CATECHU

catechu, or cutch (malay, _kachu_), an extract obtained from several plants, its chief sources being the wood of two species of acacia (_a. catechu_ and _a. suma_), both natives of india. this extract is known as black catechu. a similar extract, known in pharmacy as pale catechu (_catechu pallidum_), and in general commerce as gambir, or _terra japonica_, is produced from the leaves of _uncaria gambir_ and _u. acida_, cinchonaceous plants growing in the east indian archipelago. a third product to which the name catechu is also applied, is obtained from the fruits of the areca or betel palm, _areca catechu_. ordinary black catechu is usually imported in three different forms. the first and best quality, known as pegu catechu, is obtained in blocks externally covered with large leaves; the second and less pure variety is in masses, which have been moulded in sand; and the third consists of large cubes packed in coarse bags. the wood of the two species of _acacia_ yielding catechu is taken for the manufacture when the trees have attained a diameter of about 1 ft. the bark is stripped off and used for tanning, and the trunk is split up into small fragments, which are covered with water and boiled. when the extract has become sufficiently thick it is cast into the forms in which the catechu is found in commerce. catechu so prepared is a dark brown, or, in mass, almost black, substance, brittle, and having generally a shining lustre. it is astringent, with a sweetish taste. in cold water it disintegrates, and in boiling water, alcohol, acetic acid and strong caustic alkali it is completely dissolved. chemically it consists of a mixture of a peculiar variety of tannin termed catechu-tannic acid with catechin or catechuic acid, and a brown substance due to the alteration of both these principles. catechu-tannic acid is an amorphous body soluble in cold water, while catechin occurs in minute, white, silky, needle-shaped crystals, which do not dissolve in cold water. a very minute proportion of quercetin, a principle yielded by quercitron bark, has been obtained from catechu. gambir, which is similar in chemical composition to ordinary catechu, occurs in commerce in the form of cubes of about an inch in size, with a pale brown or yellow colour, and an even earthy fracture. for the preparation of this extract the plants above mentioned are stripped of their leaves and young twigs, and these are boiled down in shallow pans. the juice is strained off, evaporated, and when sufficiently concentrated is cast into shallow boxes, where, as it hardens and dries, it is cut into small cubes. gambir and catechu are extensively employed in dyeing and tanning. for dyeing they have been in use in india from the most remote period, but it was only during the 19th century that they were placed on the list of european dyeing substances. catechu is fixed by oxidation of the colouring principle, catechin, on the cloth after dyeing or printing; and treated thus it yields a variety of durable tints of drabs, browns and olives with different mordants (see dyeing). the principal consumption of catechu occurs in the preparation of fibrous substances exposed to water, such as fishing-lines and nets, and for colouring stout canvas used for covering boxes and portmanteaus under the name of tanned canvas. black catechu is official in most pharmacopoeias except that of great britain, in which pale catechu is the official drug. the actions and uses of the two are similar, but black catechu is the more powerful. the dose is from five to twenty grains. the _pulvis catechu compositus_ contains catechu and kino, and may be given in doses twice as large as those named. the drug has the actions and uses of tannic acid, but owing to the relative insolubility of catechu-tannic acid, it is more valuable than ordinary tannic acid in diarrhoea, dysentery and intestinal haemorrhage. catechumen (lat. _catechumenus_, gr. [greek: katechoumenos], instructed, from [greek: katechein], to teach orally), an ecclesiastical term applied to those receiving instruction in the principles of the christian religion with a view to baptism. as soon as christianity became a missionary religion, it was found necessary to make arrangements for giving instruction to new converts. at the beginning the apostles themselves seem to have undertaken this duty, and the instruction was apparently given after baptism, for in acts ii. 41, 42, we are told that "they that gladly received the word were baptized ... and they continued stedfastly in the apostles' teaching." there are two instances in the new testament where reference is made to individual instruction in this technical sense. luke (i. 4) in dedicating the third gospel to theophilus tells him that his aim in writing the book was "that thou mightest have certainty in the things in which thou has been instructed" ([greek: katechethes]) and we are told that apollos was instructed ([greek: katechemenos]) "in the way of the lord" (acts xviii. 25). with the development of christianity the instruction became more definite and formal. it is probable that the duty of instructing converts was assigned to "the teachers," who are ranked by paul immediately after the apostles and prophets (1 cor. xii. 28), and occupied an important position in the christian ministry. in the _didache_, or teaching of the apostles, we have an excellent illustration of the teaching which was given to candidates for baptism in early times. there can be little doubt that the _didache_ was used as a manual for catechumens for several centuries. athanasius (_festal epistles_, 39), for instance, says that "it was appointed by the fathers to be read by those who are just recently coming to us, and wish to be instructed in the word of godliness" ([greek: katecheisthai ton tes eusebeias logon]). the instruction prescribed by the _didache_ is very largely ethical, and stands in striking contrast to the more elaborate doctrinal teaching which came into vogue in later days. the _shepherd of hermas_ too is another book which seems to have been used for the purpose of catechesis, for eusebius says that it "was deemed most necessary for those who have need of elementary instruction" (_eccles. hist._ iii. 3-6). with the rise of theological controversy and the growth of heresy catechetical instruction became of vital importance to the church, and much greater importance was attached to it. after the middle of the 4th century it was regarded as essential that the candidate for baptism should not only be acquainted with the spiritual truths and ethical demands which form the basis of practical christianity, but should also be trained in theology and the interpretation of the creeds. two books have been preserved which throw a striking light upon the transformation which had taken place in the conception of catechesis; (1) the catechetical lectures of cyril of jerusalem; (2) the _de rudibus catechizandis_ of augustine. cyril's lectures may be termed the _pearson on the creed_ of the 4th century. he takes each article separately, discusses it clause by clause, explains the meaning of each word, and justifies each statement from scripture. augustine's treatise was written at the request of a catechist, named deogratias, who had asked him for advice. after replying to the question of deogratias, and giving sundry counsels as to the best method of interesting catechumens, augustine concludes by giving a model catechetical lecture, in which he covers the whole of biblical history, beginning from the opening chapters of genesis, and laying particular stress on the doctrinal parts of scripture. cyril and augustine differ, as we should expect, in the doctrines which they select for emphasis, but they both agree in requiring a knowledge of sound doctrine on the part of the candidates. in spite of the numerous references to catechumens in patristic literature, our knowledge of the details of the system is often very deficient, and upon some points there is considerable diversity of opinion amongst experts. the following are the most important questions which come under consideration. 1. _the classification of catechumens_.--bingham and many of the older writers held that there were four classes of catechumens, representing different stages in the process of instruction: (a) "the inquirers" whose interest in christianity had been sufficiently aroused to make them desire further information, and who received private and individual instruction from the teachers before they were admitted into the second class, (b) "the hearers" (_audientes_), who were admitted into the church for the purpose of listening to sermons and exhortations, (c) the _prostrati_ or _genu flectentes_, who were allowed also to take part in the prayers, (d) the _electi_ or _competentes_, who had completed the period of probation and were deemed ready to receive baptism. modern scholars, however, for the most part, deny that there is sufficient basis to justify this elaborate classification, and think that its advocates have confused the catechumenate with the system of penance. the evidence does not seem to warrant more than two classes, (a) the _audientes_, who were in the initial stages of their training, (b) the _competentes_, who were qualified for baptism. 2. _the relation of catechumens to the church_.--catechumens were allowed of course to attend church services, but at a certain point were dismissed with the words "ite catechumeni, missa est." the moment at which the dismissal took place cannot be exactly determined, and it is not clear whether the catechumens were allowed to remain for a portion of the communion service, and if so, whether as spectators or as partial participants. a passage in augustine seems to imply that in some way they shared in the sacrament, "that which they (the catechumens) receive, though it be not the body of christ, is yet an holy thing and more holy than the common food which sustains us, because it is a sacrament" (_de peccatorum meritis_, ii. 42). the explanation of these words has occasioned considerable controversy. many scholars hold (and this certainly seems the most natural interpretation) that consecrated bread was taken from the eucharist and given to the catechumens. bingham, however, maintains that the reference is not to the consecrated bread, but to salt, which was given to them as a symbol "that they might learn to purge and cleanse their souls from sin." 3. _the duration of the training_.--various statements with regard to the duration of the catechumenical training are found in ecclesiastical authorities. the apostolical constitutions, for instance, fix it at three years;[1] the synod of elvira at two.[2] the references in the fathers, however, imply that for practical purposes it was limited to the forty days of lent. very probably, however, the forty days of actual instruction were preceded by a period of probation. 4. _the relation between the catechumenate and baptism_.--catechetical instruction was designed as a preliminary to baptism. there were two directions, however, in which this purpose was enlarged: (a) we have no reason to suppose that when infant baptism was introduced, those who had been baptized in infancy were excluded from the catechetical training, or that instruction was deemed unnecessary in their case, though as a matter of fact we have no definite reference to their admission. the custom of postponing baptism, which was very general in the 4th and 5th centuries, probably made such cases more rare than is generally supposed, and so accounts for the absence of any allusion to them in connexion with the catechumenate. (b) we have no reason to suppose that the instruction given in the famous catechetical schools of alexandria and carthage was restricted to candidates for baptism. there is no doubt that "catechetical" is used in a much wider sense when applied to the lectures of origen than when used of the addresses of cyril of jerusalem. the "instruction" of origen was given to all classes of christians, and not merely to those who were in the initial stages. 5. _characteristics of the catechumenical training_.--besides instruction there were some other important features connected with the catechumenate. (a) the duty of _confession_ was impressed on the candidates. (b) the ceremony of _exorcism_ was often performed in order to free the catechumen from evil spirits. (c) at a certain point in the training the creed and the doctrine of the sacraments were delivered to the candidates by the bishop with much impressive ceremonial. this teaching constituted the "holy secret" or "mystery" (_disciplina arcani_) of christianity, and could only be imparted to those who were qualified to receive it. the acquisition of this arcanum was regarded as the most essential element in the catechetical discipline, and marked off its possessors from the rest of the world. there can be little doubt that this conception of the "holy secret" came into the church originally from the greek mysteries, and that much of the ceremonial connected with the catechumenate and baptism was derived from the same source. authorities.--cyril, _catecheses_; gregory of nyssa, _oratio catechetica_; chrysostom, _catecheses ad illuminandos_; augustine, _de rudibus catechizandis_; mayer, _geschichte des katechumenats ... in den ersten sechs jahrhunderten_ (1868); s. cheetham, _the mysteries, pagan and christian_. (h. t. a.) footnotes: [1] _apost. constit._ viii. 2. [2] canon 42. category (gr.: [greek: kategoria], "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 verb [greek: kategorein], to accuse, in the specific logical sense, to predicate; [greek: tho kategoroumenon] becomes the predicate; and [greek: kategorikhe protasis] may 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. hindu philosophy. 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 (see an article by richard garbe in _monist_, 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 is _padartha_, 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, [greek: tha katha medemian sueplokhen legomena]. 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. _substance_ is the permanent substance in which _qualities_ exist. _action_, belonging to or inhering in substances, is that which produces change, _genus_ belongs 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. _concretion_ or co-inherence denotes inseparable or necessary connection, such as that between substance and quality. under these six classes, [greek: gene tou hontos], kanada then proceeds to range the facts of the universe.[1] greek philosophy 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 the eleatic 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. their starting-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] plato. 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. special terms also are anticipated at various times, e.g. [greek: poiotes] in the _theaetetus_, [greek: poiein] and [greek: paschein] in the _gorgias_, and [greek: pros ti] in the _sophist._[3] but 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 the _sophist_, being, rest and motion ([greek: tho on autho kahi stasis kahi kinesis]) are laid down as [greek: megista ton genon].[4] to these are presently added the same and the other ([greek: tauthon kai thateron]), and out of the consideration of all five some light is cast upon the obscure notion of non-being [greek: (to mhe on)]. in the same dialogue (262 seq.) is found the important distinction of [greek: onoma] and [greek: rhema], noun and verb. the _philebus_ presents 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 ([greek: tho apeiron, tho peras, he summixis, he aitia]). 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. aristotle. the aristotelian doctrine is most distinctly formulated in the short treatise [greek: kategoriai], which generally occupies the first place among the books of the _organon_. the authenticity of the treatise was doubted in early times by some of the 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 either _pro_ or _con_ with anything like certainty; but this is of little moment, for the doctrine of the categories, even of the _ten_ categories, 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--[greek: k. tou ontos] or [greek: tes ousias, gene tou ontos] or [greek: ton onton, gene] simply, [greek: tha prota] or [greek: tha koina prota, ai ptoseis], or [greek: ai diaireseis]--only indicate that the categories are general classes into which being as such may be divided, that they are _summa genera_. the expressions [greek: gene ton kategorion] and [greek: schemata ton k.], which are used frequently, seem to lead to another and somewhat different view. [greek: kategoria] being taken to mean that which is predicated, [greek: gene ton k.] 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 to _first intentions_, the latter to _second 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, [greek: ousia], in one of its aspects cannot be predicate at all. in the [greek: kategoriai] aristotle 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 ([greek: ton katha medemian sumplokhen legomenon]), each signifies either substance ([greek: ousia]), or quantity ([greek: poson]), or quality ([greek: poion]), or relation ([greek: pros ti],) or where (i.e. place, [greek: pou]), or when (i.e. time, [greek: pote]), or position ([greek: keisthai]), or possession ([greek: echein]), or action ([greek: poiein]), or passion ([greek: paschein]). [greek: ousia], the first category, is subdivided into [greek: prote ousia] or primary substance, which is defined to be [greek: tode ti], the singular thing in which properties inhere, and to which predicates are attached, and [greek: deuterai] [greek: onsiai], genera or species which can be predicated of primary substances, and are therefore [greek: onsia]. only in a secondary sense. nevertheless, they too, after a certain fashion, signify the singular thing, [greek: tode ti]" (k. p. 3 b 12, 13). it is this doctrine of [greek: prote onsia] that has raised doubts with regard to the authenticity of the [greek: kategoriai] but the tenfold classification, which has also been captiously objected to, is given in an acknowledged writing of aristotle's (see topica, i. 9, p. 103 b 20).[5] at 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, [greek: exein] and [greek: keisthai] being omitted. in other passages[6] six, five, four, and three are given, frequently with some addition, such as [greek: kai ai allai k]. 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 the [greek: kategoriai], which bears all the marks of an early and preliminary study. for true understanding we must turn to the _metaphysics_, 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. [greek: tho on] is spoken of in many ways; of these four are classified--[greek: tho on katha sumbebekos, tho om hos alethes, tho on dunamei kai energeia], and [greek: tho on kata ta schemata ton kategorion]. 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. [greek: panta de ta gignomena hupo te tinos gignetai kai ek tinos kai ti. to de ti lego kath hekasten kategorian e gar tode e poson e poion e pon]. (_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 not _summa genera_ of 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 of [greek: to on] are 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 [greek: keisthai] to the intransitive verb, [greek: echein] to 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 only _ten_ categories? 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 he _had_ a 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. brentano[7] has 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. later greek. 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 of highest classes, [greek: genikotata]. [greek: to on] or [greek: ti], being, or somewhat in general, was subdivided into [greek: hypokeimena] or subjects, [greek: poia] or qualities in general, which give definiteness to the blank subject, [greek: pos echonta], modes which further determine the subject, and [greek: pros ti pos echonta], definite relative modes. these categories are so related that each involves the existence of one higher than itself, thus there cannot be a [greek: pros ti pos echon] which does not rest upon or imply a [greek: pos echon], but [greek: pos echon] is impossible without [greek: poion], which only exists in [greek: hypokeimenon], a form or phase of [greek: to hon].[8] plotinus, after a lengthy critique of aristotle's categories, sets out a twofold list. [greek: to en, kinesis, stasis, tautotes, heterotes] are the primitive categories ([greek: prota gene]) of the intelligible sphere. [greek: ousia, pros ti, poia, poson, kinesis] are the categories of the sensible world. the return to the platonic classification will not escape notice. modern philosophy. 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 metaphysical 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 of _philosophical relations_ into 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. 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 the 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 be _known_ by 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. universal \ i. / unity. particular > of quantity < plurality. singular / \ totality. affirmative \ ii. / reality. negative > of quality < negation. infinite / \ limitation. categorical \ / inherence and subsistence | iii. | (substance and accident). hypothetical > of relation < causality and dependence | | (cause and effect). disjunctive / \ community (reciprocity). problematical \ iv. / possibility and impossibility. assertoric > of modality < existence and non-existence. apodictic / \ necessity and contingency. fichte. 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 his _remarks on the table of the categories_ gave 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 whole 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, the _position_ or 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 the _prius_ in 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 the _wissenschaftslehre_ contains the only real advance in the treatment of the categories from the time of kant to that of hegel.[9] this, of course, does not imply that there were not certain elements in schelling, particularly in the _transcendental 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 of _noumena_ to which they were inapplicable. self-consciousness, which was, even with kant, the _nodus_ or 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 universal _par 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),[10] who 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. trendelenburg. 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. 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."[11] a 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 motion _per se_ is by no means adequate to self-consciousness. his theory has found little favour. ulrici. 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 tatigkeit_) of thought. thought is only possible 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 the _system der logik_ (1852), and in briefer, preciser form in the _compendium der logik_ (2nd ed., 1872); it is in many points well deserving of attention. renouvier, cousin, hamilton, mill. 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 the 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.[12] the 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.[13] the generalized category of the _conditioned_ has 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.[14] this classification proceeds on a quite peculiar view of the categories, and is here presented only for the sake of completeness. modern psychologists. 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 all 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", in _zeitschr. f. philos. und phil. krit._ cxv. (1899), pp. 9-19; e. konig in the same periodical cxiii. (1889), pp. 232-279, and cxiv. (1899), pp. 78-105; f.a. trendelenburg, _geschichte der kategorienlehre_ (1846); p. ragnisco _storia critica delle categorie_ (2 vols., florence, 1871); w. windelband _vom system der kategorien_ (tubingen, 1900); r. eisler, _worterbuch 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's _knowledge and reality_ (1885, 2nd ed. 1892); histories of philosophy. for further authorities see works quoted under aristotle and kant, and in j.m. baldwin's _dict. philos. psych._ vol. iii. pt. 2, p. 685. (r. ad.; x.) footnotes: [1] for 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's _vaiseshika-sutras_ (benares, 1873), and _philosophy of the upanishads_ (london, 1882, 1891); max muller, _sanskrit literature_, and particularly his appendix to thomson's _laws of thought_. [2] the supposed origin of that theory in the treatise [greek: perhi tou pantos], 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 century a.d. [3] prantl, _ges. der logik_, i. 74-75; f.a. trendelenburg, _kategorienlehre_, 209. n. [4] _soph_. 254 d. [5] against this passage even prantl can raise no objection of any moment; see _ges. der logik_, i. 206. n. [6] see bonitz, _iridex aristotelicus_, s.v., and prantl, _ges. der logik_, i. 207. [7] brentano, _bedeutung des seienden nach a._, pp. 148-178. [8] for 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. [9] it 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 the _metakritik_), by solomon malmon (in the _propadeutik zu einer neuen theorie des denkens_), by j.f. fries (in the _neue 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. [10] _system der metaphysik_ (1844). [11] _logische untersuchungen_, i. 376-377. [12] _essais de critique generale_ (2nd ed.), _la logique_, i. pp. 184, 190, 207-225. [13] _discussions_, p. 577. [14] _logic_, 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 the _acta 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 article mechanics, 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 = 1/2c[e^(x/c) + e^(-x/c)]; other forms are s = c sinh (x/c) and y^2 = c^2 + s^2, s being the arc measured from the vertex; the intrinsic equation is s = c tan [psi]. the radius of curvature and normal are each equal to c sec^2 [psi]. [illustration] the surface formed by revolving the catenary about its directrix is named the _alysseide_. 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 (see variations, calculus of). the involute of the catenary is called the _tractory_, _tractrix_ or _antifriction_ curve; it has a cusp at the vertex of the catenary, and is asymptotic to the directrix. the cartesian equation is _ _ | c - [root](c^2 - y^2) | x = [root](c^2 - y^2) + 1/2c log |-----------------------| |_c + [root](c^2 + y^2)_| 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 (see mechanics: _applied_). cateran (from the gaelic _ceathairne_, 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.