Class (set theory)

“ Better than any work, avowedly on history, it graphically traces the special features of the several systems of class-rule as they succeeded each other from epoch to epoch, together with the nature of the struggle between the contending classes. ”

“ And if there be any class which includes Socrates without including man, that class is not a real Kind. Let the class, for example, be flat-nosed; that being a class which includes Socrates, without including all men. ”

“ It was, no doubt, natural to assume that we first perceive individuals, which now stand clearly before us, and then, having compared them, arrive at general ideas. But if knowledge grows by the assimilation and differentiation of experiences, the class on the one hand and the individual on the other, must be joint products of this process: classes becoming clearer as more and more individuals are discriminated. Classes, or class-ideas never stand before us as individuals do; but the greater part of the meaning of every perception of an individual is the kind of thing it is. ”

“ It has no right arbitrarily to dispose of the common weal, to put it in peril according to its caprice, to subordinate it to the application of a theory or to the interest of a single class, even if this class is the most numerous. ”

“ But this, though a convenient mode of expression for some purposes, is objectionable as a definition, since it explains the clearer of two things by the more obscure. It would be more logical to reverse the proposition, and turn it into a definition of the word class: "A class is the indefinite multitude of individuals denoted by a general name."
It is necessary to distinguish general from collective names. A general name is one which can be predicated of each individual of a multitude; a collective name can not be predicated of each separately, but only of all taken together. ”

“ If the minor premise asserted nothing more than that something belongs to a class, and if the major premise asserted nothing of that class except that it is included in another class, the conclusion would only be that what was included in the lower class is included in the higher, and the result, therefore, nothing except that the classification is consistent with itself. ”

“ By elimination of the minor, incidental characteristics and by gathering together the essential, primary characteristics they have in common. The division of phenomena into classes is thus an abstraction, a result of scientific thinking: we must first recognise which characteristics are incidental and which essential. In social economics we, as Marxists, divide society into two or three classes, that is, into capitalists, proletarians, and landed interests, though the units of one class may differ in some points from each other or may have points in common with units of another class. ”

“ I wouldn't start in by hammering them over the head with the idea that there are only one or two classes that anybody wants to belong to. I'd jump with all my weight on that idiotic notion that one class is better than another, as if any class was any good at all for you, if it's not the one you belong to naturally! ”

“ In a modern state, on the other hand, though class distinctions are clearly enough marked, yet the point of view from which they are regarded is fundamentally different. They are attributed rather to accidents of fortune than to varieties of nature. ”

“ To terminate the subject of Fallacies of Generalization, it remains to be said, that the most fertile source of them is bad classification: bringing together in one group, and under one name, things which have no common properties, or none but such as are too unimportant to allow general propositions of any considerable value to be made respecting the class. ”

“ That which constitutes a Party, or class, is always some community of Interest: in other words, some thing or things, to be obtained, secured, or augmented, by the common endeavours of the class, and operating as a cause of pleasure to all of them.
The People, that is, the Mass of the community, are sometimes called a class; but that is only to distinguish them, like the term Lower Orders, from the 228 Aristocratical class. In the proper meaning of the term class, it is not applicable to the People. No interest is in common to them, which is not in common to the rest of the community. ”

“ In fact, a class is not an ideal, but a clearly defined group of things between which internal relationships exist, similar to those of kindred. Now the only groups of this sort known from experience are those formed by men in associating themselves. Material things may be able to form collections of units, or heaps, or mechanical assemblages with no internal unity, but not groups in the sense we have given the word. A heap of sand or a pile of rock is in no way comparable to that variety of definite and organized society which forms a class. ”

“ Every class is, in its eyes, only an aggregate of individuals, and to exalt one class above another is to appreciate some individuals at the expense of others, to place marks of comparative social worth upon the members of different groups which do not correspond to the relative values of their natural qualities. ”

“ HOW FAR WEALTH IS THE BASIS OF OPEN CLASSES Impersonal Character of Open Classes—Various Classifications—Classes, as Commonly Understood, Based on Obvious Distinctions—Wealth as Generalized Power—Economic Betterment as an Ideal of the Ill-Paid Classes—Conclusion.
Where classes do not mean separate currents of thought, as in the case of caste, but are merely differentiations in a common mental whole, there are likely to be several kinds of classes overlapping one another, so that men who fall in the same class from one point of view are separated in another. ”

“ Now whenever a class has been properly formed, a definition must have been laid down, stating the qualities and circumstances possessed by all the objects which are intended to be included in the class, and not possessed completely by any other objects. ”

“ When these consequences of the purely arbitrary classification to which we allude have been pointed out and complained of, the only answer which we have ever seen made to the objection is, that the line of demarcation must be drawn somewhere, and that in every classification there are intermediate cases, which might have been included, with almost equal propriety, either in the one class or in the other. ”

“ In the working of the machine of society, class moves pretty much with class; that is, one class moves pretty much with its equals in the community (equals so far as social station is concerned) , and apart from other classes, as much those below as those above itself ”

“ One class is composed of the tendencies which in a state of nature would promote the happiness of the individual or the crude necessities of the race, but are in conflict with the traditional standards of thought and conduct of the society to which the individual belongs. ”

“ We perform the same process with these higher classes and thus proceed until we are at last arrested in the highest class, that of Being. Having reached the pinnacle of Generalization, we may descend the ladder by reversing the process through which we ascend."
A Concept, then, is seen to be a general idea. It is a general thought that embraces all the individuals of its own class and has in it all that is common to its own class, while it resembles no particular individual of its class in all respects. ”

“ Nothing is more calculated to impress upon a class a worthy and moral character, than the consciousness that it is destined to become a ruling class, that it is called upon to raise the principle of its class to the principle of the entire age, to convert its idea into the leading idea of the whole of society and thus to form this society by impressing upon it its own character. ”

“ Though in a Natural group of objects a definition can no longer be of any use as a regulative principle, classes are not therefore left quite loose, without any certain standard or guide. The class is steadily fixed, though not precisely limited ”

“ For an arrangement of these different classes according to the ideas of Pure Reason, which is quite possible, a foundation must be sought in a complete enumeration of all the natural capacities and wants of man; not, however, of his merely artificial wants. A particular class in society may be devoted to the cultivation of each faculty, or, what is the same thing, to the satisfaction of each want founded on an original impulse in human nature. ”

“ Class distinctions, to a greater or less extent, will creep in—in fact, they do not have to creep in. They are there at the commencement, and they are born of the different conditions of the members.
These class distinctions are not always made by men of wealth. For instance, some men obtain money, and are what we call snobs. Others obtain it and retain their democratic principles, and meet men according to the law of affinity, or general intelligence, on intellectual grounds, for instance. ”

“ And this comparison is by no means strained, as I believe it will be found, that each and every class is indeed numerically greater than all the classes higher in social rank—the idlers than the industrious—the workers than the employers—the children than the parents—the illiterate than the instructed—and so on. ”

“ The class distinctions simply result from the different degrees of success with which men have availed themselves of the chances which were presented to them. Instead of endeavoring to redistribute the acquisitions which have been made between the existing classes, our aim should be to increase, multiply, and extend the chances. ”

“ The point of grouping facts into classes, whether by analysing them into qualities or classifying them into “real things,” is that we can then apply to the particular fact all that we know to be true in general of whatever belongs to these various classes: in a word, once we have fitted a fact into a class we can apply to it all the general laws which are known to apply to that class. ”

“ Now, however, when it is known that a class, a universal, a genus or species, is not an entity _per se_, but neither more nor less than the individual substances themselves which are placed in the class, and that there is nothing real in the matter except those objects, a common name given to them, and common attributes indicated by the name; what, I should be glad to know, do we learn by being told, that whatever can be affirmed of a class, may be affirmed of every object contained in the class? ”

“ Common terms, other than attributives, ought always to admit of definition. For things are distributed by the mind into classes owing to their possessing certain attributes in common, and the definition of the class-name can be effected by detailing these attributes, or at least a sufficient number of them. ”

“ If the properties which are fittest to be selected as marks of other common properties are also obvious and familiar, and especially if they bear a great part in producing that general air of resemblance which was the original inducement to the formation of the class, the definition will then be most felicitous. But it is often necessary to define the class by some property not familiarly known, provided that property be the best mark of those which are known. ”

“ We can not ascertain general truths, that is, truths applicable to classes, unless we have formed the classes in such a manner that general truths can be affirmed of them. In the formation of any class, there is involved a conception of it as a class, that is, a conception of certain circumstances as being those which characterize the class, and distinguish the objects composing it from all other things. ”

“ The simplest and narrowest class is that of actual Individuals. The next is formed by the cohesion of individuals into groups, creating Institutions. The third is made by the artistic conversion of individuals into fictitious characters, sufficiently artificial to be designated as Types,—more or less complex, according to the nature of their creator, but never entirely simple, if they are fashioned of human stuff.
Even more than usual, however, is the caution necessary that the classification is artificial and the classes inseparable. ”

“ According to this view, our social classes must possess a clear-cut regularity of outline such as the insensible gradation of forms of social life renders impossible. We have previously referred to this irrational requirement, and can only repeat that the fallacy proceeds from the assumption that a class can ever possess the defined unity of individual being. ”

“ Since we are dealing with an element in human character which preserves a fixed value, it is evident that we may study the relation of any class in any community to these constantly-recurring phenomena, provided we can isolate this class from all others. ”

“ Propositions, therefore, in which objects are referred to a class because they possess the attributes constituting the class, are so far from asserting nothing but resemblance, that they do not, properly speaking, assert resemblance at all. ”

“ All our ideas are of individuals, or of numbers of individuals, and are clothed with more or fewer of the attributes which are peculiar to the individuals thought of. Still, a class-name stands in a very different relation to the definite resemblances which it is intended to mark, from that in which it stands to the various accessory circumstances which may form part of the image it calls up. There are certain attributes common to the entire class, which the class-name was either deliberately selected as a mark of, or, at all events, which guide us in the application of it. ”