FOOTNOTES:

[A] Sometimes on suddenly awaking from a profound sleep a person finds himself for the moment deprived of his personal stock of memories, unable to recall where and in what circumstances he is. No one who has experienced such a condition can ever forget the terrifying sense of helplessness it brings.

[B] More precisely, a very pale blue.

[C] It cannot be objected that inorganic nature also is known to be subject to the law of causation. The causal mode of regarding inorganic phenomena is a distinctly human one, and nothing justifies the assertion that the same phenomena cannot be viewed in an entirely different manner.

[D] Mathematicians who busy themselves a great deal with the formal theory of four-dimensional space, seem to acquire a capacity for imagining this form as easily as the three-dimensional form with which we are all familiar. Therefore, despite the oft-repeated statements to the contrary, it is not impossible to imagine four-dimensional space. Only, we must not attempt to represent to ourselves four-dimensional space in three-dimensional space, especially not without a knowledge of its properties.

[E] The usual designation of the larger groups, ten, hundred, thousand, million, billion, etc., is also quite irrational. If it is our object to secure expressions for place values in as few words as possible, we find that the numbers of the form 10²ⁿ, in which n is a whole number, must receive their own names, that is, 10, 100, 10,000, 100,000,000 etc. In this way the problem of designating as many numbers as possible by as few words as possible is solved.

[F] It is not difficult to perfect musical notation with a view to unambiguity, a thing which would greatly facilitate the study of music.

[G] For the sake of the layman it must be observed that those "quantities" are not energy magnitudes but factors of the electrical and magnetic energies. Energy itself in its various forms is an exclusively positive magnitude, and the result of the additions of their various amounts is always the sum, never the difference, of their numerical values. By the negative sign is understood the energy expended in contradistinction to the energy received. It is therefore nothing more than the indication of a mathematical operation.

[H] Lately changes of elements into one another have been observed in individual instances, but in such peculiar circumstances that for the present we need not consider these discoveries, which have only just begun.

[I] At the present time "Ido" is the best. It is a highly practicable artificial language, and its advocates have succeeded in organizing it to insure its normal development. An older and still rather widespread form called "Esperanto" has failed to organize itself so as to insure its development and it must inevitably die out.

[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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Transcriber's notes

Mid-sentence capital letters are used by the Author to indicate the beginning of a quote or question, which terminates at the end of the sentence.

Typographical errors corrected:

p. 100: approprate changed to appropriate (... to a more appropriate evaluation ...).
p. 108: meassure changed to measure (By the application of the unit measure ...).
p. 184: correspondng changed to corresponding (... signifies a corresponding economy ...).
p. 191: A single period deleted from index.
p. 188, 189: limit-case changed to limit case (2 occurrences), to mirror text (3 occurrences).

Alphabetical sequencing adjusted in index:

p. 189: Two 'Energy' entries moved after Energetic mechanics
p. 191: Photographic objective moved below Photochemical processes.
p. 191: Physics: The order of the sub-entries swapped.
p. 192: Pure science moved down four places to end of "P" entries.
p. 193: Two 'Teleological' entries moved after Telegraph, optical

Index references to footnotes link to the footnote, not the original page. The return link, however, goes to the original page.