John Wesley Powell

“ Deduction is abstraction which posits induction, and induction is abstraction when deduction is posited. Deduction and induction cannot be carried on apart, for deduction is dependent upon induction, and induction is dependent upon deduction, and the attempt to dissever them leads the mind into a fog of speculation where men are lost on the shoreless sea of metaphysics or the endless trail of unrelated facts. ”

“ Often the term physical is used to distinguish certain properties from those which are called intellectual. This is not a logical classification of properties, but a convenient schematization which if understood as a classification leads to error. It always leads to error when the abstract property of judgment or conception is held to be a substance, and to exist apart from time, motion, space, and number, or from causation, force, form, and kind. Then thought becomes a ghost.
As classes are found in nature and discovered by science, so groups are also produced by art for a purpose. ”

“ No horse exists which is only a vertebrate, but we may consider only those characteristics which make it a vertebrate. No horse exists only as a mammal, but we may consider only those characteristics which constitute the mammal. No horse exists only as a horse, but we may consider those characteristics which constitute the horse and still there will remain the characteristics which distinguish it from other horses. Thus, in the different groups into which the horse is thrown in the series, we may consider its different attributes in every class, but it is only a method of consideration. ”

“ It is not strange that those who believe in a substrate of substance should also believe in an essence of kind; then this essence becomes the noumenon, and the characteristics of class become the phenomena; this dream is the reality of metaphysic; the knowledge of science is the identification of phenomenon with noumenon.
It has already been asserted that classification is a tool of logic; and this assertion now requires demonstration. The first law of deduction may be formulated in the following terms: whatever is true of anything is true of its class identity. ”

“ This semblance of dichotomous classification has led to many errors, for the habit has been formed and philosophers have sometimes diverted the method from its use in perception and attempted a dichotomous classification of the universe. It has rarely been suggested as a complete system, but it has been practically used by many in this manner, and is still so used. Thus, we hear of space and matter as if space were not one of the properties of matter; we hear of motion and matter as if motion were not one of the properties of matter ”

“ When a classification is once established upon a logical basis, it need not undergo dissolution to be reclassified, for when the germs of classification are established on a logical basis it has but to grow with increasing knowledge. ”

“ It therefore becomes necessary in the arts, both industrial and linguistic, to classify, and mankind through all the history of culture has been engaged in classification. But the reduction of the other properties to kinds does not reduce the whole of science to classification any more than the reduction of quantities to number reduces all verification to mathematics. There is still a logical verification independent of mathematical verification, and there are still forms, forces and causations to be considered, although for deductive logic it is necessary to reduce them to kinds. ”

“ While measure is thus conventional there is still another conventional usage in the science of mathematics. In natural units bodies are the higher units of particles, the particle and the body are units of different orders, and the different orders of units in nature are thus coextensive with all the bodies of the universe. Thus there is an infinite system of orders of numbers; but man devises a numerical system where a definite plurality is considered as a higher unity, and such a system serves him a valuable purpose as a labor-saving device for the mental faculties. ”

“ A variety is an inchoate species not marked by gaps or discrete degrees. Species are further classified in hierarchies, when the species becomes one of a series of species. The production of a species is nature’s method of summating a series, and a production of any higher class is still another method of more distinctly summating’ a series of series. Series spring from the division of trunks, and may be traced back to their origin; classification, then, becomes seriation of species in such a manner as to exhibit their origin in less differentiated species. ”

“ Here we measure the force which the body exerts through the action of gravity and determine its mass in units of weight, and these mass units serve the same purpose in our computations that higher units of number would serve if we were able to count the particles. Thus the science of number is natural, but the device of measure is conventional. It serves a useful purpose in that it enables us to represent by numbers certain facts about bodies which we are not able to discover as natural numbers by reason of their multiplicity and minuteness ”

“ Thus it is that in the minute and vast alike, in stars and in molecules, in systems and ethereal particles, science is interested chiefly in quantitative properties, and through them classific properties are revealed.
Plants and animals, which are molar bodies by our definition, first come to be investigated in modern or national civilization when they are treated as kinds and classified; but as we discover their kinds we discover relations of form, force, causation, and mentation, and a multitude of appliances for research are developed. ”

“ This nothing which has been entertained by philosophers is a fallacy. It is an easy thing to be lost in the maze of speculation about classes in which fallacies fill the mind and obscure the real world. Abstraction is simply a method of consideration useful and necessary in cognition, but to suppose that the things which we consider abstractly have a disjunct existence is to enter the realm of metaphysical illusions.
In early society the origin of names was not understood, and often names were believed to be properties, especially when properties were considered as qualities. ”

“ In these realms research deals with categoric properties, and reduces all phenomena to kinds, and the ultimate expression of all knowledge is classification verified by quantification. In plants bodies are reduced to particles when a minimum of computation can be used. So animals are reduced to particles by research, and again computation can be used. The goal reached by research is the particle, the way traveled is by classific logic, while in etheronomy and astronomy the goal reached is the body, and the road pursued is mathematical computation. ”

“ When we count horses in the field we count a natural kind, but we seriate only those in the field as a conventional series. We must not confound horses with stumps if we are to get a valid sum. We may place stones, blocks of wood and fragments of paper as marks of sites where trees are to be planted, but we classify them not as stones, blocks of wood, and fragments of paper, but as marks. In this case the kinds are conventional. Conventional counting and classification differ in this respect only that in counting the series is conventional, while in classification the series is natural. ”

“ When we study a group of plants or animals that are intimately related, as, for example, the members of an order, and compare them with the members of another order, the two orders are found related not by their highest members but by their lowest. It is thus that two branches of phytonomic or zoönomic species are found related to each other by discovering the synthetic form which belonged to the ascending or trunk series. ”

“ It has been held by some that classes are inventions and not discoveries, especially by those who have reified and personified the world as pure mind. Some who have not fallen into this error have still considered classes as artificial, invented for the purpose of economizing thought, and that real classes are found only because all of the units are not apprehended, and that classification is thus a product of ignorance and an infirmity of language. ”

“ A fallacy has tainted philosophy from the early history of civilization to the present time through the entanglement which has arisen from considering an object as belonging to different classes. It has been supposed that there is an entity which represents the class as distinct from every individual of the class to which the characteristics of the individual adhere. ”

“ The kinds of nature considered in the series of nature are classes, and these are regrouped in hierarchies which are systems of classes. Every science of such a grand group of bodies gives rise to a special science and thus we have systematic mineralogy, systematic botany and systematic zoölogy.
We have seen that the other properties of a particle when treated in the science of mathematics require conversion into terms of number. Space properties are measured by conventional units, and are thus reduced to number. ”

“ Every physical body is like every other physical body in its essentials and unlike in its relations.
The natural classes which exist and those which have existed in the past (for the processes of extirpation have always existed in the world) have a meaning for us in expressing the agencies which have been at work in producing the present stage of the world, for every gap represents some event of history. ”

“ Bodies are composed of particles, and the elementary particles are probably alike. They have been reduced to about seventy kinds by chemical analysis. Logical analysis reduces them to one kind, and if it is valid then they are alike in being composed of one substance with like properties. If only the chemical analysis is valid, then there are seventy kinds, but they are alike in having the same properties, and unlike only in having different quantities or proportions of these properties. All bodies have a fundamental likeness in essentials, and a contingent unlikeness in relations. ”

“ The growth of a mineral is a progressive change by internal metamorphosis of the molecules. The growth of the individual plant is accomplished by successive additions of particles, and is thus a serial kind, while the growth of the individual in the animal is accomplished not only by a constant addition of particles, but also by a concomitant subtraction of particles; the individual is doubly a serial kind.
A species is a series of connected individuals differing from one another by minute distinctions but differing from other species by gaps ”

“ At the same time we smell heterogeneous odors from heterogeneous bodies, and taste heterogeneous flavors from heterogeneous bodies, and touch heterogeneous surfaces of heterogeneous bodies, and discover heterogeneous forces in heterogeneous bodies, perhaps all in one second of time; but as the instances come new sensations come in the most heterogeneous manner, and the things presented to the senses seem to constitute a chaos. Out of this chaos a cosmos arises, for sensation, which is the fundamental faculty of the mind, is classification. ”

“ The animal has the same identity and difference as the plant; but it has other differences, for the substance of the animal grows and decays coincidently. The same animal is not composed of the same identical substance from time to time, but only of the same kind of substance, for its food is continuously assimilated and used in function and discharged as new food is absorbed. ”

“ An organic body undergoes a secular change in kind, form, force, causation, and by hypothesis, conception, and differs from itself at different times in these respects. At different times the same body in part is identical in its different phases and in part different ”

“ As the products of nature are used in art a regrouping may arise which has in view only the characteristics of the things of nature and art as they are utilized in art. The builder recognizes the group of building materials as a class of things in which he is especially interested ”

“ The fewer but more fundamental the identities the greater the number of the individuals in the class; the fewer the number of variables and the less fundamental the variables, the smaller the number of individuals within the class. ”

“ The analogy between systematic science and mathematical science is perfect, and both are partly conventional. As it is necessary to reduce properties to number in order to treat them mathematically, so it is necessary to reduce properties to kinds in order to treat them logically. ”

“ As bodies have appeared and disappeared upon the stage of time and the actors changed with every act, a history of transcendent interest is involved, for in the discovery of classes we may restore the history of the earth. ”

“ In perceiving the horse, the horse is distinguished from the rest of the environment, and in order that this may be expressed in speech some logicians speak of the horse and the non-horse, the tree and the non-tree, the house and the non-house. This is but a method of naming, but that which is expressed is the whole world except that which is included under the positive name. ”