Truth and Error or the Science of Intellection/Chapter 3

by John Wesley Powell

CHAPTER III

QUANTITIES OR PROPERTIES THAT ARE MEASURED

Two short chapters must now be presented which will be found rather dry, but they must be mastered if the subsequent chapters are to be understood. The principles therein stated are the A, B, C, of the work—the multiplication table of our logic. I beg of my reader not to be deterred from their careful consideration by reason of their simplicity.

I

The universe is a concourse of related bodies composed of related particles. Every relation must exist between two or more particles or bodies, and every particle or body is related to every other particle or body directly or indirectly. The universe is a hierarchy of bodies, and thus there is a hierarchy of relations. A relation cannot exist independent of terms. We may consider a relation abstractly, but it cannot exist abstractly. To affirm a relation the terms must be implied. When an abstract is reified, that is, supposed to exist by itself independent of other essentials, and the illusion is entertained that there is something independent of the essentials which support them, a mythology is created so subtle as to simulate reality. So when relations are reined and supposed to exist independent of terms, the mind is astray in the realm of fallacies. When it is discovered that rest is only a relation, the mind is prone to believe that nothing exists but relation, for we have often discovered that which we thought was absolute was in fact relation; but rest is a relation between terms which are absolute. The internal or molecular motions of the body at rest have a certain relation to the external or astronomic motions of the body which are changed when the body is given molar motion, but the absolutes still remain, though deflected.

Human beings are molar bodies, and have a deep interest in one another as such and in the other molar bodies with which they are associated. Molar bodies and their relations are the first bodies discovered by primitive man, and his converse with the external world at first seems to be wholly with molar bodies. Molar bodies are those in which he first discovers relations and with which he first consciously and purposely associates, and they become the type of the others. Molecular bodies are known as such only to science. The stellar bodies are first believed to be molar bodies, and it is long before the corporeal structure of the earth is discovered as a body of great magnitude associated with other bodies more nearly commensurate with them, as the sun, moon and stars.

Of the internal relations of molecular bodies little is known even yet, and in the same manner of the internal relations of stellar bodies, but little is yet known. Our ideas of molecular and stellar bodies are largely ideas of their individuality, or as units related to units of the same order, while their constituent units scarcely receive consideration. In the mechanical or molar world the relations of parts are immeasurably more numerous than the parts themselves. Not only are rocks multifarious and the imperfect embodiments of air and water multifarious, but special classes of embodiments are discovered as plants and animals distributed over all the earth in multitudinous kinds with multitudinous relations, and men as molar bodies are related to one another and in all of these relations men are fundamentally interested.

Relations, therefore, are so great in number and so many in kind that the subject of relations is apt to overwhelm the mental powers, for man discovers that in his reasoning he is forever dealing with relations far more than directly with the bodies themselves. In this manner he discovers that the world is a congress of molar bodies that are related to one another through their properties; when they are analyzed into related particles or synthesized into related bodies, relation seems to swallow all else, so that philosophers often assume and sometimes affirm that all that is known of the universe is these relations, and finally that the universe is only a system of relations and the substantiality of the universe is denied. The universe thus becomes a universe of relations without terms. The confounding of concomitancy with relativity is a cause of inextricable confusion—a snare to the intellect and a vice of logic. Unity and extension are concomitant but not related, while one unit may be related to another unit and one extension may be related to another extension. Concomitancy and relativity must always be distinguished or there can be no sound psychology. The antithesis of this doctrine is sometimes held, which is an affirmation that the substrates of the universe are unknown reifications of number, space, motion, time and judgment. About unknown and unknowable things any assertion may be made, and all philosophies that are founded upon these reifications are therefore philosophies of disputation, as no two are alike. That which some great mind imposes upon his generation is by a succeeding generation gradually found to be more or less erroneous, and new philosophies are thus forever springing up, the one not founded upon the other; but gradually from generation to generation science establishes some things.

The relations which we are now to consider are those which are discovered when bodies are considered as particles. Quite a new class is discovered when we consider bodies as bodies.

As every particle of inanimate matter is a combination of four essential factors there are four classes of relations, namely: relations of plurality, relations of position, relations of path and relations of change, and these are all concomitant in number, space, motion and time. The same fact may be expressed in this manner. Relations of number are founded upon pluralities; relations of extension are founded upon position; relations of motion are founded upon trajectory; relations of time are founded upon change. Thus we have four classes of relations that must exist between particles. Then bodies have internal relations of particles and external relations when the body is considered as a particle in a higher body.

II

In a former chapter we spoke of the essentials of a particle of matter and considered them separately. Now we must consider them as they are related. There is a multeity of units, and plurality is founded upon units. The units are the terms that are related to constitute a plurality. A unit is unrelated or absolute in unity, that is, its unity does not depend upon others, but a plurality is dependent upon a number of related units; for example, the plurality may be ten; then ten as a plurality depends upon the units of which it is composed; nine is also a plurality, but it depends only upon nine units. A plurality is therefore a relation of units considered as a sum. Unity is constant only in ultimate particles. Bodies are combined, dissolved again and recombined, making variable units of plurality.

I am writing on a sheet of paper; it is one. With a match it is ignited and disappears; it is many. It was many before the conflagration, but many in one. After the combination these molecules though disembodied as a sheet of paper are still related to one another by all the concomitants, but now their more immediate relations are with the other particles of the molecules in which they are combined, while the new bodies thus formed have relations to one another of a higher degree or order in the corporeal world, for fixed internal relations constitute incorporation. Incorporation consists in the establishment or fixation of internal relations. When a body is disincorporated its particles dissolve their relation as one and assume relation with others to constitute new bodies or enlarge other bodies.

There is a great variety of relations between numbers. Numbers in nature are unified in orders of various kinds. The orders thus developed are multitudinous and quite beyond human comprehension. As the several units are compounds of individuals of lower units they are related to one another in infinite ways, as one is a multiple or sub-multiple of another. Thus we have one-fourth, one-half, equal to, twice, four times, etc. Mass is a sum of units measured in terms of force, and such units may become constituent parts in higher orders of units. One number is thus a measure of another. Out of these relations ratios and proportions arise. It seems unnecessary to enter into a discussion of the relations of numbers, as they are developed in the science of arithmetic and algebra.

III

Extension is exclusive occupancy of space. As there is more than one extension, and every one excludes all others, there is relative position. Thus we have positions derived from many extensions. Position is the relation of one extension to another. Space is founded on extension, for if a particle had no extension it could not be an element of space; a plurality of particles, each having extension, constitutes space. If they are in juxtaposition the space is the sum of their extensions. If they are separated by a medium, as for example an intervening fluid, the space is marked by their position and in this sense is related position; position, therefore, depends upon relation, but there can be no related positions if the extensions are annihilated. Extension is absolute, position is relative and space is absolute in extension and relative in position; extension is constant or persistent in ultimate particles.

In space one particle may be related to another in distance and in direction. These relations give rise to geometry and trigonometry and are the relations chiefly dealt with in astronomy.

In order that space may be discussed mathematically it must be reduced conventionally to number; this is done through the agency of measure. Then units of measure are devised giving rise to fractions and whole numbers, multiples, and sub-multiples, when it becomes amenable to the operations of mathematics.

IV

Speed exists in the unit of extension whether there be other units or not; speed, therefore, is unrelated or absolute. But the extended unit having motion must also have path, which is a change of position to others and variable by collision with others. It is thus relative. Speed is constant in the ultimate unit, which will be demonstrated in a subsequent chapter; but path is change of position in relation to others, and motion therefore is absolute in speed and relative in path.

There is persistence or indestructibility in the fundamental unit of extension and motion, but this unit changes its relation to other units in position and also in trajectory; the persistence is absolute and constant, the change relative and variable.

Motions are related to one another in direction and also in the positions of trajectories. Directions may differ in innumerable ways and paths may have innumerable deflections and thus trajectories may have innumerable variables. In order that direction and trajectory may be treated mathematically it becomes necessary to devise methods for the measurement of directions which are expressed in degrees and of lengths which are expressed in various measures. By these conventions motions are reduced to spaces and spaces to numbers, all giving an inconceivably great number of relations. But there are no motions without particles in motion, and there are no speeds without particles having speed, and there are no trajectories without particles having trajectories. There is no path without a particle having the essentials of a particle.

The science of the mathematics of motion deals with the speed of one and its trajectory, the speed of another and its trajectory, and of their collisions, and for this purpose it has to deal with the measure of their relations, and forever relation is considered and thus an illusion is sometimes produced, when motion itself seems to be wholly relation. Every particle of matter is in motion, and while this motion is absolute it is also relative. There can be nothing relative which is not also absolute, nor can there be anything absolute which is not also relative, and motion being thus absolute and relative it is quite proper to affirm this of motion, but it is not correct to affirm that motion is a relation any more than it is correct to affirm that motion is an absolute, if by these assertions it is implied that motion is one rather than the other; but if these assertions are made with regard to one correlative implying the other, then they are both correct. It is better form of speech to say that motion is absolute or relative when it is desired to call attention to one factor or the other, rather than to say that motion is an absolute or a relation.

The motion of particles is of such a nature that paths must impinge, and then collisions arise which give rise to impulse, or collision by which paths are deflected.

As bodies are incorporated in molecules of higher and still higher orders, and through various molar forms as crystals, rocks, cells, phytons, plants, organs and animals and on into stars and systems of stars, each embodiment appropriates a part of the motion of its several particles or atoms. The molecules of the lowest orders have their motions, the molecules of the second order have their motions, the cell and the crystal have their motions, the earth has its motion and the stellar system has its motion.

The speed of every particle of matter is the sum of all the speeds of the bodies in which it is incorporated. Speed can never be increased or diminished in an ultimate particle; it may be increased or diminished in any one of its embodiments, but only by deflecting the motions in its other embodiments. This point is vital to a clear comprehension of the philosophy of science and is worthy of further illustration from the fact that it becomes necessary to rid ourselves of an illusion of sense. I see a bird perched upon a tree, then I see it flying through the air to perch upon another tree. The bird seems to have motion between the trees which it did not seem to have while perched on the one or the other; but the molecules of the bird before the flight had the motion of vitality, and in moving from tree to tree the trajectory of these multifarious minute motions are all deflected. The millions of millions of molecular motions had their trajectories changed. The bird itself was moving with the earth about its axis and with the earth about the sun, and with the sun about a point in Hercules. This is its astronomical motion. The change in the trajectory of the millions of millions of molecules was only the equivalent of the change in the trajectory of the astronomical motion of the bird. We know that all of these trajectories are changed; we do not know that the velocity or rate of speed of any particle of the bird’s body was increased or diminished. If Newton’s third law of motion, that action and reaction are equal, is true in the exact terms in which he stated it, then we must affirm that the speed of no particle was changed but only its trajectory. We do not see the astronomical motions of the bird nor its molecular motions. We do see the molar motions in flying from tree to tree and thus an illusion is produced that motion can be created or destroyed by the bird, and the persistence of motion seems to be a fallacy and the correlation of forces a fiction. We do not see the creation, continuance and annihilation of motion in the bird, but the deflection of astronomical and molecular motions as known by scientific investigation. This discussion is designed to show that motion is not a relation, but that one motion may be said to be related to another or related to any selected position.

V

Time is persistence and change, the persistence being absolute because it exists in the particle independent of other particles, and constant, for the particles cannot be annihilated. Change is relative, in that it inheres in the relations of the particles, and it is also variable, for particles are constantly changing their relations of position to each other by occupying a succession of positions. Thus time is absolute and relative, constant and variable.

The earth as a body changes the position of its particles by rotation upon its axis and thus passes through a series of daily events. It also as a particle changes its position in relation to the sun in a series of annual events. The position of the same body at one time may be related to the position of that body at another time; that is, its space relations may change.

As the motion of one body in its space element may become the measure of the motion of another body in its space elements, so the motion of one body in its time element may become the measure of another body in its time element. While particles are related to one another in number, space and motion, these relations are constantly changing so that they are also related in time; that is, particles are related to each other through their changes. A particle unmodified in its individuality may pass through a succession of changes by reason of its own proper motion determined by the motion of other particles. As the orbit of the moon around the earth may become the measure of the orbit of the earth around the sun, so the day may become the measure of the year. We have now found that numbers, spaces, motions and times are properties which can be measured, and through measurement which is conventional they can be investigated. We shall hereafter see how large a part of the scientific research pursued by man is occupied with these subjects. Quantity is the reciprocal of something else which is usually called quality, but in the course of this discussion it will be found that the term quality is badly chosen, that the real reciprocal of quantity is kind or class.