CATEGORY. 



CATENARY. 



**MU>, and wiax tar - With this account o( the probable derivation we 

 ,--.. 



Aristotle'* book of Categoric* is the flrxt of the ix which compoae 

 the ' Organon.' By the scholastic author*. Curio, Tonstius, Vive*, and 

 others, it is asserted that thit book of Categurie* was written, not by 

 Aristotle, but by the peripatetic philosopher Andronicus, who revised 

 and published the work* of Aristotle in the 1st oentury B.C. There 

 appears to be little foundation for this opinion, since Ammonias, Sim- 

 plicius, Boethius, and others, in their commentaries on it, indicate no 

 doubt of Its genuineness ; and the reason for doubt assigned in the 

 analysis of Aristotle's Logic by Dr. Reid in his ' Intellectual Powers,' 

 1887 (inserted also in Lord Kames'a ' Sketches'), namely, on incon- 

 sistency in the doctrine uf the book of categories, and that of the books 

 of analytics, is not founded on fact ; though such misconception might 

 well occur about the meaning of the first chapters of the categories, in 

 which so much subtle and abstruse definition is occasioned by the 

 Greek language having but one word oiiala. (ounia), to express ' sub- 

 stance ' (all the essential and accidental qualities of an object) and 

 'essence' (all the MStntial qualities only). Aristotle's frequent 

 mention of the book of Categories, and above all, as Mr. Taylor in his 

 translation remarks, the obscurity and difficulty of the sentences, and 

 the involved diction, are evidence that Aristotle is the author. But 

 similar classifications were formed before the appearance of the ' Orga- 

 non.' In a treatise by the Pythagorean philosopher, Archytas of 

 Tairntum, entitled wt(H rov worrit (concerning the universe, or, as 

 Taylor says, universal terms), the arrangement adopted by Aristotle 

 was set forth and discussed. Through Plato, the disciple of Archytas 

 and preceptor of Aristotle, the theory of the Aristotelian Categories 

 descended from the school of Pythagoras, in whose system 10 was a 

 number replete with sacred mystery (' Denarius PythagoricuH,' by 

 Meuraius, c. 12; and' Pythagorean Decad.,' in ' Theoretic Arith.,' by 

 T. Taylor, c. 12). The work of Archytas is copiously cited in the 

 commentary of Simnlicius on the ten Categories. The extant frag- 

 ments were also published separately in 1571, 8vo., Venice. Archytas 

 and the other Pythagoreans considered these ten universal ideas as the 

 principles of all things the causes of the universe, a doctrine which 

 requires for explanation a reference to the Pythagorean and Platonic 

 theory of ideas. By Aristotle and the peripatetics in general they 

 were proposed merely as comprehensive forms of predication, by 

 which the perplexing variety of human ideas were supposed to be con- 

 veniently arranged for the use of the dialectician. All the objects and 

 modes of human thought were thus distributed as species under ten 

 turnout yaura, or universal terms, to facilitate a comprehensive survey 

 of the ri war, the whole physical and metaphysical world, known and 

 unknown. The names of the ten Categories, as enumerated by Aris- 

 totle (' Cat.' c. 4, and ' Top.' 1. i. c. 9) are : 1, otmia or rl iart ; 2, w6<ror ; 

 3, woar; 4, wpitn; !>, wav ; 6, win; 7, KfiffOoi ; 8, fx"' ; 9, troitir; 

 10, vAtrx"" ; which are variously expressed in English by different 

 writers. In Dr. Whately's Logic they are rendered as follows : " sub- 

 stance, quantity, quality, relation, place, time, situation, possession, 

 action, suffering ;" but to perceive the meaning of the Greek terms, it 

 must be observed what Aristotle comprehends under each of these 

 general designations : lx<>*, for instance, is said to signify the having 

 something attached to the person ; to be " booted, armed " (rb Ix'if 

 fJHiulnt T& lr*otiSia<u, ri wA(<rftu 'Cat.' c. 9); but in the last 

 chapter of the Categories eight modes of having are enumerated. The 

 first four categories, namely, ' oi/aia, wiaor, wftn rl, wautr,' are elaborately 

 explained by Aristotle in four long chapters ; the definition of the 

 remaining six is despatched in a word or two, but the nature and 

 properties of all are more fully defined incidentally throughout the rest 

 of his work*. That they are classifications only of words was main- 

 tained by some of the ancient philosophers (' Philos. Arrangements,' by 

 Harris, p. 1). Concerning the question whether these universal are 

 real existences or merely names or conceptions, see the remarks on the 

 Realists and Nominalists in Dr. Reid's ' Kssays,' c. 5 and . In the 

 later ages of Latinity these Categories were denominated pnedicaments ; 

 the name by which they have since been generally designated in the 

 scholastic works on logic, in which they are usually translated and 

 placed as follows : " substantia, ouantitas, qualiUa, relatio, actio, passio, 

 uVii, quando, situs, habitus," and illustrated by the following jargon as 

 an aid to memory. 



"Arbor, MX, fervor*, p*tre>, refrigrrat, uitot, 

 Hull, crw, itibo, nee tunlcaUu cro." 



As to the utility of these ten Categories, it may be remarked that 

 they were made to form an essential part of the mediioval system of 

 logic, which was rejected as useless by many of the principal philoso- 

 phical writers of the last three centuries, such as Bacon, Hobbes, 

 Descartes, Locke, Condillac, Reid, Kames, Stewart, Brown, De Stutt 

 Tracy, ftc. But they do not properly belong to logic at all ; and those 

 who rejected logic, and those who maintained the logical chan 

 the categories, fight with each other a battle in which modern opinion 

 *M with neither. It wan affirmed that the categories were 11- 



> maintain among the illiterate the reputation of universal knowledge; 

 that they served only to support syllogistic arguments i.. n f,, r victory, 

 I imppliccl * convenient ready-reckoner, by which a prompt solution 

 MUM lw given eren to questions beyond the reach of human know- 

 ledge, and in reality quite unanswerable. The lovers of satire may 



turn to Gassendi's ' Exereitationes adversus Aristoteleos,' where the 

 ten Categoric* are unsparingly treated. The remarks of Hobbe* 

 in his Logic (' Opera Philosophic*,' 4to, 1688) are no less satirical : 

 " Kateor me preodicamentorum usum hactenus non magnum perspexisae ; 

 cepit opinor Aristotelem libido qutedam pro authoritate sua, cum 

 rerum non posset, verborum tamen oen*um peragendi," p. 16. So the 

 authors of the ' Port Royal Logique, ou 1'Art de Penser ' (Nicole and 

 Arnauld), p. 21, " Voila les dix Categories d'Aristote, dont on fait taut 

 de mysteres- a dire le vrai, c'est une chose trit pen utUc tout* arbi- 

 traire, et qui n'a de fondement que 1'imagination elle accoutunu les 

 homines a se payer de mote ; a s'imaginer qu'ils savent toutos chows, 

 lorsqu'ils n'en connnissent que dea noms arbitraires : " and D< 

 Tracy, ' Logique,' p. 22, " C'ela n'est utile absolument a rien." It would 

 be endless to quote similar opinions from the best modern works on 

 the subject On the other side, among the defenders of the Categories 

 are Monboddo, Harris, Gillies, and T. Taylor. Harris, in his elaborate 

 work on the subject (' Philosophical Arrangements,' p. 84), *ays "The 

 doctrine of these Categories is a valuable, a copious, a sublime theory 

 a theory which prepares us to study every thing with advantage : " 

 p. 462, " There are few theories so great, so comprehensive, so various, 

 as the theory of these Categories : in contemplating them we see 

 whence the sciences and arts all arise history out of substance; 

 mathematics out of quantity ; optics and medicine out of quality and 

 quantity; astronomy, music, and mechanics, out of quantity and 

 motion ; painting out of quality and site ; ethics out of relation ; 

 chronology out of when; geography out of where; electricity, mag- 

 netism, and attraction out of action and passion," Ac. In the Cate- 

 gories of Kant ('Kritik der Reinen Vernunft,' 7th ed., 1828). the 

 precise boundaries of human knowledge, a priori, are professed to be 

 exhibited ; these Categories consist of four primordial classes : 1, quan- 

 tity: :.'. quality ; 8, relation; 4, modality; each class containing three 

 Categories: 1, unity, multitude, totality ; 2, reality, negation, limita- 

 tion ; S, substance and accident, cause and effect, action and iv: 

 4, possibility, existence, necessity. 



That in treating of extensive subjects, some similar methodical clas- 

 sification is very useful and necessary for perspicuity and brevity, i-. 

 obvious. A tabulated view of Locke's arrangement of ideas (his Cate- 

 gories, as they are sometimes named) is given to great advantage on a 

 large sheet prefixed to the edition of his Essay in 1828. Among the 

 ancients different names and numbers of categories were adopted by 

 different sects : by Aristotle and the peripatetics they are variously 

 called KoftiAou Ao>oi, universal terms ; ax'tifutra aa-rlrfoftas, forms or 

 figures of predication ; xarriyoptau, categories ; yivTi ytuKunaTa, the 

 most comprehensive genera; r& wp&ra Mica firrt, the ten | 

 genera. Plato reduces them to five ; namely, oiiala, ravr6n)s, JTCJXJTTJJ, 

 xiniais, <rrdais ; substance, identity, diversity, motion, rest. The 

 stoics made four : namely, Awoxn^ea, WOOL, 'wi fxiwTo, vpfa n was 

 txorra ; subjects, substances, modes of being, relative modes of 

 Some philosophers have preferred seven : namely, spirit, matter, quan- 

 tity, substance, figure, motion, rest: others three, namely, subject, 

 accident inherent, accident circumstantial; others make onh 

 simply, substance and attribute, or subject and accident. Other 

 philosophers arrange all existent things under the following six 



, .it.-/ .,...- 



" Mrnn, meniura, quin, motui, positura, flgura, 

 Sunt, cum mttcrin, cunclarum exordia rerum." 



Cicero and guintjlmn mine the ten Categories of Aristotle ' Element! 

 Dialectic*' 



(See Aminonius, Comment, in Categ. Graccl, 12mo, Venice, 154/i; 

 wiiiii- in Latin by Silvanius, Paris, 154:.' ; Simplicii ( to 

 Arulot., fol., 1567 ; Analyst* of A n>.,c/. V Workt, by Dr. Gillie*, 4to, p. 58, 

 et teq. ; Monboddo, Oriijin of Lang., voL i. p. 81", L v., p. 



416; and Antient ifctapliyiict, vol. i. |ij. 

 Dialect, fol. 1560, p. 106, et teg. in Categor. ; Stewart's /.'' 



"1. ii.. "'i -I ; T/if Oryanon, Comment. 1'V Paeius, 4to, 



1605. The English translation by T. Taylor, 4to, 1812, contains the 

 substance of all the chief Commentaries. 



CATENARY (from Catena, a chain) is the curve in which a string 

 of perfect flexibility and uniform thickness and density will hang from 

 two points, which we may suppose to be in the same horizontal Une, as 

 ire and properties of the curve will be the same from whatever 

 points it may hang. And all catenaries are similar curves ; that is to 

 lay, let there bo any number of such curves formed by chains of 

 different lengths, then each of them will be a picture, on a reduced or 

 enlarged scale, of some portion of the longest 



Various properties of catenaries have been investigated, in case* 

 where the thickness ..r 'l.-nsity of the string are variable. 

 ticular Creswell's translation of Venturoli's Mechanics, and \Vh. 

 Analytical Statics. We shall here confine ourselves to the most com- 

 in. in properties of the catenary, which, with the m'xlitieationx : : 



I nlii-n \v.- come to apply the mathematics of a flexible and 

 to the materials of the architect, is the first step 

 towards the thwiry of the suspension bridge. Let c and n be th 

 points of suspension, CAD the chain, of which A is the lowest i 

 and A B verti.al passing through it. Let the units be 

 ounces (any others might be used), and let the weight of the chain be 

 k ounces to the inch ; let I be the length of chain equivalent to the 

 tension at A, and T that equivalent to the tension at r, a point whose 



