Discontinuity

“ The becoming of evolution will then appear to us in its true light, as phases of gradual maturation, rounded at intervals by crises of creative discovery. Continuity and discontinuity will thus admit possibility of reconciliation, the one as an aspect of ascent towards the future, the other as an aspect of retrospection after the event. ”

“ Creations, then, there must be, but they must be so small that practically they are no creations. We must have a continuity in discontinuity, and a discontinuity in continuity; that is to say, we can only conceive the help of change at all by the help of flat contradiction in terms. ”

“ The visible or sensible discontinuity reposes on, and is to be explained by, an invisible or ideal continuity. Each body, for instance, in nature, appearing to have a separate existence of its own, is only a stage isolated or insulated in a continuing process: and that process, binding, as it does, past to future, is the process of a Mind. ”

“ There is no essential difference of nature between the activities of various categories of beings, no heterogeneity, no discontinuity. We may pass from one to another without coming to an hiatus or impassable gulf. The law of continuity thus appears as a simple consequence of the fundamental postulate. And so it is with the law of evolution, for evolution is merely continuity of action. ”

“ Genetic continuity is a background for pragmatic discontinuity. The moments of discontinuity correspond to threshold values in the scale of human activity. They regard mediating devices and strategies as dynamic components of the pragmatic framework. ”

“ But, supposing this view were finally to prevail, it could only lead, on deeper study, to some other mode of analyzing of the living being, and so to a new discontinuity—although less removed, perhaps, from the real continuity of life. ”

“ But where surfaces of discontinuity are considered, a system is not regarded as practically unstable, unless the disturbance which will produce such a result is very small compared with the quantities relating to surfaces of discontinuity of any appreciable magnitude. ”

“ I take the position that the transition from nature to culture, i.e., from reactions caused by natural stimuli to reflections and awareness, is marked by both continuity and discontinuity. The continuous aspect refers to the biological structure projected into the universe of interactions with similar or dissimilar entities. ”

“ Those who live for the moment prefer discontinuity. Those who observe their natural environment are forced to the conclusion that life today is part of a sequence or progression which relates the life of yesterday to that of tomorrow. ”

“ Therefore, in a system satisfying the conditions of practical stability with respect to the possible formation of all kinds of homogeneous masses, negative tensions of the surfaces of discontinuity are necessarily excluded. ”

“ The supposed difficulties of continuity all have their source in the fact that a continuous series must have an infinite number of terms, and are in fact difficulties concerning infinity. Hence, in freeing the infinite from contradiction, we are at the same time showing the logical possibility of continuity as assumed in science. ”

“ For the identity in time of an existing thing (as in this work I have mentioned) you require both temporal continuity and again sameness in the thing’s proper character. And mutatis mutandis what is true here about temporal continuity is true also about spatial, and not to perceive this would be an error. Now whether a wholly unbroken continuity in time or space is requisite for the singleness of a thing, is a question I here pass by; [6] but some unbroken duration obviously is wanted if there is to be duration at all. ”

“ A moving continuity is given to us, in which everything changes and yet remains: whence comes it that we dissociate the two terms, permanence and change, and then represent permanence by bodies and change by homogeneous movements in space? ”

“ If we reflect upon the species of multiplicity required to constitute extension, we shall observe that it must be accompanied by continuity. Sensations of touch as well as of sight involve continuity; for it is impossible for us to see or to touch, without receiving the impression of objects continuous, immediately adjoining each other, co-existing in their duration, and at the same time presented as continuous one with another in space. Without this continuity, multiplicity does not constitute extension. ”

“ The continuity of being is lacerated; the settled course of sentiment and action is stopped; and life stands suspended and motionless, till it is driven by external causes into a new channel. But the time of suspense is dreadful. ”

“ All the Concrete Sciences familiarize the mind with certain cardinal conceptions which the Abstract and Abstract-Concrete Sciences do not yield—the conceptions of continuity, complexity, and contingency. The simplest of the Concrete Sciences, Astronomy and Geology, yield the idea of continuity with great distinctness. I do not mean continuity of existence merely; I mean continuity of causation: the unceasing production of effect—the never-ending work of every force. ”

“ This is what, as a radical empiricist, I say to the charge that the objective reference which is so flagrant a character of our experiences involves a chasm and a mortal leap. A positively conjunctive transition involves neither chasm nor leap. Being the very original of what we mean by continuity, it makes a continuum wherever it appears. Objective reference is an incident of the fact that so much of our experience comes as an insufficient and consists of process and transition. Our fields of experience have no more definite boundaries than have our fields of view. ”

“ How do we parcel out the continuity of material extensity, given in primary perception, into bodies of which each is supposed to have its substance and individuality? No doubt the aspect of this continuity changes from moment to moment; but why do we not purely and simply realize that the whole has changed, as with the turning of a kaleidoscope? Why, in short, do we seek, in the mobility of the whole, tracks that are supposed to be followed by bodies supposed to be in motion? ”

“ Any finite whole, with its incomplete conjunction of qualities and relations, entails a process of indefinite transition beyond its limits as a consequence. But with the extended, more than anything, this self-transcendence is obvious. ”

“ In all this the continuities and the discontinuities are absolutely co-ordinate matters of immediate feeling. The conjunctions are as primordial elements of 'fact' as are the distinctions and disjunctions. In the same act by which I feel that this passing minute is a new pulse of my life, I feel that the old life continues into it, and the feeling of continuance in no wise jars upon the simultaneous feeling of a novelty. They, too, compenetrate harmoniously. ”

“ By this the difficult concept of continuity is evoked in our experience. The transition from the light of day to the darkness of evening proceeds continuously, that is, at no point of the whole transition do we notice that the state just passed is different from the present one, while the difference over a wider extent of the experience is unmistakable. If we wish to bring vividly to our minds the contradiction to other habits of thought which this involves, we need only to represent to ourselves the following instance. ”

“ Every history is equally continuous, undisturbed by its beginnings and endings. Each action of time is preceded and followed by everything which precedes and follows it, and yet each action of time begins and ends with its own peculiar and individual precision. In affirming this we are affirming, by means of a particular instance, the metaphysical nature of continuity itself. For by continuity we mean the possibility of precise and definite distinctions. The continuity of a line may be divided at its middle point. ”

“ But the attitude to life, which is even more important, is something that has hardly yet been formulated. And I shall endeavour to give some first rough expression to it.
"The first constituent, then, of the new view is that of continuity. We of the new generation realize that the present is a mere transition from the past into the future; that no event and no moment is isolated; that all things, successive as well as coincident, are bound in a single system. ”

“ The definitions of continuity which we have been considering, namely, those of Dedekind and Cantor, do not correspond very closely to the vague idea which is associated with the word in the mind of the man in the street or the philosopher. They conceive continuity rather as absence of separateness, the sort of general obliteration of distinctions which characterises a thick fog. A fog gives an impression of vastness without definite multiplicity or division. ”

“ The moment a given phase is reached, it is departed from, or ceases. In these perpetual movements the present can scarcely be said to have any existence, for as the Past is ending, the Future has begun. ”

“ That all phenomena in our intermediate state, or quasi-state, represent this one attempt to organize, stabilize, harmonize, individualize—or to positivize, or to become real:
That only to have seeming is to express failure or intermediateness to final failure and final success;
That every attempt—that is observable—is defeated by Continuity, or by outside forces—or by the excluded that are continuous with the included:
That our whole "existence" is an attempt by the relative to be the absolute, or by the local to be the universal. ”

“ TRANSLATION. “Hence it is clear, from what cause many reject the notion of the continuous and the infinite. They take, namely, the words irrepresentable and impossible in one and the same meaning; and, according to the forms of sensuous evidence, the notion of the continuous and the infinite is doubtless impossible. I am not now pleading the cause of these laws, which not a few schools have thought proper to explode, especially the former (the law of continuity) . ”

“ The activity of the moment-consciousness is continuous, without break and interruption. Should the activity become arrested and the break be seemingly absolute, continuity is still present with the resumption of activity. ”

“ This element is our feeling of succession, or time—a feeling, which necessarily, involves the notion of divisibility or series of parts, that is so essential a constituent of our more complex notion of matter,—and to which notion of continuous divisibility, if the notion of resistance be added, it is scarcely possible for us to imagine, that we should not have acquired, by this union, the very notion of physical extension,—that which has parts, and that which resists our effort to grasp it. ”

“ That continuity is a concept which springs from experience can scarcely be doubted, and it can be accounted for by the inability of our crude senses to differentiate between impressions which are almost alike. ”

“ And to it, as well as to life in the bare physiological sense, the principle of continuity through renewal applies. With the renewal of physical existence goes, in the case of human beings, the re-creation of beliefs, ideals, hopes, happiness, misery, and practices. ”

“ If we now consider the defects of the Decline and Fall—which the progress of historic study, and still more the lapse of time, have gradually rendered visible, they will be found, as was to be expected, to consist in the author's limited conception of society, and of the multitudinous forces which mould and modify it. We are constantly reminded by the tone of remark that he sees chiefly the surface of events, and that the deeper causes which produce them have not been seen with the same clearness. ”

“ In the rôle of aprioristic metaphysics, the principle of continuity is destructive, and tends to plane down everything to the dead level of materialistic monism. For those who transcendentalize it, it becomes the principle “that everything is ‘nothing but’ something else, probably inferior to it.” (Santayana.) To assert continuity, they are driven to deny, or, at least, to leave unexplained and inexplicable, the obvious novelty that emerges at each higher level of the cosmic scale. ”

“ If we go on to consider persistence abstractly, we must still remember that the persistence is the persistency of a unity, an extension, a speed, and a consciousness. But between these persistent concomitants there are relations, and these relations are changeable; so when we consider persistence and change, it is the persistence of particles of essentials and change of relations of particles of essentials. Only relations are changeable, essentials are persistent. ”

“ The answer is, that we have still proof of the most wonderful provisions for permanence, but permanence for only one phase of a mighty evolution. The only difference is, that in former views of the stability of the system, we considered the mechanism as a fixed, rigid, isolated thing, whereas we are now forced to regard every part of the universe as in a state of change or progress. ”

“ True, our psychic life is full of the unforeseen. A thousand incidents arise, which seem to be cut off from those which precede them, and to be disconnected from those which follow. Discontinuous though they appear, however, in point of fact they stand out against the continuity of a background on which they are designed, and to which indeed they owe the intervals that separate them ”