Constant

“ Necessity may be defined two ways, conformably to the two definitions of cause, of which it makes an essential part. It consists either in the constant conjunction of like objects, or in the inference of the understanding from one object to another. ”

“ The constant flux and caprice of mental events do not admit of the establishment of stable experimental conditions. ”

“ This is the reason why no form remains permanently in a substance; a constant change takes place, one form is taken off and another is put on. ”

“ If we examine the matter closely, we will see that all the cases considered come under the head of form—worlds, plants, animals, men. But there is another great class of cases which fall under the head of forces or principles, and these when carefully examined are found not to be variables but constants—the constants of nature. ”

“ For so many days and years Caterina was my constant companion; I loved her as my own soul. Yet was she but a sun that dazzled my eyes so that I could not gaze upon my own soul; but a veil between me and my dead youth. The sun has sunk forever below the horizon; the veil is rent. No phantom from the other world hovers to remind me of our happiness. Those years, with all their raptures and successes, are a dull blank. It is the years of boyhood and youth which resurge in my consciousness; their tints are vivid, their tones are clear. ”

“ 'What is the meaning of my life, beyond time, cause, and space?' And I replied to quite another question: 'What is the meaning of my life within time, cause, and space?' With the result that, after long efforts of thought, the answer I reached was: 'None.'
In my reasonings I constantly compared (nor could I do otherwise) the finite with the finite, and the infinite with the infinite; ”

“ But when we come to the right-hand side of the equation we must remember that what we have got to sum up together is not all the ’s, but all such terms as ; and this will not be the same as , because is not a constant. For some of the ’s will be multiplied by big values of , and some will be multiplied by small values of , according to what happens to be. So we must bethink ourselves as to what we know about this process of integration being the reverse of differentiation. ”

“ That is to say, will be changed [1] to . Put this into the equation; but don't forget to add the “constant of integration” at the end. So we get:
.
You have actually performed the integration. How easy!
Let us try another simple case.
where is any constant multiplier. Well, we found when differentiating (see p. 29) that any constant factor in the value of reappeared unchanged in the value of . In the reversed process of integrating, it will therefore also reappear in the value of . So we may go to work as before, thus:
So that is done. ”

“ That function takes precedence of structure, seems also implied in the definition of Life. If Life is shown by inner actions so adjusted as to balance outer actions—if the implied energy is the substance of Life while the adjustment of the actions constitutes its form; then may we not say that the actions to be formed must come before that which forms them—that the continuous change which is the basis of function, must come before the structure which brings function into shape? ”

“ The theory of continuity, with which we shall be occupied in the present lecture, is, in most of its refinements and developments, a purely mathematical subject—very beautiful, very important, and very delightful, but not, strictly speaking, a part of philosophy. The logical basis of the theory alone belongs to philosophy, and alone will occupy us to-night. ”

“ Here then respecting the nature of the Universe, we seem committed to certain unavoidable conclusions. The objects and actions surrounding us, not less than the phenomena of our own consciousness, compel us to ask a cause; in our search for a cause, we discover no resting place until we arrive at the hypothesis of a First Cause; and we have no alternative but to regard this First Cause as Infinite and Absolute. ”

“ And if we carry our observation outward, we also find that light and darkness, sound and silence, motion and quiescence, equality and inequality, preceding and following, succession and simultaneousness, any positive phenomenon whatever and its negative, are distinct phenomena, pointedly contrasted, and the one always absent where the other is present. I consider the maxim in question to be a generalization from all these facts. ”

“ With some people it is a condition which is present all the time. Now you take a condition which is present all the time, and the results of that condition will be uniform; this uniformity of result will in time become monotonous; monotonousness, by the law of its being, is fatiguing. ”

“ The definite combination of heterogeneous changes, both simultaneous and successive, is a formula which fails to call up an adequate conception. And it fails from omitting the most distinctive peculiarity—the peculiarity of which we have the most familiar experience, and with which our notion of Life is, more than with any other, associated. ”

“ The series of causes and effects which we call the world, or the course of nature, may be considered as a whole, and this whole must have a cause of its existence. The whole collection of objects and events may be comprehended as a single effect, and of this effect there must be a cause. This Cause of the Universe must be superior to, and independent of the special events, which, happening in time, make up the universe of which He is the cause. He must exist and exercise causation, before these events can begin: He must be the First Cause. ”

“ All the uniformities which exist in the succession of phenomena, and most of the uniformities in their co-existence, are either, as we have seen, themselves laws of causation, or consequences resulting from, and corollaries capable of being deduced from, such laws. If we could determine what causes are correctly assigned to what effects, and what effects to what causes, we should be virtually acquainted with the whole course of nature. ”

“ We trace them one by one from highly-involved conditions, through the less and less involved, until at last the simple force, divorced from all associated relations, is lost in the azure blue of the infinite—infinite in the space it may occupy—infinite in its duration—infinite in the diversity of effects that may arise from association with other simple forces, and finite or comprehensible alone in the duration of these conditions. ”

“ Exactly thus, if once thou holdest true That certain seeds are finite in their tale, The various tides of matter, then, must needs Scatter them flung throughout the ages all, So that not ever can they join, as driven Together into union, nor remain In union, nor with increment can grow— But facts in proof are manifest for each: Things can be both begotten and increase. 'Tis therefore manifest that primal germs, Are infinite in any class thou wilt— From whence is furnished matter for all things. ”

“ The mode of discovering and proving laws of nature, which we have now examined, proceeds on the following axiom: Whatever circumstances can be excluded, without prejudice to the phenomenon, or can be absent notwithstanding its presence, is not connected with it in the way of causation. [pg 280] The casual circumstances being thus eliminated, if only one remains, that one is the cause which we are in search of: if more than one, they either are, or contain among them, the cause; and so, mutatis mutandis, of the effect. ”

“ There is one matter, one power, one space, one efficient cause, God and Nature, everywhere equally, and everywhere powerful.—We insult the infinite cause when we say that it may be the cause of a finite effect ”

“ And, as we have already seen, and in the present lecture shall further illustrate, the relation of partial and total meaning is, at the same time, the relation of any finite will to the expression of the complete intent of that same will. Without contradiction, therefore, you are unable to assert the real Being of any world, unless you conceive that world as the expressed will whose partial momentary embodiment you even now observe, whenever you get any rational idea before your mind. ”

“ How form to ourselves an idea of a substance, void of extent, yet acting on our senses; that is to say, on those organs which are material, which have extent? How can a being without extent be moveable ”

“ Let us imagine this universe filled with the greatest conceivable number of active principles, all identical, diffused uniformly throughout immensity, and consequently in a state of perfect equilibrium. ”

“ But when we have asserted, as we have now done, that every moment of every finite consciousness has some unique character, and when we have asserted, as we have also done, that in our rational life our momentary will and its finite expression belong to this very unique aspect of our finite life, we have indeed found, in our finite will, an aspect which no causation could ever by any possibility explain. ”

“ Far, too, as her splendors shine, system on system shooting like rays, upward, downward, without centre, without circumference,—in the mass and in the particle, nature hastens to render account of herself to the mind. ”

“ It is to say that reason, whether finite or infinite, must be consistent with itself; and that, therefore, the finite must be able to comprehend the infinite, to travel from any one province of the moral and material universe to any other, to trace their bearing, and to connect their boundaries. ”

“ It follows that, theoretically, the whole state of the material universe at time t must be capable of being exhibited as a function of t. Hence our universe will be deterministic in the sense defined above. ”

“ Now on account of the various relations that exist between the different modes of being, relations of cause and effect, whole and part, means and end, ground and consequence, etc.—relations which constitute the orders of existing and possible things, the physical and the metaphysical orders—being is of course predicated of its modes by analogy of attribution; and in such predication infinite being is the primary analogue for finite beings, and the substance-mode of being for all accident-modes of being. ”

“ Each comes out of the second or theoretic stage of mental functioning, with its definition of the essential nature of things, its formula of formulas prepared. The whole array of active forces of our nature stands waiting, impatient for the word which shall tell them how to discharge themselves most deeply and worthily upon life. ”

“ And, taught as we have been to regard these definitions as complete, we naturally and rightly reject the monstrous notion that out of such matter any form of life could possibly arise. But are the definitions complete? Every thing depends on the answer to be given to this question. Trace the line of life backward, and see it approaching more and more to what we call the purely physical condition. ”

“ Consciousness and change, so far as we can watch them, are as functionally interdependent as mind and matter, or condition and substance, are—for the condition of every substance may be considered as the expression and outcome of its mind. ”

“ So long as it is supposed that the physical world is composed of stable and more or less permanent constituents, the fact that what we see is changed by changes in our body appears to afford reason for regarding what we see as not an ultimate constituent of matter. But if it is recognised that the ultimate constituents of matter are as circumscribed in duration as in spatial extent, the whole of this difficulty vanishes. ”

“ Outside one another as the phenomena in this phenomenal world are, they form a totality, and are wholly contained in their self-relatedness. In this way the self-relation of the phenomenon is completely specified, it has the Form in itself: and because it is in this identity, has it as essential subsistence. So it comes about that the form is Content: and in its mature phase is the Law of the Phenomenon. ”

“ The seemingly fixed character of such a world is found in the generally fixed conditions which underlie the type of problems which we find. We determine the important conditions incident to the working out of the great problems which face us. Our conception of a224 given universe is formed in the effort to mobilize all the material about us in relation to these problems—the structure of the self, the structure of matter, the physical process of life, the laws of change and the interrelation of changes. ”

“ We take elements which at the first glance are unconnected; these arrange themselves in an unexpected order, and form a harmonious whole. We cannot believe that this unexpected harmony is a mere result of chance. ”

“ This doctrine of the regular subordination of beings, the scale of existence, and the chain of nature, I have often considered, but always left the inquiry in doubt and uncertainty.
That every being not infinite, compared with infinity, must be imperfect, is evident to intuition; that, whatever is imperfect must have a certain line which it cannot pass, is equally certain. ”

“ But the conditions which make many moments of experience, many thoughts, or many people, refer to the same content or moment of experience, or to the same fact in any sense, are not themselves, as conditions of the sameness of reference, contents of anybody’s experience, or part of the flow of its ceaseless stream. These conditions, then, presupposed in all rationality, are ipso facto transcendent. ”

“ Allowing a margin for perturbations, the life will continue only while the correspondence continues; the completeness of the life will be proportionate to the completeness of the correspondence; and the life will be perfect only when the correspondence is perfect. ”

“ The transformation of matter and energy, then, is the essence of causation: because it is continuous, causation is immediate; and because in the same circumstances the transformation always follows the same course, a cause [Pg 183] has invariably the same effect. ”