Part 4 — INDEX

Above and below, distinction between, 121

Abstract, concrete and, 16 ff.

Abstraction, 20

Action, conscious, 174;

instinctive, 174

Adaptation, 172 ff.

Aeromechanics, 147

Algebra, 80

Alikeness, definition of, 51 ff.

Allotropic changes, 161

Analysis, infinitesimal, 111

Analytic geometry, 122 ff.

Analytic judgments, 66

Anthropology, 57

Ants, specialization of, 181

Applied sciences, 57 ff.

A priori judgments, 44

Aristotle, 38, 66

Aristotle's logic, 22

Arithmetic, 79 ff.

Assertions, never absolutely correct, 53

Association, 63 ff., 81

Astronomic objective, 6

Astronomy as an applied science, 58

Atomic hypothesis in chemistry, 142

Atoms, 141

Bees, specialization of, 181

Biological sciences, 55;

life most general concept in, 56

Botany, 56

Cæsar, Julius, 76

Capillary phenomena, 146

Capillary theory, 147

Carbon, its circulation through plants and animals, 171;

life based on the energy of, 168

Carbonic acid, 171

Carnot, Sadi, 151

Causal relation, purification of, 34 ff.

Causation, the law of, 31 ff.

Chemical combinations, 71 ff.;

quantitative relations in, 74

Chemical energy, 159 ff.;

capable of powerful concentration, 161;

different forms of, 159

Chemical formulas represent concepts not sounds, 95

Chemistry, 20, 47, 55;

significance of, 160 ff.

Chinese script based on direct co-ordination, 93

Civilization, 184 ff.

Classification, not definite, 2;

purpose of, 2-4

Classification of the sciences, 53 ff.

Collective activity, 181

Combination, sequence in, 73 ff.

Combinations, theory of, 71

Combinatory schematization, 73;

in chemistry, 71 ff.;

in physics, 72

Communication, 181

Community among plants and animals, 179

Comparison, 82

Comte, Auguste, 54

Concept, the most general, 61 ff.

Concepts, arbitrary, 23;

complex, 23;

complex empirical, 23;

definition of, 16;

empirical, 18;

formation of, 19;

general, 26;

in ceaseless flux, 88;

science of, 15 ff., 122;

simple, 20;

simple and complex, 19 ff.

Conclusion, the, 24 ff.;

analytic, 66;

scientific, 27, 30, 66 ff.

Concrete and abstract, 16 ff.

Conjugacy, most general concept in formal sciences, 56

Conscious action, 174

Conscious thinking, willing, and acting, 178

Conservation of energy, the law of the, 135 ff.

Conservation of matter, 138

Conservation of the sum of work and kinetic energy, the law of the, 134

Conservation of work, the law of the, 130

Conservation, quantitative, 131

Continuity, 101 ff.;

the law of, 113 ff.

Co-ordinated signs, change in, 88 ff.

Co-ordination, 80 ff.;

a means of obtaining facts without dealing directly with the corresponding realities, 87;

between concept and word not unambiguous, 89;

between concept and written sign, direct and indirect, 92 ff.;

identity the limit case in, 82;

integral numbers the best basis of, 85;

in use among primitive men and higher animals, 87;

its importance, 85;

methodology of the sciences based upon, 85;

of numbers with signs, 90 ff.;

possibility of unambiguous, 88

Copernican theory, 117 ff.

Copernicus, 117, 141

Corpuscular theory of light, 5, 157

Counting, 85 ff.;

defined, 85;

purpose of, 86

Culture, see Civilization

Darwin, his fundamental theory, 173

Deduction, 40 ff.;

the process of, 41 ff.

Deductive sciences, 38

Determinateness, absolute, only in ideal world, 50

Determinateness of things, the, 47 ff.

Determinism, 48, 51

Differential Calculus, see Differentials

Differentials, 112

Double numbers or double points in a group, 82

Dynamics, 128 ff.;

definition of, 139

Elasticity, 145

Elastic undulatory theory of light, see Wave theory of light

Electricity, principal source of, 156

Electricity and magnetism, 154 ff.

Electromagnetic theory of light, 157 ff.

Electrotechnics, 156

Empirical sciences, 38

Energetic mechanics, 138 ff.

Energy, a substance, 136;

at rest, 154;

free, 154;

importance of concept of, 128;

in nerves, 177;

the most general concept in the physical sciences, 56;

of form, 145;

of volume, 145

Energy intensity, 153

Erg, definition of, 150

Esperanto, 183, note

Euclid, 44, 140

European-American scripts based on indirect co-ordination, 93

Experience, incompleteness of, 27;

more limited than the conceivable, 118

Experiences, distinguished by being familiar, 31;

limited knowledge of, 31

Experiential sciences, see Empirical sciences

Extrapolation, 46, 50, 104

Familiarity due to recalling former similar experiences, 11

Fechner, 102

Feeling, thinking, acting, 174 ff.

Force, 129 ff., 153

Formal sciences, 54;

are empirical sciences, 55;

order most general concept in, 56

Foucault's pendulum experiment, 121

Freedom of the will, 50 ff.

Frequency of process facilitates repetition, 11 ff.

Function, 109 ff.;

continuous and discontinuous, 110;

most general concept in formal sciences, 56

Functional relation, the application of the, 112 ff.

Functions, the theory of, 111

Fundamental principle, the second, 150 ff.

Gases, 145

Generalization, suitable place for, in text-books, 9 ff.

Geometry, 47, 54, 119, 127;

ancient and modern methods of, 110 ff.

Goethe, 99

Good usage in language, 100

Grammatical correctness, importance attached to, 99

Grammatical rules, 97

Gravitation potential, the, 112

Group, the, 65 ff.;

double members or double points in, 82;

linear arrangement of members of, 75 ff.

Groups, artificial and natural, 69 ff.;

closed, among animals, 179;

infinite, equality of, 84;

related, 69 ff.;

unequivocal order of, 83

Heat, mechanical equivalent of, 149;

theory of, 147 ff.

Heat energy, 148 ff.

Heat engine, 151;

ideal, 151 ff.

Heat quantity, 148 ff.

Heliotrope, 90

Herbart, 102

Heredity, 180

Higher analysis, 111

Homonym, 89

Hydromechanics, 147

Ideal cases, 44 ff.

Ideal machines, 132

Identity, the limit case in co-ordination, 82

Ido, 183, note

Imperfection, indestructible quality of science, 4

Incompleteness, no hindrance to efficiency of science, 5

Indestructibility of matter, see Conservation of matter

Indo-Arabic notation, 91

Induction, 38;

the complete and the incomplete, 39

Inductive sciences, 38

Inference, by induction, 38;

from analogy, 140

Infinitesimal analysis, 111

Inorganic world, lack of memory and foresight in, 33

Insoluble problems, 142

Instinctive action, 174

Intercourse, language and, 182 ff.

Isolation among plants and animals, 179

Isomeric, 74

Isomeric changes, 161

Judgments, analytic, 66

Kant, 44, 66, 105

Kepler, 141

Kinetic energy, 132;

and work, their sum constant, 133 ff.;

transformed into work and vice versa, 134

Knowledge, aim of, 19;

individual, compared to telephone, 7 ff.;

limited, 31;

possibility of error in, ineradicable, 40;

social character of, 183

Language, beginnings of, 88;

defective in co-ordination, 96;

distinction between science and knowledge of, 98;

good usage in, 100;

and intercourse, 182 ff.;

needless inflections in, 99 ff.;

of words more imperfect than written language, 92;

purpose of its cultivation, 99;

the science of, 97 ff.;

unambiguity the ideal of, 89;

a universal auxiliary, 100;

written, 89 ff.

Leibnitz, 88;

his doctrine of pre-established harmony, 143;

inventor of differentials, 112

Life, 163 ff.;

the most general concept in the biological sciences, 56

Light, 5, 156 ff.

Liquids, 145

Locke, John, 21 ff., 88;

his elaboration of the notion of simple and complex "ideas," 21;

his secondary qualities, 127

Logic, 54, 67 ff.;

content of, 19;

definition of, 15 ff.

Luther, 99

Magnetism, electricity and, 154 ff.

Man, compared to pair of sieves, 34;

his capacity for perfection, 180

Manifold, the science of the, 54

Mass, 132 ff., 136 ff.;

a substance, 138

Mathematical laws, accuracy of, 105

Mathematics, 54;

an empirical science, 55;

influence on, of concept of continuity, 111;

its progress after introduction of Indo-Arabic numerals and algebraic signs, 101

Matter, definition of, 138

Mayer, Julius Robert, 149;

his discovery of the law of conservation, 151

Measurement, 107

Mechanical energies, 144

Mechanics, 55, 128 ff.;

complementary branches of, 144 ff.;

definition of, 138;

early development of, 139;

energetic, 138 ff.;

the first branch of physics treated mathematically, 139;

pure or classical, 144

Mechanistic hypothesis, the, as an interpretation of all natural phenomena, 142;

especially injurious in study of mental phenomena, 142

Mechanistic theories, 140 ff.

Mechanistic theory of the universe, 132

Mechanization of astronomy, 141

Memory, 16, 32, 180;

definition of, 172;

general characteristic of, 61;

lack of, in inorganic world, 53

Metabolism, 165

Methodology of the sciences based upon co-ordination, 85

Microscope, 6

Motion, the science of, 54, 122;

uninfluenced, 122

Musical notation, 93

Names, arbitrariness of, 62;

signs and, 86 ff.

Natural laws, 28 ff.;

definition of, 28;

their extent dependent upon stage of knowledge in each science, 7;

their usual origin, 42 ff.;

prediction from, only approximate, 48

Natural philosophy, definition of, 1;

importance of, in study of science, 10;

place of, in text-books, 9 ff.

Negation, 68 ff.

Nerves, 177

Nervous discharge, 177

Newton, Sir Isaac, 141

Number groups, unlimited, 78

Numbers, 78 ff.;

theory of, 80

Numerals, co-ordination of, with signs, 86

Numerical names different in different languages, 86

Numerical signs international, 86

Nutrition, 165

Objective, astronomic, 6;

photographic, 6

Objective character of the world, 34

Optical telegraph, 90

Optics, geometric, 5

Optic signs, 90

Order, most general concept in formal sciences, 56

Organisms, standard for measuring relative perfection of, 176;

stationary forms, 163

Orthography, efforts to improve, 99;

English, defective in co-ordination, 96;

exaggerated importance of correctness in, 99;

mistakes in, 97;

reform of, 97

Parabolic curve, 48

Paradoxes of the infinite, 84

Pasigraphy, 92 ff.;

Chinese system of, 94

Permanent in change, the, 131

Perpetual motion, 130

Perpetual motion machine, 153

Philology, 97 ff.

Philosophy, limited progress in, 101

Phonetic writing, 33 ff.

Phoronomy, 54, 119, 122, 127

Photochemical processes, foundation of terrestial life, 169

Photographic objective, 6

Physical sciences, 55

Physics, 47, 55;

each branch of, treats of a special kind of energy, 139

the science of the different kinds of energy, 72;

Physiology, 55 ff.

Plato, his distinction between mental and physical life, 178

Polarity of electricity and magnetism, 155

Political organizations, conflicts between, 185

Prediction, 12

Pre-established harmony, 143

Pressure, 146, 154

Progress, depends on collective labor, 185;

economy of energy, 184;

evaluation of, 176

Pseudo-problems in science, 142

Psychology, 47, 55 ff.

Psycho-physical parallelism, 143

Ptolemy's system, 117

Pure science, 57

Quantity, the science of, see Mathematics, 54

Radiant energy, 157;

its importance to man, 158

Rational sciences, see Deductive sciences

Rays, straight lines of, 5

Reaction, teleological, 173

Reality, 16 ff.

Reflection, 5

Reflex action, 173

Refraction, 5

Repetition, basis of conscious life, 174

Reproduction, 165 ff.

Roman notation, 91

Science, aim of, 13 ff.;

comparison of, to a network, 42;

comparison of, to a tree or forest, 6;

definition of, 13;

eternal truth of, 6 ff.;

"for its own sake," 13 ff.;

the facts of, unalterable, 8 ff.;

the function of, 23, 37;

importance of theoretical, 15;

its procedure, 45;

the study of happiness, 28

Sciences, the table of the, 54 ff.

Scientific discoveries, independent simultaneous, 185

Scientific instinct, 43

Scientific materialism, 138

Scientific written language based on direct co-ordination, 93

Self-preservation, 180

Sense organs, 176 ff.

Shakespeare, 99

Signs and names, 86 ff.

Social characteristics, importance of, 179 ff.

Social classes, conflicts between, 185

Socialization of human capacities, 180

Social order still barbarous, 185

Social organization, 180;

how best obtained, 182;

its tendency to equalize conditions, 185;

secures permanence among specialized individuals, 181

Social problems, 179 ff.

Society, 179 ff.;

centrifugal and centripetal forces in, 181 ff.;

division of functions in, 181

Sociology, 47, 55, 57

Solar radiation, 169

Soul, the, 171 ff.

Sound signs, advantage and disadvantage of, 89 ff.

Sound writing, 33 ff., 92 ff.

Space, four-dimensional, 77, note;

homogeneity of, in horizontal direction, 121;

the science of, 54;

symmetrical and tri-dimensional, 118;

time and, 118 ff.;

tri-dimensional, 76

Specialization, one-sidedness of, 180 ff.

Spelling reform, 97

Stable forms, 163

Statics, 128 ff.;

definition of, 138 ff.

Stationary bodies, capable of regeneration, 164

Stationary forms, 163

Substance, 132

Surface-energy, 146

Syllogism, the, classic method of argumentation, 65 ff.

Synonym, 89

Table of the sciences, 54 ff.

Telegraph, optical, 90

"Teleological" properties of organisms, 173

Teleological reaction, 173

Telescope, 5

Temperature, 148

Theoretical science, importance of, 15

Theory of functions, 111

Theory of numbers, 80

Thermo-chemistry, 37

Thermo-dynamics, 153

Thing, definition of, 62 ff.

Thought conceived of as energetic, 178

Threshold, 102

Time, a form of inner life, 76;

measurement of, 122;

one-seried, or one-dimensional, 118;

and space, 118 ff.

Unambiguity, in language, 89;

of co-ordination of numbers to signs, 90

Universal auxiliary language, 100, 183

Velocity, 133

Volume energy, 145

War, 185

Wave surface, 6

Wave theory of light, 5, 157

Weight, 132, 137 ff.;

a substance, 138

Work, mechanical, 129;

product of the force and the distance, 130;

a substance in a limited sense, 136

Written language, 89 ff.

Written signs, 90

Zoology, 56

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