Truth and Error or the Science of Intellection/Chapter 9
CHAPTER IX
CLASSIFICATION[edit]
The science of number is natural, for units and pluralities are found in nature, but measure is conventional, for conventional units of measure are used in order that undiscovered numbers may be represented by their equivalents in computation, for while we may not be able to discover the number of natural units in a body we may be able to measure its form in conventional units of extension, and for some purposes of computation these units serve the desired purpose.
There are other computations which are not properly subserved by the measurement of form. 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; so we assume that one concomitant property represents the others. This we measure. We do not search with the microscope for atoms and count them, but we consider their forms as extensions or their forces as masses and reason about the artificial numbers derived therefrom by measurement with the same degree of certainty that we would have if we should actually count the particles. Thus measure is devised in order that we may consider numbers when the actual numbers are concealed from observation. That every property is concomitant with all others is thus assumed as the fundamental doctrine of mathematics where quantitative reasoning is held to be exact and irrefragable. All this depends upon the law that the essentials are persistent in the particle.
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. He cannot stretch his mind to the concepts of natural units of particles in natural higher units of bodies, but he creates a representative system, so that the multiplicities of nature, which are infinite, may be representatively considered by the finite mind.
In conventional number the units of different orders are compounded symmetrically in constant ratios. Early in the history of language, while it was largely gesture speech, the fingers of one or both hands or the fingers and toes were used as an abacus by which numbers were told off; and this led to a habit which has continued and developed so that in the various languages of the world it is found that the number five, the number ten or the number twenty has been used as the normal ratio between conventional orders. Of the three methods the decimal has been retained in civilization as the one used in enumeration, computation and notation. By this device a plurality of units are arranged in a system of orders, ten units constituting the first order, ten of these the second, etc. In this manner numbers are classified as kinds in series for the purpose of convenient counting. Counting is a compound process of two coordinate elements; one determines the kind, the other the series, and determination of kind logically precedes enumeration. The kind must first be determined and then seriated. The kinds may be natural or conventional, one or both, and the series may be natural or conventional, one or both. 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. In counting the all of the kind is the all of our purpose; in classification the all is the all of nature. Then we must remember that in mathematics, number is taken as the representative of the other concomitant properties of quantity and that they are reduced to number by measurement, while in classification kinds are used to represent the other properties and they are reduced to kinds by logical convention. While in conventional counting we consider kinds in series, so in classifying the bodies and properties of nature we are compelled to consider kinds in series.
It was more than a chance that produced the decimal system, for the universe is pentalogic, as all of the fundamental series discovered in nature are pentalogic by reason of the five concomitant properties. The origin of the decimal system was the recognition by primitive man of the reciprocal pentalogic systems involved in the two hands of the human body, and the pentalogic properties are always in pairs. While the properties are five, they are manifested in reciprocal pairs.
The universe is not an endless series of infinitesimal variables, but it is a universe of divergent series which spring from an ascending series as branches spring from a trunk. In the branches the extreme variation appears in the extremities of the divergent branches, but the branches are not linked to one another by these peripheral extremities but by their trunk connections, and the grand advance in nature is made as an ascending series as by a trunk.
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.
Synthetic forms are often extirpated by time, and to a large extent living species are found in well-demarcated groups, this demarcation being the clearer by reason of the extirpation of the synthetic types of the trunk, while the branch groups divergently elongate until an extreme differentiation is found. Sometimes whole branches are extirpated and thus are found as fossils. Species multiply by the splitting of branches and each new branch consitutes a lineal series of individuals which are separated by the extirpation of the main branch; while the main branch remains the new branches are held as varieties.
The true method of classification, therefore, is not by invention but by discovery.
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; such a group is the lowest demarcated class. 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.
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. Motion or force properties are measured in terms of space and these again are also expressed in number. Times are measured in terms of motion, the motion in terms of space and the space reduced to terms of number. It is thus by the device of measure that all the other properties of matter are reduced to number for the purpose of verification. Abstract mathematics is therefore the science of number, but applied mathematics is the utilization of the laws of mathematics in concrete investigation by the device of measure, while chemistry is the science of natural orders of number.
Now, that which is true in the conventional science of mathematics finds its analogue in the natural sciences, for all the other properties of bodies are reduced to kinds for the purpose of logic. Forms are explained as kinds, forces as forms and then as kinds, and finally causations are reduced to forces, the forces to forms and these forms to kinds. Thus all the natural categories are reduced to kinds, as quantitative properties in mathematics are reduced to conventional numbers.
It is for practical reasons that man has reduced all other properties to numbers, for as counting can be accomplished only by classification, so properties can only be treated in mathematics when they are reduced to number by measure. Counting serves to determine the extent of a conventional group, while classification serves to determine the extent of a natural group.
Language is impossible without classification, for most words are class words. 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.
Kinds as species become orders of kinds or classes, and are thus multiplied. When kinds are considered two correlates are found which cannot be expunged; likeness and unlikeness; and when considered in this manner they are classes. A fundamental likeness is discovered in all bodies, for all bodies are composed of matter.
In mathematics bodies are considered in their quantitative properties, which are number, space, motion, time, and, in animate bodies, judgment. But in systematic science bodies are treated as categories, which are kinds, forms, forces, causations, and, in animate bodies, concepts. So, in mathematics, while quantitative properties are reduced to number, in the natural sciences properties are reduced to kinds. 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.
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. 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. Planes of demarcation are thus landmarks of history to guide in research. 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.
It is seen that classification is the discovery of kinds in series. If classification is discovery, classes are not conventional but natural. In any stage of classification, while yet all of the attributes are not known, there may be imperfections in distinguishing kinds in series; the kinds depend upon properties, but all the properties may not be known, and there may be gaps in our knowledge of the series, so that imperfect knowledge is imperfect recognition of kinds in series; therefore, classification is always tentative by reason of imperfect knowledge.
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.
While classification may grow it will always be recognized that there is but one system, as the individual is but one individual, though he may grow from infancy to maturity. The classification of which we speak is genetic, and while but one may exist that one may undergo changes on the way to perfection.
The test of classification is this: First, within the class all of the individuals must constitute an unbroken series, with a beginning and an ending, each class demarcated by a gap or discrete degree. Second, the classes themselves must be seriated with the least possible gaps. Third, the series thus produced must be traced to convergence. A classification guided by these three laws is valid, when all the facts are known, and it is relatively valid when these laws are observed in the consideration of the known facts. The goal of the science of classification is to discover kinds in series and coordinate series of kinds in systems, and systems again in series.
In every perception there is a semblance of dichotomous classification of that of which the ego is aware, as distinguished from the environment. Such a process is involved in the first act of judgment, and continues to the end, but it is simply distinguishing the object of judgment from its environment or the world outside of the object. 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. By this expression we must not conceive that the non-object in any way negates the object, nor that the object denies the existence of the non-object, but must consider the particle “non” as a device in naming. This method of naming is accomplished by another method in modern biological science when it speaks of the individual and the environment. In logic this method of naming has led to much confusion, and in the logic of Hegel it has led to strange absurdities, all of which are cleared away when the non-individual is called the environment.
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; we hear of time and matter as if time were not one of the properties of matter, and we hear of thought and matter as if thought were not one of the properties of animate matter. Would a sane person speak of the horse and head, the horse and body, the horse and legs, the horse and tail, and then consider the horse as one thing, the head, body, and tail as other things? Yet this is the error of those who consider matter as one thing and properties as other things. All such methods are not only vague and idle, but pernicious in that they deform all the concepts involved.
There is another method of dichotomous classification just as pernicious, exhibited in the attempt to classify the properties of matter as dynamic and static, which was Spencer’s classification. Here forces and causations are classified in one group as dynamics, and kinds, forms, and thoughts as statics; thus the distinction between causations and force as categories are confounded, as also the distinction between kinds, forms, and thoughts. For some purposes of discussion a schematization may be of more or less value, but it easily degenerates into illogical classification, especially when it becomes the foundation of a philosophy. This classification is a relic from an earlier stage of philosophy when properties were confounded with qualities, and both properties and qualities were classified as primary and secondary, with sometimes a third class as secundo-primary.
There are only five properties, quantitative and categoric. As abstractions they are wholly unlike one another, but in the concrete they are identical, for every particle of matter and every body compounded of particles has number, space, motion, time, and, if it be an animate body, judgment. The properties, therefore, are phases of the same body, and their abstraction must be pentalogic. In the science of mathematics the four properties are always recognized by every physicist. During the latter half of the present century the fifth property has been clearly recognized in the new science of psychophysics, which seeks to measure mental operations and treat psychology mathematically. In this field of modern research a large body of literature is already developed.
Mill, in his work on Logic, groups phenomena in a dichotomous scheme as the simultaneous and the successive; this is not a logical classification of phenomena, but simply a device in naming. Other writers divide phenomena into the coexistent and sequent, using other terms for Mill’s scheme, while Mill himself used it as a classification, and thereby fell into many errors of logic. Spencer used it also, but legitimately.
Names are developed before classes are logically distinguished, and, although naming involves a mode of classification, many devices of naming are very illogical methods of classification, but still convenient in schematization; a schematic name, therefore, must always be distinguished from a classific name.
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. 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 mariner the group of stores which he must provide for his voyage; the traveler his outfit which he must carry in his trunk. Such groups can be illustrated to an indefinite extent. They are always dichotomous on the plan of perception which groups things into the perceived this and the not this, or the individual and the environment. The two groups are composed of heterogeneous things, as they are known in natural classification, selected for a purpose and distinguished from those not selected.
In the presentation of a theme the speaker or writer is prone to arrange his material in a scheme which may be very wise for the purpose intended for distinct presentation and clear understanding. Such a piece of valuable literature may live, and the schematization may be taken as a classification with disastrous results. Schematization is valuable for ephemeral purposes, but classification has enduring value. The author who uses a valid classification as a schematization is always clear, while the author who uses a schematization which is not a valid classification thereby introduces an element of confusion.
Before the rise of science artificial and natural classes were often confounded. This especially appears in the development of names. Among many tribes of Indians things are classified into the standing, sitting, and lying; or into standing, sitting, lying, and moving, which is a classification by attitudes. In other languages things are classified by their states. A fundamental classification existed among the Greeks as the four elements, earth, air, fire, and water.
As science first develops, classes are based on inadequate characters; that is, a few characters only are taken as the basis, as in the Linnean classification of plants. But as science progresses, classes are discovered which more thoroughly express the facts; to these classes names are given, and the names as they are thus classed are the names of the things classed and the metaphoric names of the concepts of the classes.
Now we must consider identity and difference. Mineral bodies are identical in having the four properties of number, space, motion, and time, and by hypothesis, judgment; but they differ in relations. 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; thus there is identity and difference in the individual at different times.
In the plant there is the same identity as in the mineral, but there is an additional difference, for the plant grows by minute increments through the addition of new matter.
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.
But there is another identity to be explained, namely, class identity, for the member of a class is identical with every other member of the class in some respects, and different from every other member of the class in other respects. In minerals the individuals are identical in being composed of the same substance, and different in being composed of different quantities of the same substance. The individuals of a class of plants are identical in substance, but different in quantity and in history. In animals the individuals are identical in kind of substance, different in quantity and history, and also different in that their substance undergoes a secular change by absorbing new substance and throwing off the old. In common ideation animals differ in other respects from plants and minerals, in that they are animate bodies, and have the property of judgment or consciousness.
The same body is relegated to different classes in a hierarchy of classes by the consideration of different degrees of identity. 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. Following the methods of classification as bodies are found in nature, the same object is found to fall within different classes, which constitute a hierarchy. Thus every object has its identities grouped in a hierarchy of classes. A horse is identical with all other horses in certain attributes, but it is also identical with all animals in a fewer number of attributes, though it may be considered as an object. No horse exists solely as an animal; but it may be considered only as an animal, that is, we may consider those properties which make it an animal. 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. This is a concrete world, and objects are concrete in all their classes, and no entity or body exists which corresponds solely to the class to which the object belongs.
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. 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. When the characteristics which belong to a kind and make it a kind were considered as the attributes of distinct entities, called essences, then the name was considered to be one of these essential attributes or properties by which the class was designated. Thus a fallacy was made to breed a fallacy, and the two fallacies grew up together and are often connected, and how can you dispel the fallacy of essence without dispelling the fallacy of inherent name? Thus a pair of ghosts stalk the world together, and fight each other’s battles. How these ghosts waltzed in the dance of philosophy seems a marvelous feat—a Tam O’Shanter dance of warlock and witch.
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. Inductive reasoning is the discovery of the members of a class; that is, it is classification; deductive reasoning is the application of the first law of reason as given above.
A drop of water is analyzed and found to be composed of oxygen and hydrogen in certain proportions; other analyses verify this conclusion. Now, by the first law of deduction every drop of pure water in the sea, on the land, and in the air has a like composition; but in every drop of water found in nature there are other substances, and for the analysis of the water these substances are eliminated. Now I take water from a spring, and though satisfied that water is oxygen and hydrogen in certain proportions, yet in this water there are other substances for which I must seek, and by induction I discover them. Induction is here the discovery of the nature of pure water and other kinds of water, and as these facts are learned by induction the several kinds are classified, and then the first law of deduction applies to each class. Induction is the discovery of class, and thus the discovery of the law; deduction is the application of law.
All laws may be reduced to this form, and are but variants of it. There is nothing occult or wonderful in the nature of law; law is just as simple as relation, just as simple as persistence, just as simple as speed, just as simple as extension, just as simple as unity. In scientific philosophy the process of reasoning reduces the complex to the simple. In metaphysical philosophy the attempt is made to explain the simple in terms of the complex.
Many errors have arisen in respect to the nature of classification, of which two are of such importance to our present work as to require elucidation. 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. To a mind having infinite comprehension classification would be unnecessary; the whole would be grasped in mind simultaneously. Now ideas are evolved serially, hence it becomes necessary to take them one by one as they come and to group them and regroup them in hierarchies, for while the bodies of which they are ideas are presented to the mind serially of themselves, they exist in systems of hierarchies, and they are thus presented in nature in a hierarchy of bodies of different orders.
The things of this world are presented to the senses in a chaos of phenomena. At every glance of waking life we see a number of heterogeneous colors and a number of heterogeneous bodies. While this goes on we hear a number of heterogeneous sounds arising from heterogeneous bodies. 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. This classification is fundamentally mechanical. The eye sees the colors and classifies them, the ear hears the sounds and classifies them, the nose smells the odors and classifies them, the tongue tastes the flavors and classifies them, the touch feels the surfaces and classifies them, the muscular sense feels the forces and classifies them, and behold, all of these sensations are wrought into systems as if by magic!
In one chapter we considered bodies as particles, and ‘found that we were discussing quantitative properties, as number, space, motion, time, and judgment. In another chapter we considered particles as incorporated, and found ourselves to be dealing with categoric properties, as kinds, forms, forces, causations, and concepts. Then in another chapter we discussed the reincorporation of bodies as they are revealed in geonomy, and found ourselves dealing with both quantitative and classific properties. In another chapter we discussed methods of reincorporation in plants, or the bodies of phytonomy, in which we were compelled again to consider quantitative and classific properties. Finally, a chapter was devoted to a third method of the reincorporation of bodies as they are revealed in zoönomy, and again we were led to consider both quantitative and classific properties.
Here it becomes necessary to more clearly distinguish those bodies which we have called molar, for the term has been used in a somewhat restricted sense which should be understood. By a molar body we mean one which is revealed to the senses without the use of instruments such as the telescope, the microscope, the spectroscope, or the crucible, aided by computation and logical ideation.
All geonomic bodies are molar bodies, and so are plants and animals. Savage and barbaric men supposed the stars to be molar bodies, while ethereal bodies were wholly unknown, their manifestations being interpreted as phenomena due to molar bodies. Thus the concepts of mankind were first compounded of judgments about molar bodies, or such as were supposed to be molar, and intellection progressed in this manner until the dawn of civilization and the invention of instruments of research, mathematical computation and logical ideation.
Man seems to occupy a position in the world midway between extremes of magnitude. On the one side there are bodies which are vast systems of stars like the solar system, and these are revealed by the employment of instruments as aids to vision, and are further revealed by careful investigation as magnitudes are measured and computed; on the other hand there are magnitudes that are so minute that they are revealed only by the microscope and other methods of investigation, especially in chemistry where molecules and atoms appear, and are further revealed when we investigate the nature of the ether and find ourselves immersed in the contemplation of magnitudes that are lost in immeasurable numbers. Between these extremes we find molar bodies that are revealed to the senses as bodies without the supplementary devices. Thus we use the terms molar, stellar, and molecular to designate in a general way the magnitude of bodies as they are compared with the magnitude of our bodies and the means by which these comparative magnitudes are determined.
When we go on to discover stellar bodies we find that we observe them from our standpoint by considering their quantitative properties, that is, considering them as particles, and ultimately find that these stellar particles are combined in systems. Again, when we investigate the minute constitution of bodies we also consider them as particles, and deal with quantitative properties, and through the quantitative properties discover their forms as structure and figure. 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.
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. In geonomy both methods of research are used. The quantitative and categoric methods of research are conventional. Quantities are measured by conventional or artificial methods, with artificial or conventional units. Kinds are also in the same sense and by equivalent processes selected as the representative of forms, forces, causations and mentations in order that classification may proceed and logical results be reached. Thus logic and mathematics are reciprocal methods of procedure in the cognition of the world. The mathematical method is chiefly deductive, the logical method is chiefly inductive, but they cannot be separated. There is no deduction without its reciprocal induction, and there is no induction without its reciprocal deduction. 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.