This higher form of generalization is treated of under INDUCTIOIS% On the other and simpler form, a few further explanations are added here. In the operation of forming a general notion, the first step is something of the nature of classification. We must assemble in our view a number of particular objects, being moved to bring them together by the attractive bond or association of similarity. The objects thus assembled are a class. In natural history, for example, we bring together in the mind all the quadrupeds that we have ever had any knowledge of, and the array constitutes a class, grounded on the peculiarity of walking on all-fours. Another class is made up of the animals that fly in the air: a third, of those that live in the sea. By such successive groupings of creatures that have a kindred nature, in one or more respects, we gradually include the whole of the animal kingdom known to us in a series of classifications, whereby method and order are introduced into the otherwise heterogeneous mass. So in plants and minerals, and all through nature. According as likenesses have been discerned in the constituent parts of the universe of things, the individuals are placed with those related to them, and a great simplification of view and extension of knowledge are the results. For it happens very frequently, that likeness in one point is accompanied with likeness in other points, so that we can couple several peculiarities together, and rise to general truths as well as general notions. When a classification has been arrived at that leads to this consequence, we put a more than ordinary value upon it; we consider that we have seized upon some fundamental and pregnant point of resemblance, something that cenveys'the most essential nature of the objects classified, and we are accustomed to style the group that so arises a natural or a philosophkai classification. The arranging of animals according to the element they live in, as land, water, air, so very obvious to the first observers, has given place to one founded on other kinds of likeness—namely, the structure of the skeleton and the mode of bringing forth and rearing the young; it being proved that a greater number of important attributes are bound up with those characteristics than with the element that the animals inhabit. See Mill's Logic, book iv. chap. 7.
The forming/if a class leads to the adoption of a class-name, in other words, of a general name, which is a name applicable to every individual member of the class, in consequence of being understood to express no more than they all have in common. Thus we have the name " round" to express all round objects, omitting any reference to other peculiarities that may attach to them. So the names " bird," " heath," " salt," are applicable alike to a vast number of individual things. When the general name has been devised, we can by means of it speak of. all the particulars in one breath, on con dition that we intend only to refer to the points of community.
The process called abstraction is further implied. When we bring together, or con stitute a class, in virtue of a prevailing resemblance, we are said to " abstract" from the individuals everything else except the points of agreement. In the language of Sir W. Hamilton, we attend to the likeness, and abstract the differences. The notion that we have of the common quality is termed by the same philosopher the concept; but it has been usual to employ the phrase " abstraction," or " abstract idea" for the same purpose. although a perversiOn of the original application of that word. The common
attribute of round bodies, the round figure, or form, is the concept, or the abstract idea of roundness. The precise character of this mental element or process has been much disputed in philosophy, there being three different sects that have grown up in connec tion witl•it; the Realists, Nominalists, and Conceptualists. The Realists gave an actual independent existence to the prototypes of our general notions, maintaining that, apart from all circular bodies, there existed in. nature a circular form, having no other attri bute soever, like a circle of Euclid bereft of the actual _line required to mark the figure to the eye. The Nominalists considered that the only general thing was the common name; the Conceptualists allowed a mental existence to the generalized attributes, but no more. (Sir W. Hamilton's Metaphysics, vol. ii. p. 296). The last are, no doubt, near the truth; for although we cannot, with Plato, affirm the existence in nature of "generals" that have no embodiment in particulars (which would beta contradict the very essence of generalization, namely, likeness among untikenesses), we must still grant to the mind the power of attending in thought to what is common, neglecting for the time the disagreements. We can think of all the consequences of the circular figure, without specially attending to the other peculiarities of any individual circle. This abstractive process is performed in different ways, according to the nature of the subject. In geometry, for example, we can draw diagrams that arc little other than naked forms, although we must make them of a definite size; and in contemplating these, we are enabled to think of form without substance. We cannot use this method in natural history ; we cannot form a conception of a bird by a diagram that gives nothing but what is common to all birds. If we are reasoning upon the properties of the class, we may first call into view some one as an example, sad- a pigeon; from considering which, we can go so far as to note the common peculiarities of feathers. wings, bill, etc. ;. and when we have completed the description, we run over in our minds a number of other birds, to see that we have not mentioned points special to the pigeon. In fact, we mitst have within call the whole of the members of the class, if we would reason generally respecting it. After we have thus checked and corrected our generalized description, we can embody the abstract idea in a,form of very wide occurrence in our general reasonings, namely, a verbal statement.of the common attributes. By means of this, we may often dispense with the reference to the particulars, except to know the precise meaning of the language, which ineaningis still some sort of general conception of the objects. We must have a general notion of feathers, and of the structure of the bill in birds, upon the plan above mentioned of holding in the mind some typical instance, subject to correction, by a comparison of all the instances coming under the genus. So that, in point of fact, no genera] reasoning has ever been invented to supersede totally this reference to the particulars; the formal reasonings of mathematics require us still to have in the mind concrete quantity, or one thing as equal to, greater than, or less than another.