Page:Encyclopædia Britannica, Ninth Edition, v. 1.djvu/75

Rh A B S A B U sented to it in intuition, to recognise and attend exclusively to their points of agreement, and so to classify them in accordance with their perceived resemblances. Further, this process is admitted without much dispute to belong to the discursive or elaborative action of the intellect ; although, perhaps should the view of some modern psychologists be correct, that all intelligence proceeds by the establishment of relations of likeness and unlikeness abstraction will be better conceived as thus related to intelligence in general and typical of all its processes, than as the action merely of a special and somewhat indefinite faculty. No such harmony, however, exists regarding the nature of the product of abstraction; for that is the subject- matter of Nominalism and Realism, which has produced more controversy, and stimulated to more subtlety of thought, than any other subject ever debated in philo sophy. The concept or abstract idea has been represented in a multitude of ways : sometimes as an idea possessing an objective existence independent of particulars, even more real and permanent than theirs ; sometimes as an idea composed of all the circumstances in which the par ticulars agree, and of no others ; again, as the idea of an individual, retaining its individualising qualities, but with the accompanying knowledge that these are not the pro perties of the class ; and yet again, as the idea of a miscellaneous assemblage of individuals belonging to a class. It is still impossible to say that the many-sided controversy is at an end. The only conclusion generally admitted seems to be, that there exists between the con cept and the particular objects of intuition some very intimate relation of thought, so that it is necessary, for all purposes of reasoning, that the general and particular go hand in hand, that the idea of the class if such exists be capable of being applied, in every completed act of thought, to the objects comprised within the class. To the student of ontology, also, abstraction is of special interest, since, according to many distinguished thinkers, the recognition of abstraction as a powerful and universal mental process is to explain all ontology away, and give the ontologist his eternal quietus. The thorough going nominalist professes to discover in the mind an inveterate tendency to abstraction, and a proneness to ascribe separate existence to abstractions, amply sufficient to account for all those forms of independent reality which metaphysics defend, and to exhibit them all in their true colours as fictitkms assumptions. In reply, the ontologist, strengthened by the instinct of self-preservation, commonly contends that the analogy between general notions and metaphysical principles does not hold good, and that the latter are always more than simple abstractions or mere names. Only after abstraction is understood can the question be settled. In like manner to logic, whether regarded as the science of the formal laws of thought, or, more widely, as the science of scientific methods, a true understanding of abstraction is of the greatest importance. It is important in pure logic, because, as we have seen, every act of judgment and reasoning postulates a concept or concepts, and so pre supposes abstraction. Abstraction, determining the possi bility alike of reason and speech, creates those notions that bear common names ; it is indispensable to the formation of classes, great or small; and just according as it ascends, increasing the extension and diminishing the intension of classes, the horizon visible to reason and to logic gradually recedes and widens. And to logic as the science of the sciences a true doctrine of abstraction is not less necessary ; because the process of extending know ledge is, in all its developments, essentially the same as the first rudimentary effort to form a concept and think of particulars as members of a class ; a &quot; natural law,&quot; at least in its subjective aspect, is invariably an abstraction made by comparing phenomena an abstraction under which phenomena are classed in order to the extension of knowledge, just as under a concept are grouped the par ticulars presented in intuition. As proof of this identity it is found that the same differences exist regarding the objective or subjective nature of. the &quot;natural law&quot; as regarding that of the concept. Some affirm that the law is brought ready-made by the mind and superinduced on the facts ; others, that it is never in any sense more than a mere mental conception, got by observing the facts ; while there are yet others who maintain it to be such a sub jective conception, but one corresponding at the same time to an external relation which is real though unknowable. ABSURDUM, REDUCTIO AD, a mode of demonstrating the truth of a proposition, by showing that its contra dictory leads to an absurdity. It is much employed by Euclid. ABU, a celebrated mountain of Western India, between 5000 and 6000 feet in height, situated in 24 40 N. lat., and 72 48 E. long., within the Rajputana State of Sirohf. It is celebrated as the site of the most ancient Jain temples in India, and attracts pilgrims from all parts of the country. The Jains are the modern Indian representatives of the Buddhists, and profess the ancient theistic doctrines of that sect, modified by saint worship and incarnations. The elevations and platforms of the mountain are covered with elaborately sculptured shrines, temples, and tombs. On the top of the hill is a small round platform containing a cavern, with a block of granite, bearing the impression of the feet of Data-Bhrigu, an incarnation of Vishnu. This is the chief great place of pilgrimage for the Jains, Shrawaks, and Banians. The two principal temples are situated at Deulwara, about the middle of the mountain, and five miles south-west of Guru Sikra, the highest summit. They are built of white marble, and are pre-eminent alike for their beauty and as typical specimens of Jain architecture in India. The following description is condensed from Mr Fergusson s History of Architecture, vol. ii. pp. 623 to 625 : The more modern of the two was built by two brothers, rich merchants, between the years 1197 and 1247, and for delicacy of carving and minute beauty of detail stands almost unrivalled, even in this land of patient and lavish labour. The other was built by another merchant prince, Bimala Shah, apparently about 1032 A.D., and although simpler and bolder in style, is as elaborate as good taste would allow in a purely architectural object. It is one of the oldest as well as one of the most complete examples of Jain architecture known. The principal object within the temple is a cell lighted only from the door, con taining a cross-legged seated figure of the god Paresnath. The portico is composed of forty-eight pillars, the whole enclosed in an oblong court-yard about 140 feet by 90 feet, surrounded by a double colonnade of smaller pillars, forming porticos to a range of fifty-five cells, which enclose it on all sides, exactly as they do in a Buddhist monastery (vihdra). In this temple, however, each cell, instead of being the residence of a monk, is occupied by an image of Paresnath, and over the door, or on the jambs of each, are sculptured scenes from the life of the deity. The whole interior is magnificently ornamented. The Emperor Akbar, by a farrnan dated in the month of Rabi-ul-aul, in the 37th year of his reign, corresponding with 1593, made a grant of the hill and temples of Abu, as well as of the other hills and places of Jain pilgrimage in the empire, to Ilarbijai Sur, a celebrated preceptor of the Setambari sect of the Jain religion. He also prohibited the slaughter of animals at these places. The farman of this enlightened monarch declared that &quot; it is the rule of the worshippers of God to preserve all religions.&quot;