists.cognition or in all cognition of a certain kind.” He then treats External (or Physical) Reality, Space, Time, Causality and “Thinghood” from the standpoint of the perceptual consciousness; showing in what sense the categories of causality, substance and the rest exist in the sphere of perception. As contrasted with the ideational, the perceptual consciousness is concerned with practice. Perception tells the child of things as separate entities, not in their ultimate relations as parts of a coherent whole. G.T. Ladd (Psychology Descriptive and Explanatory, ch. xxi., on “Space, Time and Causality”) defines the categories from the psychological standpoint as “those highly abstract conceptions which the mind frames by reflection upon its own most general modes of behaviour. They are our own notions resulting from co-operation of imagination and judgment, concerning the ultimate and unanalyzable forms of our own existence and development.” In other words, the categories are highly abstract, have no content, and are realized as a kind of thinking which has for its object all the other mental processes.

Authorities.—Besides those quoted above, see Eduard v. Hartmann,Kategorienlehre(Leipzig, 1896), and “Begriff der Kategorialfunktion”, inZeitschr. f. Philos. und phil. Krit.cxv. (1899), pp. 9-19; E. König in the same periodical cxiii. (1889), pp. 232-279, and cxiv. (1899), pp. 78-105; F.A. Trendelenburg,Geschichte der Kategorienlehre(1846); P. RagniscoStoria critica delle categorie(2 vols., Florence, 1871); W. WindelbandVom System der Kategorien(Tübingen, 1900); R. Eisler,Wörterbuch der philospphischen Begriffe(Berlin, 1899), pp. 400-409; S. Joda,Studio critico su le categorie(Naples, 1881); H. Vaihinger,Die transcendentale Deduktion der Kategorien(Halle, 1902); H.W.B. Joseph,Introduction to Logic(Oxford, 1906), ch. iii.; F.H. Bradley,Principles of Logic(1883); B. Bosanquet’sKnowledge and Reality(1885, 2nd ed. 1892); histories of philosophy. For further authorities see works quoted underAristotleandKant, and in J.M. Baldwin’sDict. Philos. Psych.vol. iii. pt. 2, p. 685.

(R. Ad.; X.)

1For details of this and other Hindu systems see H. T. Colebrooke,Miscellaneous Essays(1837; new ed., E. B. Cowell, 1873); H. H. Wilson,Essays and Lectures on the Religions of the Hindus(1861-1862); Monier Williams,Indian Wisdom(4th ed., 1893); A. E. Gough’sVaiseshika-Sutras(Benares, 1873), andPhilosophy of the Upanishads(London, 1882, 1891); Max Müller,Sanskrit Literature, and particularly his appendix to Thomson’sLaws of Thought.2The supposed origin of that theory in the treatiseπερὶ τοῦ παντός, ascribed to Archytas (q.v.), has been proved to be an error. The treatise itself dates in all probability from the Neo-Pythagorean schools of the 2nd centurya.d.3Prantl,Ges. der Logik, i. 74-75; F.A. Trendelenburg,Kategorienlehre, 209. n.4Soph. 254 D.5Against this passage even Prantl can raise no objection of any moment; seeGes. der Logik, i. 206.n.6See Bonitz,Iridex Aristotelicus,s.v., and Prantl,Ges. der Logik,i. 207.7Brentano,Bedeutung des Seienden nach A., pp. 148-178.8For detailed examination of the Stoic categories, see Prantl,Ges. d. Logik, i. 428 sqq.; Zeller,Ph. d. Griech.iii. 1, 82, sqq,; Trendelenburg,Kateg.p. 217.9It does not seem necessary to do more than refer to the slight alterations made on Kant’s Table of Categories by J.G. von Herder (in theMetakritik), by Solomon Malmon (in thePropadeutik zu einer neuen Theorie des Denkens), by J.F. Fries (in theNeue Kritik der Vernunft), or by Schopenhauer, who desired to reduce all the categories to one—that of Causality. We should require a new philosophical vocabulary even to translate the extraordinary compounds in which K.C.F. Krause expounds his theory of the categories. Notices of the changes introduced by Antonio Rosmini-Serbati, and of Vincenzo Gioberti’s remarkable theory, will be found in Ragnisco’s work referred to below.10System der Metaphysik(1844).11Logische Untersuchungen, i. 376-377.12Essais de critique générale(2nd ed.),La Logique, i. pp. 184, 190, 207-225.13Discussions, p. 577.14Logic, i. 83; cf. Bain,Ded. Log., App. C.

2The supposed origin of that theory in the treatiseπερὶ τοῦ παντός, ascribed to Archytas (q.v.), has been proved to be an error. The treatise itself dates in all probability from the Neo-Pythagorean schools of the 2nd centurya.d.

3Prantl,Ges. der Logik, i. 74-75; F.A. Trendelenburg,Kategorienlehre, 209. n.

4Soph. 254 D.

5Against this passage even Prantl can raise no objection of any moment; seeGes. der Logik, i. 206.n.

6See Bonitz,Iridex Aristotelicus,s.v., and Prantl,Ges. der Logik,i. 207.

7Brentano,Bedeutung des Seienden nach A., pp. 148-178.

8For detailed examination of the Stoic categories, see Prantl,Ges. d. Logik, i. 428 sqq.; Zeller,Ph. d. Griech.iii. 1, 82, sqq,; Trendelenburg,Kateg.p. 217.

9It does not seem necessary to do more than refer to the slight alterations made on Kant’s Table of Categories by J.G. von Herder (in theMetakritik), by Solomon Malmon (in thePropadeutik zu einer neuen Theorie des Denkens), by J.F. Fries (in theNeue Kritik der Vernunft), or by Schopenhauer, who desired to reduce all the categories to one—that of Causality. We should require a new philosophical vocabulary even to translate the extraordinary compounds in which K.C.F. Krause expounds his theory of the categories. Notices of the changes introduced by Antonio Rosmini-Serbati, and of Vincenzo Gioberti’s remarkable theory, will be found in Ragnisco’s work referred to below.

10System der Metaphysik(1844).

11Logische Untersuchungen, i. 376-377.

12Essais de critique générale(2nd ed.),La Logique, i. pp. 184, 190, 207-225.

13Discussions, p. 577.

14Logic, i. 83; cf. Bain,Ded. Log., App. C.

CATENARY(from Lat.catena, a chain), in mathematics, the curve assumed by a uniform chain or string hanging freely between two supports. It was investigated by Galileo, who erroneously determined it to be a parabola; Jungius detected Galileo’s error, but the true form was not discovered until 1691, when James Bernoulli published it as a problem in theActa Eruditorum. Bernoulli also considered the cases when (1) the chain was of variable density, (2) extensible, (3) acted upon at each point by a force directed to a fixed centre. These curves attracted much attention and were discussed by John Bernoulli, Leibnitz, Huygens, David Gregory and others.

The mechanical properties of the curves are treated in the articleMechanics, where various forms are illustrated. The simple catenary is shown in the figure. The cartesian equation referred to the axis and directrix is y = c cosh (x/c) or y = ½c(ex/c+ e−x/c); other forms are s = c sinh (x/c) and y² = c² + s², s being the arc measured from the vertex; the intrinsic equation is s = c tan ψ. The radius of curvature and normal are each equal to c sec² ψ.The surface formed by revolving the catenary about its directrix is named thealysseide. It is a minimal surface,i.e.the catenary solves the problem: to find a curve joining two given points, which when revolved about a line co-planar with the points traces a surface of minimum area (seeVariations, Calculus of).The involute of the catenary is called thetractory,tractrixorantifrictioncurve; it has a cusp at the vertex of the catenary, and is asymptotic to the directrix. The cartesian equation isx = √ (c² − y²) + ½c log [ {c − √ (c² − y²)} / {c + √ (c² + y²)} ],and the curve has the geometrical property that the length of its tangent is constant. It is named the tractory, since a weight placed on the ground and drawn along by means of a flexible string by a person travelling in a straight line, the weight not being in this line, describes the curve in question. It is named the antifriction curve, since a pivot and step having the form of the surface generated by revolving the curve about its vertical axis wear away equally (seeMechanics:Applied).

The surface formed by revolving the catenary about its directrix is named thealysseide. It is a minimal surface,i.e.the catenary solves the problem: to find a curve joining two given points, which when revolved about a line co-planar with the points traces a surface of minimum area (seeVariations, Calculus of).

The involute of the catenary is called thetractory,tractrixorantifrictioncurve; it has a cusp at the vertex of the catenary, and is asymptotic to the directrix. The cartesian equation is

x = √ (c² − y²) + ½c log [ {c − √ (c² − y²)} / {c + √ (c² + y²)} ],

and the curve has the geometrical property that the length of its tangent is constant. It is named the tractory, since a weight placed on the ground and drawn along by means of a flexible string by a person travelling in a straight line, the weight not being in this line, describes the curve in question. It is named the antifriction curve, since a pivot and step having the form of the surface generated by revolving the curve about its vertical axis wear away equally (seeMechanics:Applied).

CATERAN(from the Gaelicceathairne, a collective word meaning “peasantry”), the band of fighting men of a Highland clan; hence the term is applied to the Highland, and later to any, marauders or cattle-lifters.

CATERHAM,an urban district in the Wimbledon parliamentary division of Surrey, England, 20 m. S. of London by the South-Eastern & Chatham railway. Pop. (1901) 9486. It lies in a healthy, hilly district, and has grown in modern times from a village into a large residential town. There are large barracks in the neighbourhood, and the Metropolitan lunatic asylum is close to the town.

CATERPILLAR,the popular name of the larva of various insects, particularly of butterflies and moths (seeLepidoptera,Hexapoda,Metamorphosis). The word appears first in the formcaterpyl(Promptorium Parvulorum, about the middle of the 15th century). This may be the original form, with the addition of-aror-er; if so, it represents the O. Fr.chatepeloseorchatepeleuse,i.e.“hairy-cat” (chat, cat, andpelouse, hairy, Lat.pilosus), a name applied to the hairy caterpillar, and also according to Cotgrave to a weevil. The use of “cat” in this connexion is paralleled by the Swiss name for a caterpillar,teufelskatz, and the popular English name for the blossom of the willow, “catkin,” somewhat resembling a caterpillar (cf. “palmer”); the modern French ischenille, Latincanicula, a little dog. The termination of the word seems to have been early connected with “piller,” a robber, plunderer from the destructive habits of the larva, cf. Joel i. 4—”That which the palmer-worm hath left, hath the locust eaten.” The spelling “caterpillar,” a 17th century corruption, has been the usual form since Johnson.

CATESBY, ROBERT(1573-1605), English conspirator, son of Sir William Catesby of Lapworth in Warwickshire, a prominent recusant who was a descendant of Sir William Catesby, speaker of the House of Commons in 1484, executed by Henry VII. after the battle of Bosworth, was born in 1573, and entered Gloucester Hall (now Worcester College), Oxford, in 1586. He possessed a considerable estate, and was said to be wild and extravagant in his youth. In 1596 he was one of those arrested on suspicion during an illness of Queen Elizabeth. In 1601 he took part in the rebellion of Essex, was wounded in the fight and imprisoned, but finally pardoned on the payment of an enormous fine, to obtain which he was forced to sell a portion of his property. In 1602 he despatched Thomas Winter and the Jesuit TesimondaliasGreenway to Spain to induce Philip III. to organize an invasion of England, and in 1603, after James’s accession, he was named as an accomplice in the “Bye Plot.” Catesby was a man of great beauty of person, “above 2 yards high,” says Father Gerard, “and though slender, yet as well-proportioned to his height as any man one should see.” He possessed a clear head and unflinching courage, and with a strong determination and fascinating manner mastered the minds of his associates and overpowered all opposition. He was, however, headstrong, wilful and imprudent, fit for action, but incapable of due deliberation, and entirely wanting in foresight. Exasperated by his personal misfortunes and at the repressive measures under which his co-religionists were suffering, and blinded by a religious zeal which amounted to fanaticism, he was now to be the chief instigator of the famous Gunpowder Plot, which must in any event have brought disaster upon the Roman Catholic cause. The idea of some great stroke seems to have first entered his mind in May 1603. About the middle of January 1604 he imparted his scheme of blowing up the Parliament House to his cousin Thomas Winter, subsequently taking in Guy Fawkes and several other conspirators and overcoming all fears and scruples. But it was his determination, from which he would not be shaken, not to allow warning to be given to the Roman Catholic peers that was the actual cause of the failure of the plot. A fatal mistake had been made in imparting the secret to Francis Tresham (q.v.), in order to secure his financial assistance; and there is scarcely any doubt that he was the author of the celebrated letter to his brother-in-law, Lord Monteagle, which betrayed the conspiracy to the government, on the 26th of October. On receiving the news of the letter on the 28th, Catesby exhibited extraordinary coolness and fortitude, and refused to abandon the attempt, hoping that the government might despise the warning and still neglect precautions; and his confidence was strengthened by Fawkes’s report that nothing in the cellar had been touched or tampered with. On the 2nd of November his resolution was shaken by Tresham’s renewed entreaties that he would flee, and his positive assurance that Salisbury knew everything. On the evening of the 3rd, however, he was again, through Percy’s insistence, persuaded to stand firm and hazard the great stroke. The rest of the story is told in the articleGunpowder Plot. Here it need only be said that Catesby, after the discovery of the conspiracy, fled with his fellow-plotters, taking refuge ultimately at Holbeche in Staffordshire, where on the night of the 8th of November he was overtaken and killed. He had married Catherine, daughter of Thomas Leigh of Stoneleigh, Warwickshire, and left one son, Robert, who inherited that part of the family estate which had been settled on Catesby’s mother and was untouched by the attainder, and who is said to have married a daughter of Thomas Percy.

CAT-FISH,the name usually applied to the fishes of the familySiluridae, in allusion to the long barbels or feelers about the mouth, which have been compared to the whiskers of a cat. TheSiluridaeare a large and varied group, mostly inhabitants of fresh waters; some of them by their singular form and armature are suggestive of the Devonian mailed fishes, and were placed at one time in their vicinity by L. Agassiz. Even such authorities as T.H. Huxley and E.D. Cope were inclined to ascribe ganoid affinities to theSiluridae; but this view has gradually lost ground, and most modern ichthyologists, if not all, have adopted the conclusions of M. Sagemehl, who has placed theSiluridaenear the carps and Characinids in the group Ostariophysi. The Silurids and Cyprinids may be regarded as two parallel series derived from some common stock which cannot have been very different from the existing Characinids. In spite of the archaic appearance of some of its members, the familySiluridaedoes not appear to extend far back in time, its oldest known representative being theBucklandium diluviiof the Lower Eocene (London Clay) of Sheppey. A great number of forms were placed by Cuvier and his successors in the familySiluridae, which has since been broken up by T. Gill and other American authors into several families, united under the name of Nematognathi. A middle course appears the more reasonable to thepresent writer, who has divided theSiluridaeof Cuvier into three families, with the following definitions:—

Siluridae—ribs attached to strong parapophyses; operculum well developed.

Loricariidae—ribs sessile; parapophyses absent; operculum more or less developed.

Aspredinidae—ribs sessile; strong parapophyses; operculum absent.

These three families may be defined among the Ostariophysi by having the parietal bones fused with the supraoccipital, no symplectic, the body naked or with bony scutes, the mouth usually toothed, with barbels, and usually an adipose dorsal fin.

TheSiluridaeembrace more than one thousand species, spread over the fresh waters of all parts of the world, but mostly from between the tropics. They are absent from western Europe and north-west Africa, and from North America west of the Rocky Mountains, but this deficiency has been made good by now, the introduction ofAmiurus nebulosusand allied species in various parts of continental Europe and California having proved a success. Only a few forms are marine (Plotosus,Arius,Galeichthys).

The species which has given the name to the whole family is the “Wels” of the Germans,Silurus glanis, the largest European fresh-water fish, inhabiting the greater part of Europe from the Rhine eastwards and north of the Alps. Its head is large and broad, its mouth wide, furnished with six barbels, of which those of the upper jaw are very long. Both jaws and the palate are armed with broad bands of small closely-set teeth, which give the bones a rasp-like appearance. The eyes are exceedingly small. The short body terminates in a long, compressed, muscular tail, and the whole fish is covered with a smooth, scaleless, slippery skin. Specimens of 4 and 5 ft. in length, and of 50 to 80 ℔ in weight, are of common occurrence, and the fish grows to 10 ft., with a weight of 400 ℔, in the Danube. Its food consists chiefly of other bottom-feeding fishes, and in inland countries it is considered one of the better class of food fishes. Stories about children having been found in the stomach of very large individuals are probably inventions. An allied species (S. aristotelis) is found in Greece.

TheClariasandHeterobranchusof Africa and south-eastern Asia have an elongate, more or less eel-shaped body, with long dorsal and anal fins, and are known to be able to live a long time out of water, being provided with an accessory dendritic breathing organ situated above the gills. Some species live in burrows during the dry season, crawling about at night in search of food. The common Nile species, the “Harmoot” (Clarias lazera), occurs abundantly in the Lake of Galilee and was included in, if not chiefly aimed at, by the Mosaic law which forbade the Jews to eat scaleless fishes, a prohibition which has been extended to eels in spite of the obvious presence of minute scales in the latter.

TheSaccobranchusof India and Ceylon, a genus more nearly related toSilurus, have also an accessory organ for breathing atmospheric air. It consists of a long sac behind the gill-cavity, extending far back on each side of the body under the muscles.

In the majority of theSiluridae, called by A. Gunther theProteropterae, a section extremely numerous in species, and represented throughout the tropics, the dorsal fin consists of a short-rayed and an adipose portion, the former belonging to the abdominal vertebral column; the anal is always much shorter than the tail. The gill-membranes are not confluent with the skin of the isthmus; they have a free posterior margin. When a nasal barbel is present, it belongs to the posterior nostril. This section includes among many others the genusBagrus, of which the bayad (B. bayad) and docmac (B. docmac) frequently come under the notice of travellers on the Nile; they grow to a length of 5 ft. and are eaten.

Of the “cat-fishes” of North America (Amiurus), locally called “bull-heads” or “horned-pouts,” with eight barbels, some twenty species are known. Some of them are valued as food, especially one which is abundant in the ponds of New England, and capable of easy introduction into other localities (A. nebulosus). Others which inhabit the great lakes (A. nigricans) and the Mississippi (A. ponderosus) often exceed the weight of 100 ℔PlatystomaandPimeloduspeople the rivers and lakes of tropical America, and many of them are conspicuous in this fauna by the ornamentation of their body, by long spatulate snouts, and by their great size.

The genusAriusis composed of a great number of species and has the widest distribution of all Silurids, being represented in almost all tropical countries which are drained by large rivers. Most of the species live in salt water. They possess six barbels, and their head is extensively osseous on its upper surface; their dorsal and pectoral spines are generally developed into powerful weapons.Bagarius, one of the largest Silurids of the rivers of India and Java, exceeding a length of 6 ft., differs fromAriusin having eight barbels and the head covered with skin.

R. Semon has made observations in Queensland on the habits ofArius australis, which builds nests in the sandy bed of the Burnett river. These nests consist of circular basin-like excavations about 20 in. in diameter, at the bottom of which the eggs are laid and covered over by several layers of large stones. In the marine and estuarine species ofArius, GalcichthysandOsteogeniosus, the male, more rarely the female, carries the eggs in the mouth and pharynx; these eggs, few in number, are remarkably large, measuring as much as 17 or 18 millimetres in diameter inArius commusonii, a fish 3 or 4 ft. in length.

The common North AmericanAmiurus nebulosusalso takes care of its eggs, which are deposited beneath protecting objects at the bottom of the water, failing which both parents join in excavating a sort of nest in the mud. The male watches over the eggs, and later leads the young in great schools near the shore, seemingly caring for them as the hen for her chickens.

In theSiluridae Stenobranchiaeof Gunther the dorsal fin consists of an adipose portion and a short-rayed fin which belongs to the abdominal vertebral column, and, like the adipose fin, may be sometimes absent. The gill-membranes are confluent with the skin of the isthmus. The Silurids belonging to this section are either South American or African. Among the former we notice specially the genusDoras, which is distinguished by having a series of bony scutes along the middle of the side. The narrowness of their gill-openings appears to have developed in them a habit which has excited the attention of all naturalists who have visited the countries bordering upon the Atlantic rivers of tropical America, viz. the habit of travelling during seasons of drought from a piece of water about to dry up to ponds of greater capacity. These journeys are occasionally of such a length that the fish have to travel all night; they are so numerousthat the Indians fill many baskets of them. J. Hancock supposes that the fish carry a small supply of water with them in their gill-cavity, which they can easily retain by closing their branchial apertures. The same naturalist adds that they make regular nests, in which they cover up their eggs with care and defend them—male and female uniting in this parental duty until the eggs are hatched.Synodontisis an African genus and common in the Nile, where the various species are known by the name of “Shal.” They frequently occur among the representations of animals left by the ancient Egyptians. The upper part of their head is protected by strong osseous scutes, and both the dorsal and pectoral fins are armed with powerful spines. Their mouth is small, surrounded by six barbels, which are more or less fringed with a membrane or with branched tentacles.

The curious fact of some species ofSynodontishaving the lower parts darker than the upper, some being whitish above and blackish beneath, appears to be connected with their habit of swimming in a reversed position, the Belly turned upwards. This habit, known to the ancient Egyptians, who have frequently represented them in that attitude, has been described by E. Geoffrey, who says they nearly constantly swim on their back, moving quite freely forwards and sidewards; but if alarmed, they revert to the normal position to escape more rapidly.

The electric cat- or sheath-fishes (Malopterurus) have been referred to the same section. Externally they are at once recognized by the absence of a rayed dorsal fin, of which only a rudiment remains as a small interneural spine concealed below the skin. The entire fish is covered with soft, villose skin, an osseous defensive armour having become unnecessary in consequence of the development of a powerful electric apparatus, the strength of which, however, is exceeded by that of the electric eel and the large species ofTorpedo.

The electric organ ofMalopterurusdiffers essentially from that of other fishes provided with such batteries, being part of the tegumentary system instead of being derived from the muscles. It consists of rhomboidal cells of a fine gelatinous substance immediately under the skin. It is put into action by a single ganglionic cell at the anterior extremity of the spinal cord. Contrary to what takes place in other electric fishes, the current proceeds from the head to the tail.

The electric cat-fish, which grows to a length of 3 ft. in the Congo, has a wide distribution in Africa, extending from the Nile to the Zambezi and from the Senegal to the Congo. It was well known to the ancient Egyptians, who have depicted it in their mural paintings and elsewhere, and an account of its electric properties was given by an Arab physician of the 12th century; then as now the fish was known under the suggestive name ofRaadorRaash, which means “thunder.”

Günther’sSiluridae Branchicolaecomprise the smallest and least developed members of the family; they are referred to two genera only from South America,StegophilusandVandellia, the smallest of which does not exceed the length of 2 in. Their body is soft, narrow, cylindrical and elongate; the dorsal and anal fins short; the vent far behind the middle of the length of the body; gill-membranes confluent with the skin of the isthmus. Each maxillary is provided with a small barbel; and the gill-covers are armed with short stiff spines. Their small size notwithstanding, these Silurids are well known to the Brazilians, who accuse them of entering and ascending the urethra of persons while bathing, causing inflammation and sometimes death. Some certainly live parasitically in the gill-cavity of large Silurids, and F. Silvestri has observedStegophilus insidiosusto suck the blood in the gills ofPlatystoma coruscans, a Silurid growing to a length of 6 ft.

The mailed cat-fish of the South American genusCallichthysbuilds regular nests of grass on leaves, sometimes placed in a hole scooped out in the bank, in which they cover their eggs and defend them, male and female sharing in this parental duty. In the alliedCorydorasa lengthy courtship takes place, followed by an embrace, during which the female receives the seminal fluid in a sort of pouch formed by the folded membranes of her ventral fins; immediately after, five or six eggs are produced and received in the pouch, to be afterwards carefully placed in a secluded spot. This operation is repeated many times, until the total number of eggs, about 250, have been deposited. In accordance with these pairing habits, the pectoral spines of the male, which are used in amplexation, are larger and stronger than those of the female. These fish are monogamous, and both parents remain by the side of the nest, furiously attacking any assailant.

The allied familyLoricariidaeis entirely confined to the fresh waters of Central and South America. C.T. Regan, who has recently published an elaborate monograph of them, recognizes 189 species, referred to 17 genera. Many of them are completely mailed; but all have in common a short-rayed dorsal fin, with theventrals below or rarely in front of it. Their gill-openings are reduced to a short slit. The first group of this section comprises alpine forms of the Andes, without any armature, and with a very broad and pendent lower lip. They have been referred to several genera (Stygogenes, Arges, Brontes, Astroblepus), but are collectively called “preñadillas” by th natives, who state that they live in subterranean craters within the bowels of the volcanoes of the Andes, and are ejected with streams of mud and water during eruptions. These fishes may, however, be found in surface waters at all times, and their appearance in great quantities in the low country during volcanic eruptions can be accounted for by numbers being killed by the sulphuretted gases which escape during an eruption and by their being swept down with the torrents of water issuing from the volcano. The lowland forms have their body encased in large scutes, either rough, scale-like, and arranged in four or five series (Chaetostomus), or polished, forming broad rings round the slender and depressed tail (Loricaria, fig. 5). They are mostly of small size.

In certain of the mailed genera the secondary sexual differences may be very pronounced, and have given rise to many nominal species. The shape of the snout may differ according to the sex, and its margin may be beset with tentacles in the male, whilst it frequently happens that the head of the latter is margined with spines or bristles which are either absent or considerably shorter in the female.

TheAspredinidae, which are also closely related to theSiluridae, are represented by four genera and eighteen species from South America.Aspredo batrachus(fig. 6), of the Guianas, the largest form, reaching to about a foot in length, deserves notice from the manner in which the female carries her eggs attached to the belly and paired fins, in a single layer, each egg being connected with the skin by a cup-shaped pedunculate base supplied with blood-vessels and coated with a layer of epithelium, the formation of which is still unexplained.

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