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From the very outset of the philosophical study of the diversities of the universe, it has been noticed, that in many cases, where common sense is content to enumerate two, or three, or some other limited number of aspects or constituents of a supposed object, closer analysis shows that the variety contained in this object, if really existent at all, must be boundless, so that the dilemma: “Either no true variety of the supposed type my paper is real, or else this variety involves an infinity of aspects,” has often been used as a critical test, to discredit some commonly received view as to the unity and variety of the universe or of some supposed portion thereof. Mr. Bradley has not been wanting in his appeal to this type of critical argument. But to give this argument its due weight, when it comes as a device for discrediting all efforts to define the nature of Individuals, requires one to attack the whole question of the actual Infinite, a question that recent discussions of the Philosophy of Mathematics have set in a decidedly new light, but that these discussions have also made more technical than ever. If I am to be just to this matter, I must therefore needs wander far afield. Nobody, I fear, except a decidedly technical reader, will care to follow. I have, therefore, hesitated long before venturing seriously to entertain the plan of saying, either here or elsewhere, anything about what seems to me the true, and, as I believe, the highly positive implication, of Mr. Bradley’s apparently most destructive arguments concerning Individual Being and concerning the meaning of the world of Appearance.

But if it is impossible to conceive qualities without relations, it is equally unintelligible to take qualities together with relations. For the qualities cannot be resolved into the relations. And, if taken with the relations, they “must be, and must also be related” (p. 31). But now afresh arises the problem as to how, in this instance, the variety involved in the also is reducible to the unity which each quality must by itself possess. For a quality, A, is made what it is both by its relations (since, as we have seen, these are essential to its being as a quality), and by something else, namely, by its own inner character. A has thus two aspects, both of which can be predicated of it. Yet “without the use of a relation it is impossible to predicate this variety of A,” just as it was impossible, except by the use of a relation, to predicate the various qualities of one thing. We have therefore to say that, within A, both its own inner character, as a quality, and its relatedness to other facts, are themselves, as varieties, facts; but such facts as constitute the being of A, so that they are united by a new relation, namely, by the very relation which makes them constitutive of A. Thus, however, “we are led by a principle of fission which conducts us to no end.” “The quality must exchange its unity for an internal relation.” This diversity “demands a new relation, and so on without limit.”

Meanwhile, the “mere conjunction,” if taken as such, is “for thought contradictory” (p. 565). For as soon as thought makes the conjunction its object, thought must “hold in unity” the elements of the conjunction. But finding these elements diverse, thought “can of itself supply no internal bond by which to hold them together, nor has it any internal diversity by which to maintain them apart.” If one replies that the elements are offered to thought “together and in conjunction,” Mr. Bradley retorts that the question is “how thought can think what is offered.” If thought were itself possessed of conjoining principles, of “a ‘together,’ a ‘between,’ and an ‘all at once,’” as its own internal principle, it could use them to explain the conjunction offered. But, as a fact (p. 566), “Thought cannot accept tautology, and yet demands unity in diversity. But your offered conjunctions, on the other side, are for it no connections or ways of union. They are themselves merely other external things to be connected.” It is, then, “idle from the outside to say to thought, ’Well, unite, but do not identify.’ How can thought unite except so far as in itself it has a mode of union? To unite without an internal ground of connection and distinction, is to strive to bring together barely in the same point, and that is self-contradiction.” Things, then, “are not contradictory because they are diverse,” but “just in so far as they appear as bare conjunctions.” Therefore it is that a mere together, “in space or time, is for thought unsatisfactory and, in the end, impossible.” But, on the other hand, every such untrue view must be transcended, and the Real is not self-contradictory, despite its diversities, since their real unity is, in the Absolute, present.

All this being understood, let us undertake to define a map that shall be in this sense perfect, but that shall be drawn subject to one special condition. It would seem as if, buying essays in case our map-drawing powers were perfect, we could draw our map wherever we chose to draw it. Let us, then, choose, for once, to draw it within and upon a part of the surface of the very region that is to be mapped. What would be the result of trying to carry out this one purpose? To fix our ideas, let us suppose, if you please, that a portion of the surface of England is very perfectly levelled and smoothed, and is then devoted to the production of our precise map of England. That in general, then, should be found upon the surface of England, map constructions which more or less roughly represent the whole of England, – all this has nothing puzzling about it. Any ordinary map of England spread out upon English ground would illustrate, in a way, such possession, by a part of the surface of England, of a resemblance to the whole. But now suppose that this our resemblance is to be made absolutely exact, in the sense previously defined. A map of England, contained within England, is to represent, down to the minutest detail, every contour and marking, natural or artificial, that occurs upon the surface of England. At once our imaginary case involves a new problem. This is now no longer the general problem of map making, but the nature of the internal meaning of our new purpose.

While, however, self-representative systems of ideal or of physical objects belonging to the later types play a great part in exact physical and in mathematical science, their study does not throw light upon the primal way in which the One and the Many, in the processes directly open to thought’s own internal observation, are genetically combined. For physical systems which permit these transformations of a whole into an argumentative research paper exact image of itself are given as external “conjunctions,” such as crystal forms. We do not see them made. We find them. The ideal cases of the same type in pure mathematics have also a similar defect from the point of view of Bradley’s criticism. A system that is to be made self-representative through a “group of substitutions,” shows, therefore, the same diversities after we have operated upon it as before; and, furthermore, that congruence with itself which the system shows at the end of a self-representative operation of any type wherein all elements take the place of all, is not similar to what happens where, in our dealings with the universe, Thought and Reality, the Idea and its Other, Self and Not-Self, are brought into self-evident relations, and are at once contrasted with one another and unified in a single whole. Hence, we shall indeed continue to insist, in what follows, upon those self-representations wherein proper part and whole meet, and become in some wise precisely congruent, element for element.[16] We mention the other types of self-representation only to eliminate them from the present discourse.

Hereupon, of course, Mr. Bradley’s now familiar form of argument enters with its full rights. Unquestionably a world with three facts in it, – facts such that, by definition, either f or F might have existed wholly alone, and apart from the third fact, is a world where legitimate questions can be raised about the ties that bind the third fact to the other two. These ties are themselves facts. The + is linked to f and to F, and the “endless fission” unquestionably “breaks out.” The relation itself is seen entering into what seem new relations. The reason why this fission breaks out is now more obvious to us. It lies not in the impotence of our intellect, impotent as our poor human wits no doubt are, but in the self-representative character of any relational system. In our realistic world the system is such that, to any object, there corresponds, as another object (belonging to the same system), the relation between this first object and the rest of the universe. Or, in general, if in the world there is an object, F, then there is that relation, R, whereby F is linked to the rest of the world. But to R, as itself an object, there therefore corresponds, at the very least, a research paper R’, its own relation to the rest of the world; and the whole system F + R + R’ is as self-representative, and therefore as endless, as the number-system, and for precisely the same reason: viz., because it images, and, by hypothesis, expresses, in the abstract form of a supposed “independent Being,” the very process of the Self which undertakes to say, “F exists.”