The Online Library of Liberty

A project of Liberty Fund, Inc.

• Preface.
• Part I.: Special Analysis.
• Chapter I.: A Datum Wanted.
• Chapter II.: The Universal Postulate.
• Chapter III.: Its Corollaries.
• Chapter IV.: Our Present Position.
• Part II.: Special Analysis.
• Chapter I.: Compound Quantitative Reasoning.
• Chapter II.: Compound Quantitative Reasoning (continued).
• Chapter III.: Imperfect and Simple Quantitative Reasoning.
• Chapter IV.: Quantitative Reasoning In General.
• Chapter V.: Perfect Qualitative Reasoning.
• Chapter VI.: Imperfect Qualitative Reasoning.
• Chapter VII.: Reasoning In General.
• Chapter VIII.: Classification, Naming, and Recognition.
• Chapter IX.: The Perception of Special Objects.
• Chapter X.: The Perception of Body As Presenting Dynamical, Statico-dynamical, and Statical Attributes. ∗
• Chapter XI.: The Perception of Body As Presenting Statico-dynamical and Statical Attributes.
• Chapter XII.: The Perception of Body As Presenting Statical Attributes.
• Chapter XIII.: The Perception of Space.
• Chapter XIV.: The Perception of Time.
• Chapter XV.: The Perception of Motion.
• Chapter XVI.: The Perception of Resistance.
• Chapter XVII.: Perception In General.
• Chapter XVIII.: The Relations of Similarity and Dissimilarity.
• Chapter XIX.: The Relations of Cointension and Non-cointension.
• Chapter XX.: The Relations of Coextension and Non-coextension.
• Chapter XXI.: The Relations of Coexistence and Non-coexistence.
• Chapter XXII.: The Relations of Connature and Non-connature.
• Chapter XXIII.: The Relations of Likeness and Unlikeness.
• Chapter XXIV.: The Relation of Sequence.
• Chapter XXV.: Consciousness In General.
• Chapter XXVI.: Results.
• Part III.: General Synthesis.
• Chapter I.: Method.
• Chapter II.: Connexion of Mind and Life.
• Chapter III.: Proximate Definition of Life.
• Chapter IV.: The Correspondence Between Life and Its Circumstances.
• Chapter V.: The Degree of Life Varies As the Degree of Correspondence.
• Chapter VI.: The Correspondence As Direct and Homogeneous.
• Chapter VII.: The Correspondence As Direct But Heterogeneous.
• Chapter VIII.: The Correspondence As Extending In Space.
• Chapter IX.: The Correspondence As Extending In Time.
• Chapter X.: The Correspondence As Increasing In Speciality.
• Chapter XI.: The Correspondence As Increasing In Generality.
• Chapter XII.: The Correspondence As Increasing In Complexity.
• Chapter XIII.: The Co-ordination of Correspondences.
• Chapter XIV.: The Integration of Correspondences.
• Chapter XV.: The Correspondences In Their Totality.
• Part IV.: Special Synthesis.
• Chapter I.: The Nature of Intelligence.
• Chapter II.: The Law of Intelligence.
• Chapter III.: The Growth of Intelligence.
• Chapter IV.: Reflex Action.
• Chapter V.: Instinct.
• Chapter VI.: Memory.
• Chapter VII.: Reason.
• Chapter VIII.: The Feelings.
• Chapter IX.: The Will.

CHAPTER XX.

THE RELATIONS OF COEXTENSION AND NON-COEXTENSION.

§ 87. As was shown when treating of Space and of the statical attributes of Body, all modes of extension are resolvable into relations of coexistent positions. Space is known to us as an infinitude of coexistent positions that do not resist: Body as a congeries of coexistent positions that do resist. The simplest extension therefore, as that of a line, must be regarded as a certain series of coexistent positions; equal lines, as equal series of coexistent positions; and coextension, as the equality of separate series of coexistent positions—that is, the sameness in the number of coexistent positions they include.

It was explained at considerable length, that a series of coexistent positions is known to the adult mind, through the simultaneous excitation of some series of independent sensitive agents distributed over the surface of the body: either those extremely minute and closely packed ones of which the retina consists, or those more sparingly dispersed and less individualized ones supplied to the skin. And it was also explained, that the simultaneous excitation of any series of such agents becomes known as the equivalent of their serial excitation; or rather—is a transformation of a series of states of consciousness known as having successive positions, into a quasi single state of consciousness in which these component states are presented in synchronous positions, or coexistent positions: and that these coexistent positions can become known as such, only through the previous establishment of the serial positions to which they correspond—only though those serial excitations of consciousness that result from the motion of images over the retina and objects over the skin. Whence it follows that while, eventually, extension is known in a quasi single state of consciousness produced by the synchronous excitation of a number of independent nerves, either tactual or visual; it is originally known through a series of states produced by the successive excitation of such nerves. Add to which that these synchronous excitations being simply the equivalents and symbols of the successive ones, on which they are based, and to which they are always reducible, the successive ones are those in which all phenomena of extension, subjectively considered, must ultimately be expressed.

Reduced to its lowest terms then, extension is knowable as some series of states of consciousness. But what series? Consciousness is ever passing through a series of states; but is not ever occupied about extension. In the first place then, the series is to be distinguished as more or less homogeneous. The successive states of which it consists must not be of many kinds, but of one kind—must be connatural. But this is not enough; for there are various successions of connatural states—as those produced by heat, odour, or continuous sound—which are not constituents in the idea of extension. Hence then, extension, as originally known, must be some series of connatural states of consciousness of a special order; and as before shown (§ 71) it must, in its primary form, be that order of states produced by the united sensations of motion and touch. Two equal extensions then, are originally known to us as two equal series of sensations of motion and touch. And coextension, when reduced to its lowest terms, means—equality in the lengths of such series; that is—equality in the numbers of the states they severally include.

Two objections to this definition should be noticed. It may be remarked, with apparent truth, that it is a misuse of language to call that which we feel when drawing a finger over the skin, a series of states of consciousness; seeing that the sensations of motion and touch are continuous—are not divided into successive sensations. But saying nothing of the fact that the nerves that are one after another excited by the moving finger are really independent, and must therefore be supposed actually to send successive feelings to the sensorium; it will suffice to reply, that though, in cases of this kind, the state of consciousness is apt to seem unbroken and homogeneous, it is in fact, marked out into a great number of separate portions. For it must be remembered that the very condition on which only consciousness exists, is, perpetual change. If, while a continuous sensation like the one in question were being received, consciousness could be solely occupied with it, there would—if the hibernicism may pass—be no consciousness.∗ A little consideration will show, that during one of these seemingly homogeneous states of consciousness, produced by a persistent sensation, the attention is transitorily occupied with various other things—with surrounding objects, with sounds, with the idea of self, &c. &c.—none of which are wholly absent from the mind. Whence it is clear that what we are liable to take for an unbroken state of consciousness, is really a state broken by numerous incidental states—by fleeting thoughts, which, passing through it, serve to divide it out into portions, and reduce it to a series of states. The second objection is, that coextension, as ordinarily determined by the juxtaposition of the coextensive objects, involves no comparison between two series of states of consciousness; but merely an observation that the ends of the objects coincide: and this is true. But it is clear that this mode of ascertaining coextension is nothing but an artifice, based upon the experience that extensions separately known to us through the equal series of states they produce, always manifest this coincidence of their ends when placed side by side. And as we are here dealing, not with the artificial test of coextension, but with the notion of coextension as it naturally arises, the objection is invalid: more especially as we have thus far considered, not the developed consciousness of coextension, but that primary consciousness out of which it is developed.

§ 88. After what has been said, the nature of our developed consciousness of coextension will readily be understood. The successive impressions through which extension is originally presented, having, by a process repeatedly described, been transformed into synchronous impressions—the whole chain of connatural states, at first known in their serial positions, having become known in their coexistent positions; it follows that the consolidated states of consciousness thus resulting, can be compared, and their likeness or unlikeness recognized, just as the chains of states to which they are equivalent can: or rather, they can be known as like or unlike, because the chains to which they are equivalent are known as like or unlike. When two equal lines cast their images upon the retina, the range of sensitive elements excited by each, having been primarily known as a series of states of consciousness; and the two series having been known as equal series; the equality manifestly becomes as predicable of the consolidated states as it was of the serial states. Each of these consolidated states is produced by the simultaneous stimulation of a certain number of independent nerves of a particular kind; and, physiologically considered, that likeness in the two states which constitutes the intuition in question, results from a likeness in the number and combination of the independent nerves simultaneously affected.

As implied by much that has gone before, it is this simultaneity in the excitation of independent nerves, which gives the notion of coexistence, underlying that of extension, and therefore that of coextension. Though, as will presently be shown, the relation of coexistence is not originally disclosed to consciousness by this simultaneity of excitation; but can only be so disclosed after experience has proved the independence of the simultaneously excited nerves; yet, it is only when it has come to be thus disclosed, that extension and coextension, as we comprehend them, can be conceived: seeing that extension implies coexistence in the parts of the thing extended; and, conversely, coexistence implies a duality which is impossible without space. Extension, therefore, as known by the developed mind, being made up of many elementary consciousnesses of coexistence; the relation of coextension cannot be exhaustively analyzed without analyzing the relation of coexistence. But in so far as the nature of our consciousness of coexistence has been incidentally explained, the relation of coextension, as subjectively considered, may be understood—may be defined as the likeness of two composite states of consciousness, visual or tactual, in respect of the number and order of the elementary relations of coexistence which they severally include: such composite states of consciousness being severally produced by the consolidation of what were originally known as serial states.

To which, for form's sake, it may be added, that the relation of non-coextension is definable as the unlikeness of such two composite states of consciousness.

[∗]A truth illustrated by the fact, that when, as under intense agony, the sensation ultimately becomes strong enough totally to exclude all thoughts—totally to absorb consciousness—consciousness ceases: the patient faints.