John Wesley Powell

“ 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 ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”