Truth and Error or the Science of Intellection/Chapter 4
Having considered the nature of the properties of a discrete particle of matter by reason of its own existence and the existence of others, we have now to consider how these relations are developed by incorporation. Still it is necessary only to draw upon the common stock of knowledge and deduce from it legitimate results which are easily understood. We have shown that the ultimate discrete particles are related to each other through pluralities, positions, paths and changes, and we have now to consider another method of association, for particles of matter are incorporated, and enter into fixed associations with one another by affinity, the nature of which has never been explained, although the association is well known. Every particle of matter under certain conditions seems to be able to choose its associate, and a group of such particles that have mutual affinities become compounded into that which is usually denominated a molecule. This association of particles in a molecule is not easily dissolved under ordinary conditions, yet if special conditions are provided the association is fickle and old combinations are dissolved that new combinations may be formed.
Then molecules enter into association with one another without cohesion in gases, with feeble cohesion in liquids, and a more tenacious cohesion in solids. A body thus considered of like molecules is called a substance.
II[edit]
In the combination of particles into molecules and other bodies, an interesting development of the properties is observed. Such a combination produces a new unit of a higher order. Here we find a new unity made such by combination, and it must be observed that it depends upon a plurality combined in one. It is therefore a new kind of unit. Thus a kind is developed by the combination of a plurality of units into one—a process familiar in the conventional units of arithmetic, where ten units of the lower order make one of the next higher order. That which is accomplished by convention in arithmetic, is accomplished by incorporation in nature. In this manner by combination the quantitative property of number in the particle becomes the classific property or kind in the molecule, and as there is a hierarchy of molecules and every one considered as a unit may become a particle in a higher order, we are compelled to consider it in this double and relative capacity, as one of many and as many in one. A molecule in its internal aspect appears as many; in its external aspect as one. Thus we have incorporated units, and these may be incorporated in a still higher order, and on indefinitely. There are many bodies of a kind and they constitute a class. Thus a class is a series or sum of a kind.
III[edit]
Ultimate particles, by reason of their extension and position, give rise to space; when they are incorporated positions are established in relation to one another, and thus a form is constituted. It is thus that space is developed into form by incorporation. It is seen that the particles of the molecule considered as such exhibit space with extension and position, while the molecule or other body also exhibits figure and structure. If we view the body from within as composed of particles, space is presented; if we view it from without as a body, form is presented.
Again, this same molecule may become a particle in a higher order of molecules, when it will exhibit space characteristics, and a higher molecule will exhibit form characteristics. Thus space is the reciprocal of form.
In my room there are desks, chairs, book-cases, books and many other articles. Their relations of position are relations of space. Were all these articles consolidated into one, so that one could not be moved without moving all, their relations would become relations of form. Contemplate a pile of cannon-balls; the relations of these balls to one another are relations of space; combine them into one body in such a manner that they will move together as one, their relations of space become relations of form also.
IV[edit]
It has already been asserted that a particle cannot lose speed. When we contemplate a molecule composed of particles in which relative positions are fixed, we are compelled to develop the thought one stage farther and conceive of them as still retaining their speeds. The concept of particles with relative positions fixed, and every one retaining its motion, can be realized by a consideration of facts presented by celestial bodies. The earth and moon revolve about a common axis which is within the periphery of the earth, and each retains its own speed while the relative position of each is preserved. But the sun and the earth revolve together about a common axis in the same manner, and the relative positions are preserved, while the relative position of the moon to the sun is indirect through the mediation of the earth. In like manner it can be shown that the relative positions of all the members of the solar system are preserved directly or mediately by a system of motion. Now, the solar system may be considered as the type of a molecule in which the particles retain their speeds and have their relative positions fixed by deflection in the motion of revolution. Yet the concept is not complete; for every one of the members of the solar system is rotating about its own axis. So that there is a complex system of motions within the solar system by which the orbs are kept within the theater of the system itself, even though the system as a unit may be revolving about some other point in the heavens; and the fixity of position of celestial particles is fixity of space relations about axes of revolution.
We do not know that the particles of a molecule move within the sphere of the molecule by a system of rotations and revolutions, though such a system can be conjectured; but whatever the system may be, it must accomplish the same results by confining a certain portion of the speeds of the particles within the theater of the molecule by a system of deflections, and, whatever may be the motion of the molecule itself in relation to other molecules, the speed of the particle must be partly taken up within the molecule, and it must then be divided between internal motion and external motion. Let us vivify this concept into greater distinctness.
Imagine a particle moving to and fro in vibration at the rate of millions of vibrations a second; the sphere of this motion is measured by the amplitude of the vibration. If the deflection is something less than one hundred and eighty degrees at both extremities of the vibration and on the same side, the particle will move off in the direction normal to the vibration. Its motion in the new direction increases inversely with the angle of deflection, until it reaches ninety degrees.
Now consider the speed of the particle in vibration when the deflection is one hundred and eighty degrees; then the total speed is represented in the vibration, but when the particle is moved in a direction normal to the vibration, the speed of the vibration is less by the amount of speed taken up in the new motion; thus the speed of the particle is divided between its two motions. In this manner we may conceive of the speed of the ultimate particle as being divided among the speeds of the bodies of a hierarchy in which the particle is incorporated. What we have shown about the speed of a particle in rectilineal motion is true of it in all forms of curvilineal motion. When one molecule collides with another each has its path deflected inversely proportional to its mass, for its mass is the sum of its particles, every one in motion and having a path of its own, and all of the particle paths must be deflected to a greater or less degree in order that the molecular path may be deflected. The force, therefore, with which one body deflects another and by which it resists deflection itself is the sum of the motion of its particles. Force, therefore, is a compound of motions. Thus motion in the particle becomes force in the molecule or other body. But the molecule itself may become a particle in a higher molecule, when its force becomes a motion which again must be composed.
V[edit]
We have now to consider the development of time by incorporation. It has been seen that time is persistence and change. The endless persistence of the particle is interrupted by changes in its relation to other particles, but when these relations are incorporated and become established as kinds, forms, and forces, time undergoes a development, for it then becomes causation as antecedent and consequent, or cause and effect. In ultimate particles collisions result in deflections and the changes which occur relate to paths; but the particles themselves are unmodified. When bodies are considered another set of relations are generated. With every collision the body may be modified, and a succession of these collisions may ultimately produce a great change. The change which bodies undergo in this manner is called causation. Thus, a body may be deformed or broken up, it may grow or decay when cause and effect are involved. Whatever happens to a molecule is distributed to its particles and is observed in its particles. If, now, we discover an effect and desire to learn its cause, we find the effect distributed to all of the particles which constitute the molecule and must go outside the molecule for its cause. This is what is known as the infinite regressus of causes. The total cause of any event to a molar body stretches out through all the earth, and as the earth is a particle in the solar system the total cause embraces the sun and its planets and their satellites. Now, when we are considering an event as an effect, we are considering it as a change in the individual, but when we are considering the total cause of the change, we are considering the environment. The effect again becomes cause, which proceeds onward as a multiplication of causes distributed to all the environment. In the regressus of causes the total cause is multifarious; but we may from time to time consider any one of the effects of the total cause as the cause which may be varied in the production of an effect; then out of the effects of the total cause the one selected may be known as the special cause. This is the cause to which reference is made in common speech. An effect is observed in the explosion of gunpowder. We may consider the cause as the instability of the compound, the ignition of the powder with a match, or the purpose of the mischievous boy, etc. In like manner we may go on in an indefinite regressus to catalogue the causes of the explosion. When I am considering the conduct of the boy I attribute the cause to him; when I am considering the flame I attribute the cause to the flame; when I am considering the constitution of the powder I attribute it to the explosiveness of the substance. These are special causes as distinct from the total cause. Man comes to consider cause in this manner for a practical reason, for he interferes in causation for his own ends, and is forever searching for the most economic means of changing events.
I am not familiar with any discussion of causation equal to that of John Stuart Mill in his work on Logic; but he failed to distinguish causation as an abstraction from force, form and kind. In his chapter on the Composition of Forces, he says:
“I shall give the name of the Composition of Causes to the principle which is exemplified in all cases in which the joint effect of several causes is identical with the sum of their separate effects.
“This principle, however, by no means prevails in all departments of the field of nature. The chemical combination of two substances produces, as is well known, a third substance with properties entirely different from those of either of the two substances separately, or of both of them taken together. Not a trace of the properties of hydrogen or of oxygen is observable in those of their compound, water.”
In the chemical union of oxygen and hydrogen a new kind is produced as water. Here we have composition of kind; when causes are composed new conditions are developed; thus the oxygen and the hydrogen are found under new conditions of incorporation. In these new conditions there is a change in space relations, so that water occupies less space than the gases of which it is composed; thus the composition of kinds gives rise to the composition of conditions, but is not itself the composition of conditions as an abstraction. To discuss the composition of conditions it is necessary to discuss the very things to which Mill refers when he speaks of the development of new properties.
Heretofore we have used the terms total cause and special cause and have shown that the special cause is that one of a multiplicity of causes which is considered. Recurring to the illustration used before, it will be remembered that the cause of the explosion might be considered as the constitution of the dynamite, or it might be considered as the spark by which the powder was ignited, or it might be considered as the act of the incendiary, and in this manner we obtain the infinite regressus of causes. The considered cause may be any one near or remote in the infinite regressus. When any one is selected all the others become conditions; hence we have a cause and its conditions. So cause is related to effect and cause is also related to condition.
At this moment a man is climbing to the roof of my house. The cause of his climbing is a breach in the roof which he intends to repair. The cause of his climbing is his intention; the cause of his climbing is my request; the cause of his climbing is my knowledge of the breach in the roof; the cause of his climbing is the information given me by another that my roof leaks; the cause of his climbing is his desire to earn a fee; the cause of his climbing is his desire to purchase food; the cause of his climbing is his love of his family; the cause of his climbing is the hunger of his children. So we may go on forever to enumerate remote and distinct causes, and when we consider any one of them, the others become conditions which must be assumed as necessary to the operation of the selected cause.
We have considered teleologic causes; now we must consider genetic causes. The man falls from the roof. The cause of his falling is the misstep he makes; the cause of his falling is gravity; the cause of his falling is the greater distance of the roof than the surface of the earth to the center of the earth; the cause of his falling is the ascent to the roof; the cause of his falling is his coming to make repairs. If any one of these conditions had been omitted he would not have fallen, and we can go on to multiply these conditions to an indefinite degree and discover that if any one was omitted this particular case of falling would not have occurred.
Why is one condition selected rather than another? This question might be answered by referring to the seriality of thought, which is the name for the law by which many things cannot be considered simultaneously. To comprehend all of the causes it is necessary to consider them separately; and while this is not a complete answer, it must be considered as an important condition to be understood that the answer itself may be understood. Man himself is a causator, and changes the currents of events in himself and in external nature. All human activities are designed to interfere with the course of natural events. Man bent upon the modification of events is forever intent upon the discovery of the most easily variable cause, and no small proportion of his energies are devoted to this discovery, and the invention of the way by which his discoveries may be made of avail. Hence it comes that particular causes are selected as those of most interest. Every act performed by man, every word spoken is an interference in the laws of causation and is designed as such. The artisan who repaired my roof interfered in the laws of causation by making the repair, but this interference can only be accomplished by the substitution of a new cause.
VI[edit]
We have now discovered that there is an additional property of the inanimate particle when it is incorporated, and that this is affinity. All we know of affinity is that it is the choice of one particle for another as its associate or is their mutual choice. Here we are introduced to the multitudinous phenomena of affinity, which can be explained only as choice. We must yet go on to consider other bodies than molecules to obtain a clearer idea of the nature of affinity itself.
VII[edit]
Class is the reciprocal of number. It is class in the body as kind and series, and it is number in the particle as unity and plurality. Form is the reciprocal of space, which is form in the body as figure and structure, and it is space in the position of the extensions of the particle. Force is the reciprocal of motion; it is force in the body as action and passion; it is motion in the particles as speed and path. Causation is the reciprocal of time; it is causation in the body as cause and effect; it is time in the body as persistence and change.
Number, space, motion and time are concomitant as they inhere in the same particle; kind, form, force and causation are concomitant because they inhere in the same body. These distinctions are radical, and must be firmly grasped if the argument herein presented is to be understood.