Уильям Стэнли Джевонс

«Принципы науки: Трактат о логике и научном методе»

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альфа-таблица

Abacus, logical, 104;

arithmetical, 107;

Panchrestus, 182.

Aberration of light, 561;

systematic, 547.

Abscissio infiniti, 79, 713.

Abstract terms, 27;

number, 159.

Abstraction, 704;

logical, 25;

numerical, 158;

of indifferent circumstances, 97.

Accademia del Cimento, 427, 432, 436, 527.

Accident, logical, 700.

Accidental discovery, 529.

Achromatic lenses, 432.

Actinometer, 337.

Adamantine medium, 605, 751.

Adjectives, 14, 30, 31, 35;

indeterminate, 41.

Adrain, of New Brunswick, 375.

Affirmation, 44.

Agassiz, on genera, 726;

on creation of species, 763.

Agreement, 44.

Airy, Sir George Biddell, on perpetual motion, 223;

new property of sphere, 232;

pendulum experiments, 291, 304, 348, 567;

standard clock, 353;

book on Errors of Observation, 395;

tides, 488;

extra-polation, 495;

Thales’ eclipse, 537;

interference of light, 539;

density of earth, 291.

Alchemists, 505;

how misled, 428.

Algebra, 123, 155, 164;

Diophantine, 631.

Algebraic, equations, 123;

geometry, 633.

Allotropic state, 663, 670.

Alloys, possible number, 191;

properties, 528.

Alphabet, the Logical, 93, 104, 125;

Morse, 193.

Alphabet, permutations of letters of the, 174, 179.

Alphabetic indexes, 714.

Alternative relations, 67;

exclusive and unexclusive, 205.

Ampère, electricity, 547;

classification, 679.

Anagrams, 128.

Analogy, 627;

of logical and numerical terms, 160;

and generalisation, 596;

in mathematical sciences, 631;

in theory of undulations, 635;

in astronomy, 638;

failure of, 641.

Analysis, logical, 122.

Andrews, Prof. Thomas, experiments on gaseous state, 71, 613, 665, 753.

Angström, on spectrum, 424.

Angular magnitude, 305, 306, 326.

Antecedent defined, 225.

Anticipation of Nature, 509.

Anticipations, of Principle of Substitution, 21;

of electric telegraph, 671.

Apparent, equality, 275;

sequence of events, 409.

Approximation, theory of, 456;

to exact laws, 462;

mathematical principles of, 471;

arithmetic of, 481.

Aqueous vapour, 500.

Aquinas, on disjunctive propositions, 69.

Arago, photometer, 288;

rotating disc, 535;

his philosophic character, 592.

Archimedes, De Arenæ Numero, 195;

centre of gravity, 363.

Arcual unit, 306, 330.

Argyll, Duke of, 741.

Aristarchus on sun’s and moon’s distances, 294.

Aristotelian doctrines, 666.

Aristotle, dictum, 21;

singular terms, 39;

overlooked simple identities, 40;

order of premises, 114;

logical error, 117;

definition of time, 307;

on science, 595;

on white swans, 666.

Arithmetic, reasoning in, 167;

of approximate quantities, 481.

Arithmetical triangle, 93, 143, 182, 202, 378, 383;

diagram of, 184;

connection with Logical Alphabet, 189;

in probability, 208.

Asteroids, discovery of, 412, 748.

Astronomy, physical, 459.

Atmospheric tides, 553.

Atomic theory, 662.

Atomic weights, 563.

Atoms, size of, 195;

impossibility of observing, 406.

Augustin on time, 307.

Average, 359, 360;

divergence from, 188;

etymology of, 363.

Axes of crystals, 686.

Axioms of algebra, 164.

Babbage, Charles, calculating machine, 107, 231, 743;

lighthouse signals, 194;

natural constants, 329;

Mosaic history, 412;

universal and general truths, 646;

change of law, 230;

persistence of effects, 757.

Bacon, Francis Lord, Novum Organum, 107;

on induction, 121;

biliteral cipher, 193;

First Aphorism, 219;

on causes, 221;

Copernican system, 249, 638;

deficient powers of senses, 278;

observation, 402;

Natural History, 403;

use of hypothesis, 506;

his method, 507;

experimentum crucis, 519;

error of his method, 576;

ostensive, clandestine instances, &c., 608, 610;

latens precessus, 619.

Bacon, Roger, on the rainbow, 526, 598.

Baily, Francis, 272;

density of earth, 342, 566;

experiments with torsion balance, 370, 397, 432, 567–8;

motions of stars, 572.

Bain, Alexander, on powers of mind, 4;

Mill’s reform of logic, 227.

Baker’s poem, The Universe, 621.

Balance, use of the chemical, 292, 351, 354, 369;

delicacy of, 304;

vibrations of, 369.

Ballot, Buys, experiment on sound, 541.

Ballot-box, simile of, 150, 251–6, 765.

Barbara, 55, 57, 88, 105, 141.

Baroko, 85.

Barometer, 659;

Gay Lussac’s standard, 346;

variations, 337, 346, 349.

Bartholinus on double refraction, 585.

Base-line, measurement of, 304.

Bauhusius, verses of, 175.

Baxendell, Joseph, 552.

Beneke, on substitution, 21.

Bennet, momentum of light, 435.

Bentham, George, 15;

bifurcate classification, 695;

infima species, 702;

works on classification, 703;

analytical key to flora, 712.

Bentham, Jeremy, on analogy, 629;

bifurcate classification, 703.

Benzenberg’s experiment, 388.

Bernoulli, Daniel, planetary orbits, 250;

resisting media and projectiles, 467;

vibrations, 476.

Bernoulli, James, 154;

numbers of, 124;

Protean verses, 175;

De Arte Conjectandi quoted, 176, 183;

on figurate numbers, 183;

theorem of, 209;

false solution in probability, 213;

solution of inverse problem, 261.

Bessel, F. W., 375;

law of error, 384;

formula for periodic variations, 488;

use of hypothesis, 506;

солнечный параллакс, 560–2;

ellipticity of earth, 565;

pendulum experiments, 604.

Bias, 393, 402.

Biela’s comet, 746.

Bifurcate classification, 694.

Binomial theorem, 190;

discovery of, 231.

Biot, on tension of vapour, 500.

Blind experiments, 433.

Bode’s law, 147, 257, 660.

Boethius, quoted, 33;

on kinds of mean, 360.

Boiling point, 442, 659.

Bonnet’s theory of reproduction, 621.

Boole, George, on sign of equality, 15;

his calculus of logic, 23, 113, 634;

on logical terms, 33;

law of commutativeness, 35;

использование some, 41–2;

disjunctive propositions, 70;

Venn on his method, 90;

Laws of Thought, 155;

statistical conditions, 168;

propositions numerically definite, 172;

on probability, 199;

general method in probabilities, 206;

Laplace’s solution of inverse problem, 256;

law of error, 377.

Borda, his repeating circle, 290.

Boscovich’s hypothesis, 512.

Botany, 666, 678, 681;

modes of classification, 678;

systematic, 722;

nomenclature of, 727.

Bowen, Prof. Francis, on inference, 118;

classification, 674.

Boyle’s, Robert, law of gaseous pressure, 468, 470, 619;

on hypothesis, 510;

barometer, 659.

Bradley, his observations, 384;

accuracy of, 271;

aberration of light, 535.

Bravais, on law of error, 375.

Brewer, W. H., 142.

Brewster, Sir David, iridescent colours, 419;

spectrum, 429;

Newton’s theory of colours, 518;

refractive indices, 10, 527;

optic axes, 446.

British Museum, catalogue of, 717.

Brodie, Sir B. C., on errors of experiment, 388, 464;

ozone, 663.

Brown, Thomas, on cause, 224.

Buckle, Thomas, on constancy of average, 656;

science of history, 760.

Buffon, on probability, 215;

definition of genius, 576.

Bunsen, Robert, spectrum, 244;

photometrical researches, 273, 324, 441;

calorimeter, 343.

Butler, Bishop, on probability, 197.

Calorescence, 664.

Camestres, 84.

Canton, on compressibility of water, 338.

Carbon, 640, 728;

conductibility of, 442.

Cardan, on inclined plane, 501.

Cards, combinations of, 190.

Carlini, pendulum experiments, 567.

Carnot’s law, 606.

Carpenter, Dr. W. B., 412.

Catalogues, art of making, 714.

Cauchy, undulatory theory, 468.

Cause, 220;

definition of, 224.

Cavendish’s experiment, 272, 566.

Cayley, Professor, 145;

on mathematical tables, 331;

numbers of chemical compounds, 544.

Celarent, 55.

Centre of gravity, 363, 524;

of oscillation, gyration, &c., 364.

Centrobaric bodies, 364.

Certainty, 235, 266.

Cesare, 85.

Chalmers, on collocations, 740.

Chance, 198.

Character, human, 733.

Characteristics, 708.

Chauvenet, Professor W., on treatment of observations, 391.

Chemical affinity, 614;

analysis, 713.

Chladni, 446.

Chloroform, discovery of, 531.

Chronoscope, 616.

Cipher, 32;

Bacon’s, 193.

Circle, circumference of, 389.

Circumstances, indifferent, 419.

Circumstantial evidence, 264.

Clairaut, 650, 651;

on gravity, 463.

Classes, 25;

problem of common part of three, 170.

Classification, 673;

involving induction, 675;

multiplicity of modes, 677;

natural and artificial systems, 679;

in crystallography, 685;

symbolic statement of, 692;

bifurcate, 694;

an inverse and tentative operation, 689;

diagnostic, 710;

by indexes, 714;

of books, 715;

in biological sciences, 718;

genealogical, 719;

by types, 722;

limits of, 730.

Clifford, Professor, on types of compound statements, 143, 529;

first and last catastrophe, 744;

mathematical function, 768.

Clocks, astronomical, 340, 353.

Clouds, 447;

cirrous, 411.

Coincidences, 128;

fortuitous, 261;

measurement by, 292;

method of, 291.

Collective terms, 29, 39.

Collocations of matter, 740.

Colours, iridescent, 419;

natural, 518;

perception of, 437;

of spectrum, 584.

Combinations, 135, 142;

doctrine of, 173;

of letters of alphabet, 174;

calculations of, 180;

higher orders of, 194.

Combinatorial analysis, 176.

Comets, 449;

number of, 408;

hyperbolic, 407;

classification of, 684;

конфликт с, 746–7;

Halley’s comet, 537;

Lexell’s comet, 651.

Commutativeness, law of, 35, 72, 177.

Comparative use of instruments, 299.

Compass, variations of, 281.

Complementary statements, 144.

Compossible alternatives, 69.

Compound statements, 144;

events, 204.

Compounds, chemical, 192.

Comte, Auguste, on probability, 200, 214;

on prevision, 536;

his positive philosophy, 752, 760, 768.

Concrete number, 159.

Conditions, of logical symbols, 32;

removal of usual, 426;

interference of unsuspected, 428;

maintenance of similar, 443;

approximation to natural, 465.

Condorcet, 2;

his problem, 253.

Confusion of elements, 237.

Conical refraction, 653.

Conjunction of planets, 293, 657.

Consequent, definition of, 225.

Conservation of energy, 738.

Constant numbers of nature, 328;

mathematical, 330;

physical, 331;

astronomical, 332;

terrestrial, 333;

organic, 333;

social, 334.

Continuity, law of, 615, 729;

sense of, 493;

detection of, 610;

failure of, 619.

Continuous quantity, 274, 485.

Contradiction, law of, 31, 74.

Contrapositive, proposition, 84, 136;

conversion, 83.

Conversion of propositions, 46, 118.

Copernican theory, 522, 625, 638, 647.

Copula, 16.

Cornu, velocity of light, 561.

Corpuscular theory, 520, 538, 667.

Correction, method of, 346.

Correlation, 678, 681.

Cotes, Roger, use of mean, 359;

method of least squares, 377.

Coulomb, 272.

Couple, mechanical, 653.

Creation, problem of, 740.

Crookes’ radiometer, 435.

Cross divisions, 144.

Crystallography, 648, 654, 658, 678, 754;

systems of, 133;

classification in, 685.

Crystals, 602;

Dana’s classification of, 711;

pseudomorphic, 658.

Curves, use of, 392, 491, 496;

of various degrees, 473.

Cuvier, on experiment, 423;

on inferences, 682.

Cyanite, 609.

Cycloid, 633.

Cycloidal pendulum, 461.

Cypher, 124.

D’Alembert, blunders in probability, 213, 214;

on gravity, 463.

Dalton, laws of, 464, 471;

atomic theory, 662.

Darapti, 59.

Darii, 56.

Darwin, Charles, his works, 131;

negative results of observation, 413;

arguments against his theory, 437;

cultivated plants, 531;

his influence, 575;

classification, 718;

постоянство характера в классификации, 720–1;

on definition, 726;

restoration of limbs, 730;

tendency of his theory, 762, 764.

Davy, Sir H., on new instruments, 270;

nature of heat, 343, 417;

detection of salt in electrolysis, 428.

Day, sidereal, 310;

length of, 289.

Decandolle, on classification, 696.

Decyphering, 124.

Deduction, 11, 49.

Deductive reasoning, 534;

miscellaneous forms of, 60;

probable, 209.

Definition, 39, 62, 711, 723;

purpose of, 54;

of cause and power, 224.

De Morgan, Augustus, negative terms, 14;

Aristotle’s logic, 18;

relatives, 23;

logical universe, 43;

complex propositions, 75;

contraposition, 83;

formal logic quoted, 101;

error of his system, 117;

anagram of his name, 128;

численно определенное рассуждение, 168–172;

probability, 198;

belief, 199;

experiments in probability, 207;

вероятные дедуктивные аргументы, 209–210;

trisection of angle, 233;

probability of inference, 259;

arcual unit, 306;

mathematical tables, 331;

personal error, 348;

average, 363;

его работы по вероятности, 394–395;

apparent sequence, 409;

sub-equality, 480;

rule of approximation, 481;

negative areas, 529;

generalisation, 600;

double algebra, 634;

bibliography, 716;

catalogues, 716;

extensions of algebra, 758.

Density, unit of, 316;

of earth, 387;

negative, 642.

Descartes, vortices, 517;

geometry, 632.

Description, 62.

Замысел, 762–763.

Determinants, inference by, 50.

Development, logical, 89, 97.

Diagnosis, 708.

Dichotomy, 703.

Difference, 44;

law of, 5;

sign of, 17;

representation of, 45;

inference with, 52, 166;

form of, 158.

Differences of numbers, 185.

Differential calculus, 477.

Differential thermometer, 345.

Diffraction of light, 420.

Dimensions, theory of, 325.

Dip-needle, observation of, 355.

Direct deduction, 49.

Direction of motion, 47.

Discontinuity, 620.

Discordance, of theory and experiment, 558;

of theories, 587.

Discoveries, accidental, 529;

predicted, 536;

scope for, 752.

Discrimination, 24;

power of, 4.

Disjunctive, terms, 66;

conjunction, 67;

propositions, 66;

syllogism, 77;

argument, 106.

Dissipation of energy, 310.

Distance of statements, 144.

Divergence from average, 188.

Diversity, 156.

Divine interference, 765.

Dollond, achromatic lenses, 608.

Donkin, Professor, 375;

on probability, 199, 216;

principle of inverse method, 244.

Double refraction, 426.

Dove’s law of winds, 534.

Draper’s law, 606.

Drobitsch, 15.

Duality, 73, 81;

law of, 5, 45, 92, 97.

Dulong and Petit, 341, 471.

Duration, 308.

ε, 330, 769.

Earth, density of, 387;

ellipticity, 565.

Eclipses, 656;

Egyptian records of, 246;

of Jupiter’s satellites, 294, 372;

solar, 486.

Electric, sense, 405;

acid, 428;

fluid, 523.

Electric telegraph, anticipations of, 671.

Electricity, theories of, 522;

duality of, 590.

Electrolysis, 428, 530.

Electro-magnet, use of, 423.

Elements, confusion of, 237;

definition, 427;

classification, 676, 677, 690.

Elimination, 58.

Ellicott, observation on clocks, 455.

Ellipsis, 41;

of terms, 57.

Elliptic variation, 474.

Ellipticity of earth, 565.

Ellis, A. J., contributions to formal logic, 172.

Ellie, Leslie, 23, 375.

Ellis, W., on moon’s influence, 410.

Emanation, law of, 463.

Emotions, 732.

Empirical, knowledge, 505, 525–526;

measurement, 552.

Encke, on mean, 386, 389;

his comet, 570, 605;

on resisting medium, 523;

solar parallax, 562.

Energy, unit of, 322;

conservation of, 465;

reconcentration of, 751.

English language, words in, 175.

Eözoon canadense, 412, 668.

Equality, sign of, 14;

axiom, 163;

four meanings of, 479.

Equations, 46, 53, 160;

solution of, 123.

Equilibrium, unstable, 276, 654.

Equisetaceæ, 721.

Equivalence of propositions, 115, 120, 132;

remarkable case of, 529, 657.

Eratosthenes, sieve of, 82, 123, 139;

measurement of degree, 293.

Error, function, 330, 376, 381;

elimination of, 339, 353;

personal, 347;

law of, 374;

origin of law, 383;

verification of law, 383;

probable, 386;

mean, 387;

constant, 396;

variation of small errors, 479.

Ether, luminiferous, 512, 514, 605.

Euclid, axioms, 51, 163;

indirect proof, 84;

10th book, 117th proposition, 275;

on analogy, 631.

Euler, on certainty of inference, 238;

corpuscular theory, 435;

gravity, 463;

on ether, 514.

Everett, Professor, unit of angle, 306;

metric system, 328.

Evolution, theory of, 761.

Exact science, 456.

Exceptions, 132, 644, 728;

classification of, 645;

imaginary, 647;

apparent, 649;

singular, 652;

divergent, 655;

accidental, 658;

novel, 661;

limiting, 663;

real, 666;

unclassed, 668.

Excluded middle, law of, 6.

Exclusive alternatives, 68.

Exhaustive investigation, 418.

Expansion, of bodies, 478;

of liquids, 488.

Experiment, 400, 416;

in probability, 208;

test or blind, 433;

negative results of, 434;

limits of, 437;

collective, 445;

simplification of, 422;

failure in simplification, 424.

Experimentalist, character of, 574, 592.

Experimentum crucis, 518, 667.

Explanation, 532.

Extent of meaning, 26;

of terms, 48.

Extrapolation, 495.

Factorials, 179.

Facts, importance of false, 414;

conformity with, 516.

Fallacies, 62;

analysed by indirect method, 102;

of observation, 408.

Faraday, Michael, measurement of gold-leaf, 296;

on gravity, 342, 589;

magnetism of gases, 352;

vibrating plate, 419;

electric poles, 421;

circularly polarised light, 424, 588, 630;

freezing mixtures, 427;

magnetic experiments, 431, 434;

lines of magnetic force, 446, 580;

errors of experiment, 465;

electrolysis, 502;

velocity of light, 520;

prediction, 543;

relations of physical forces, 547;

character of, 578, 587;

ray vibrations, 579;

mathematical power, 580;

philosophic reservation of opinion, 592;

use of heavy glass, 609;

electricity, 612;

radiant matter, 642;

hydrogen, 691.

Fatality, belief in, 264.

Ferio, 56.

Figurate numbers, 183, 186.

Figure of earth, 459, 565.

Fizeau, use of Newton’s rings, 297, 582;

fixity of properties, 313;

velocity of light, 441, 561.

Flamsteed, use of wells, 294;

standard stars, 301;

parallax of pole-star, 338;

selection of observations, 358;

astronomical instruments, 391;

solar eclipses, 486.

Fluorescence, 664.

Fontenelle on the senses, 405.

Forbes, J. D., 248.

Force, unit of, 322, 326;

emanating, 464;

representation of, 633.

Formulæ, empirical, 487;

rational, 489.

Fortia, Traité des Progressions, 183.

Fortuitous coincidences, 261.

Fossils, 661.

Foster, G. C., on classification, 691.

Foucault, rotating mirror, 299;

pendulum, 342, 431, 522;

on velocity of light, 441, 521, 561.

Fourier, Joseph, theory of dimensions, 325;

theory of heat, 469, 744.

Fowler, Thomas, on method of difference, 439;

reasoning from case to case, 227.

Frankland, Professor Edward, on spectrum of gases, 606.

Franklin’s experiments on heat, 424.

Fraunhofer, dark lines of spectrum, 429.

Freezing-point, 546.

Freezing mixtures, 546.

Fresnel, inflexion of light, 420;

corpuscular theory, 521;

on use of hypothesis, 538;

double refraction, 539.

Friction, 417;

determination of, 347.

Function, definitions of, 489.

Functions, discovery of, 496.

Galileo, 626;

on cycloid, 232, 235;

differential method of observation, 344;

projectiles, 447, 466;

use of telescope, 522;

gravity, 604;

principle of continuity, 617.

Gallon, definition of, 318.

Galton, Francis, divergence from mean, 188;

works by, 188, 655;

on hereditary genius, 385, 655.

Galvanometer, 351.

Ganières, de, 182.

Gases, 613;

properties of, 601, 602;

perfect, 470;

liquefiable, 665.

Gauss, pendulum experiments, 316;

закон ошибок, 375–6;

detection of error, 396;

on gravity, 463.

Gay Lussac, on boiling point, 659;

law of, 669.

Genealogical classification, 680, 719.

General, terms, 29;

truths, 647;

notions, 673.

Generalisation, 2, 594, 704;

mathematical, 168;

two meanings of, 597;

value of, 599;

hasty, 623.

Genius, nature of, 575.

Genus, 433, 698;

generalissimum, 701;

natural, 724.

Geology, 667;

records in, 408;

slowness of changes, 438;

exceptions in, 660.

Geometric mean, 361.

Geometric reasoning, 458;

certainty of, 267.

Giffard’s injector, 536.

Gilbert, on rotation of earth, 249;

magnetism of silver, 431;

experimentation, 443.

Gladstone, J. H., 445.

Glaisher, J. W. L., on mathematical tables, 331;

law of error, 375, 395.

Gold, discovery of, 413.

Gold-assay process, 434.

Gold-leaf, thickness of, 296.

Graham, Professor Thomas, on chemical affinity, 614;

continuity, 616;

nature of hydrogen, 691.

Grammar, 39;

rules of, 31.

Grammatical, change, 119;

equivalence, 120.

Gramme, 317.

Graphical method, 492.

Gravesande, on inflection of light, 420.

Gravity, 422, 512, 514, 604, 740;

determination of, 302;

elimination of, 427;

law of, 458, 462, 474;

inconceivability of, 510;

Newton’s theory, 555;

variation of, 565;

discovery of law, 581;

Faraday on, 589;

discontinuity in, 620;

Aristotle on, 649;

Hooke’s experiment, 436.

Grimaldi on the spectrum, 584.

Grove, Mr. Justice, on ether, 514;

electricity, 615.

Guericke, Otto von, 432.

Habit, formation of, 618.

Halley, trade-winds, 534.

Halley’s comet, 537, 570.

Hamilton, Sir William, disjunctive propositions, 69;

inference, 118;

free-will, 223.

Hamilton, Sir W. Rowan, on conical refraction, 540;

quaternions, 634.

Harley, Rev. Robert, on Boole’s logic, 23, 155.

Harris, standards of length, 312.

Hartley, on logic, 7.

Hatchett, on alloys, 191.

Haughton, Professor, on tides, 450;

muscular exertion, 490.

Haüy, on crystallography, 529.

Hayward, R. B., 142.

Heat, unit of, 324;

measurement of, 349;

experiments on, 444;

mechanical equivalent of, 568.

Heavy glass, 588, 609.

Helmholtz, on microscopy, 406;

undulations, 414;

sound, 476.

Hemihedral crystals, 649.

Herschel, Sir John, on rotation of plane of polarisation of light, 129, 630;

quartz crystals, 246;

numerical precision, 273;

photometry, 273;

light of stars, 302;

actinometer, 337;

mean and average, 363;

eclipses of Jupiter’s satellites, 372;

law of error, 377;

error in observations, 392;

on observation, 400;

moon’s influence on clouds, 410;

comets, 411;

spectrum analysis, 429;

collective instances, 447;

principle of forced vibrations, 451, 663;

meteorological variations, 489;

double stars, 499, 685;

direct action, 502;

use of theory, 508;

ether, 515;

experimentum crucis, 519;

interference of light, 539;

interference of sound, 540;

density of earth, 567;

residual phenomena, 569;

helicoidal dissymmetry, 630;

fluorescence, 664.

Hindenburg, on combinatorial analysis, 176.

Hipparchus, used method of repetition, 289;

longitudes of stars, 294.

Hippocrates, area of lunule, 480.

History, science of, 760.

Hobbes, Thomas, definition of cause, 224;

definition of time, 307;

on hypothesis, 510.

Hofmann, unit called crith, 321;

on prediction, 544;

on anomalies, 670.

Homogeneity, law of, 159, 327.

Hooke, on gravitation, 436, 581;

philosophical method, 507;

on strange things, 671.

Hopkinson, John, 194;

method of interpolation, 497.

Horrocks, use of mean, 358;

use of hypothesis, 507.

Hume on perception, 34.

Hutton, density of earth, 566.

Huxley, Professor Thomas, 764;

on hypothesis, 509;

classification, 676;

mammalia, 682;

palæontology, 682.

Huyghens, theory of pendulum, 302;

pendulum standard, 315;

cycloidal pendulum, 341;

differential method, 344;

distant stars, 405;

use of hypothesis, 508;

philosophical method of, 585;

on analogy, 639.

Hybrids, 727.

Hydrogen, expansion of, 471;

refractive power, 527;

metallic nature of, 691.

Hygrometry, 563.

Hypotheses, use of, 265, 504;

substitution of simple hypotheses, 458;

working hypotheses, 509;

requisites of, 510;

descriptive, 522, 686;

representative, 524;

probability of, 559.

Identical propositions, 119.

Identities, simple, 37;

partial, 40;

limited, 42;

simple and partial, 111;

inference from, 51, 55.

Identity, law of, 5, 6, 74;

expression of, 14;

propagating power, 20;

reciprocal, 46.

Illicit process, of major term, 65, 103;

of minor term, 65.

Immediate inference, 50, 61.

Imperfect induction, 146, 149.

Inclusion, relation of, 40.

Incommensurable quantities, 275.

Incompossible events, 205.

Independence of small effects, 475.

Independent events, 204.

Indestructibility of matter, 465.

Indexes, classification by, 714;

formation of, 717.

India-rubber, properties of, 545.

Indirect method of deduction, 49, 81;

illustrations of, 98;

fallacies analysed by, 102;

the test of equivalence, 115.

Induction, 11, 121;

symbolic statement of, 131;

perfect, 146;

imperfect, 149;

philosophy of, 218;

grounds of, 228;

illustrations of, 229;

quantitative, 483;

problem of two classes, 134;

problem of three classes, 137.

Inductive truths, classes of, 219.

Inequalities, reasoning by, 47, 163, 165–166.

Inference, 9;

general formula of, 17;

immediate, 50;

with two simple identities, 51;

from simple and partial identity, 53;

with partial identities, 55;

by sum of predicates, 61;

by disjunctive propositions, 76;

indirect method of, 81;

nature of, 118;

principle of mathematical, 162;

certainty of, 236.

Infima species, 701, 702.

Infiniteness of universe, 738.

Inflection of light, 420.

Instantiæ, citantes, evocantes, radii, curriculi, 270;

monodicæ, irregulares, heteroclitæ, 608;

clandestinæ, 610.

Instruments of measurement, 284.

Insufficient enumeration, 176.

Integration, 123.

Intellect, etymology of, 5.

Intension of logical terms, 26, 48;

of propositions, 47.

Interchangeable system, 20.

Interpolation, 495;

in meteorology, 497.

Inverse, process, 12;

operation, 122, 689;

problem of two classes, 134;

problem of three classes, 137;

problem of probability, 240, 251;

rules of inverse method, 257;

simple illustrations, 253;

general solution, 255.

Iodine, the substance X, 523.

Iron, properties of, 528, 670.

Is, ambiguity of verb, 16, 41.

Isomorphism, 662.

Ivory, 375.

James, Sir H., on density of earth, 567.

Jenkin, Professor Fleming, 328.

Jevons, W. S., on use of mean, 361;

on pedesis or molecular movement of microscopic particles, 406, 549;

cirrous clouds, 411;

spectrum analysis, 429;

elevated rain-gauges, 430;

experiments on clouds, 447;

on muscular exertion, 490;

resisting medium, 570;

anticipations of the electric telegraph, 671.

Jones, Dr. Bence, Life of Faraday, 578.

Jordanus, on the mean, 360.

Joule, 545;

on thermopile, 299, 300;

mechanical equivalent of heat, 325, 347, 568;

temperature of air, 343;

rarefaction, 444;

on Thomson’s prediction, 543;

molecular theory of gases, 548;

friction, 549;

thermal phenomena of fluids, 557.

Jupiter, satellites of, 372, 458, 638, 656;

long inequality of, 455;

figure of, 556.

Kames, Lord, on bifurcate classification, 697.

Kant, disjunctive propositions, 69;

analogy, 597;

doctrine of space, 769.

Kater’s pendulum, 316.

Keill, law of emanating forces, 464;

axiom of simplicity, 625.

Kepler, on star-discs, 390;

comets, 408;

laws of, 456;

refraction, 501;

character of, 578.

Kinds of things, 718.

King Charles and the Royal Society, 647.

Kirchhoff, on lines of spectrum, 245.

Kohlrausch, rules of approximate calculation, 479.

Lagrange, formula for interpolation, 497;

accidental discovery, 531;

union of algebra and geometry, 633.

Lambert, 15.

Lamont, 452.

Language, 8, 628, 643.

Laplace, on probability, 200, 216;

principles of inverse method, 242;

solution of inverse problem, 256;

planetary motions, 249, 250;

conjunctions of planets, 293;

observation of tides, 372;

atmospheric tides, 367;

law of errors, 378;

dark stars, 404;

hyperbolic comets, 407;

his works on probability, 395;

velocity of gravity, 435;

stability of planetary system, 448, 746;

form of Jupiter, 556;

corpuscular theory, 521;

ellipticity of earth, 565;

velocity of sound, 571;

analogy, 597;

law of gravity, 615;

inhabitants of planets, 640;

laws of motion, 706;

power of science, 739.

Lavoisier, mistaken inference of, 238;

pyrometer, 287;

on experiments, 423;

prediction of, 544;

theory, 611;

on acids, 667

Law, 3;

of simplicity, 33, 72, 161;

commutativeness, 35, 160;

disjunctive relation, 71;

unity, 72, 157, 162;

identity, 74;

contradiction, 74, 82;

duality, 73, 74, 81, 97, 169;

homogeneity, 159;

error, 374;

continuity, 615;

of Boyle, 619;

natural, 737.

Laws, of thought, 6;

empirical mathematical, 487;

of motion, 617;

of botanical nomenclature, 727;

natural hierarchy of, 742.

Least squares, method of, 386, 393.

Legendre, on geometry, 275;

rejection of observations, 391;

method of least squares, 377.

Leibnitz, 154, 163;

on substitution, 21;

propositions, 42;

blunder in probability, 213;

on Newton, 515;

continuity, 618.

Leslie, differential thermometer, 345;

radiating power, 425;

on affectation of accuracy, 482.

Letters, combinations of, 193.

Leverrier, on solar parallax, 562.

Lewis, Sir G. C., on time, 307.

Life is change, 173.

Light, intensity of, 296;

unit, 324;

velocity, 535, 560, 561;

science of, 538;

total reflection, 650;

waves of, 637;

classification of, 731.

Lighthouses, Babbage on, 194.

Limited identities, 42;

вывод 59.

Lindsay, Prof. T. M., 6, 21.

Linear variation, 474.

Linnæus on synopsis, 712;

genera and species, 725.

Liquid state, 601, 614.

Locke, John, on induction, 121;

origin of number, 157;

on probability, 215;

the word power, 221.

Lockyer, J. Norman, classification of elements, 676.

Logarithms, 148;

errors in tables, 242.

Logic, etymology of name, 5.

Logical abacus, 104.

Logical alphabet, 93, 116, 173, 417, 701;

table of, 94;

connection with arithmetical triangle, 189;

in probability, 205.

Logical conditions, numerical meaning of, 171.

Logical machine, 107.

Logical relations, number of, 142.

Logical slate, 95.

Logical truths, certainty of, 153.

Lottery, the infinite, 2.

Lovering, Prof., on ether, 606.

Lubbock and Drinkwater-Bethune, 386, 395.

Lucretius, rain of atoms, 223, 741;

indestructibility of matter, 622.

Machine, logical, 107.

Macleay, system of classification, 719.

Magnetism of gases, 352.

Mallet, on earthquakes, 314.

Malus, polarised light, 530.

Mammalia, characters of, 681.

Manchester Literary and Philosophical Society, papers quoted, 137, 143, 168.

Mansel, on disjunctive propositions, 69.

Mars, white spots of, 596.

Maskelyne, on personal error, 347;

deviation of plumbline, 369;

density of earth, 566.

Mass, unit of, 317, 325.

Mathematical science, 767;

incompleteness of, 754.

Matter, uniform properties of, 603;

variable properties, 606.

Matthiessen, 528.

Maximum points, 371.

Maxwell, Professor Clerk, on the balance, 304;

natural system of standards, 311, 319;

velocity of electricity, 442;

on Faraday, 580;

his book on Matter and Motion, 634.

Mayer, proposed repeating circle, 290;

on mechanical equivalent of heat, 568, 572.

Mean (среднее), этимология, 359–360;

geometric, 362;

fictitious, 363;

precise, 365;

probable, 385;

rejection of, 389;

method of, 357, 554.

Mean error, 387.

Meaning, of names, 25;

of propositions, 47.

Measurement, of phenomena, 270;

methods of, 282;

instruments, 284;

indirect, 296;

accuracy of, 303;

units and standards of, 305;

explained results of, 554;

agreement of modes of, 564.

Mediate statements, 144.

Melodies, possible number of, 191.

Melvill, Thomas, on the spectrum, 429.

Membra dividentia, 68.

Metals, probable character of new, 258;

transparency, 548;

classification, 675;

density, 706.

Method, indirect, 98;

of avoidance of error, 340;

differential, 344;

correction, 346;

compensation, 350;

reversal, 354;

means, 357;

least squares, 377, 386, 393;

variations, 439;

graphical, 492;

Baconian, 507.

Meteoric streams, 372.

Meteoric cycle, 537.

Metre, 349;

error of, 314.

Metric system, 318, 323.

Michell, speculations, 212;

on double stars, 247;

Pleiades, 248;

torsion balance, 566.

Middle term undistributed, 64.

Mill, John Stuart, disjunctive propositions, 69;

induction, 121, 594;

music, 191;

probability, 200–201, 222;

supposed reform of logic, 227;

deductive method, 265, 508;

elimination of chance, 385;

joint method of agreement and difference, 425;

method of variations, 484;

on collocations, 740;

erroneous tendency of his philosophy, 752.

Miller, Prof. W. H., kilogram, 318.

Mind, powers of, 4;

phenomena of, 672.

Minerals, classification of, 678.

Minor term, illicit process of, 65.

Mistakes, 7.

Modus, tolendo ponens, 77;

ponendo tollens, 78.

Molecular movement, or pedesis, 406.

Molecules, number of, 195.

Momentum, 322, 326.

Monro, C. J., correction by, 172;

on Comte, 753.

Monstrous productions, 657.

Moon, supposed influence on clouds, 410;

atmosphere of, 434;

motions, 485;

fall towards earth, 555.

Morse alphabet, 193.

Mother of pearl, 419.

Müller, Max, on etymology of intellect, 5.

Multiplication in logic, 161.

Murphy, J. J., on disjunctive relation, 71.

Murray, introduced use of ice, 343.

Muscular susurrus, 298.

Music, possible combinations of, 191.

Names, 25;

of persons, ships, &c., 680.

Nature, 1;

laws of, 737;

uniformity of, 745.

Nebular theory, 427.

Negation, 44.

Negative arguments, 621.

Negative density, 642.

Negative premises, 63, 103.

Negative propositions, 43.

Negative results of experiment, 434.

Negative terms, 14, 45, 54, 74.

Neil on use of hypothesis, 509.

Neptune, discovery of, 537, 660.

Newton, Sir Isaac, binomial theorem, 231;

spectrum, 262, 418, 420, 424, 583;

rings of, 288, 470;

velocity of sound, 295;

wave-lengths, 297;

use of pendulum, 303;

on time, 308;

definition of matter, 316;

pendulum experiment, 348, 443, 604;

centrobaric bodies, 365;

on weight, 422;

achromatic lenses, 432;

resistance of space, 435;

absorption of light, 445;

planetary motions, 249, 457, 463, 466, 467;

infinitesimal calculus, 477;

as an alchemist, 505;

his knowledge of Bacon’s works, 507;

hypotheses non fingo, 515;

on vortices, 517;

theory of colours, 518;

corpuscular theory of light, 520;

fits of easy reflection, &c., 523;

combustible substances, 527;

gravity, 555, 650;

density of earth, 566;

velocity of sound, 571;

third law of motion, 622;

his rules of philosophising, 625;

fluxions, 633;

theory of sound, 636;

negative density, 642;

rays of light having sides, 662.

Newtonian Method, 581.

Nicholson, discovery of electrolysis, 530.

Ninth Bridgewater Treatise quoted, 743, 757.

Nipher, Professor, on muscular exertion, 490.

Noble, Captain, chronoscope, 308, 616.

Nomenclature, laws of botanical, 727.

Non-observation, arguments from, 411.

Norwood’s measurement of a degree, 272.

Nothing, 32.

Number, nature of, 153, 156;

concrete and abstract, 159, 305.

Numbers, prime, 123;

of Bernoulli, 124;

figurate, 183;

triangular, &c., 185.

Numerical abstraction, 158.

Observation, 399;

mental conditions, 402;

instrumental and sensual conditions, 404;

external conditions, 407.

Obverse statements, 144.

Ocean, depth of, 297.

Odours, 732.

Oersted, on electro-magnetism, 530, 535.

Or, meaning of, 70.

Order, of premises, 114;

of terms, 33.

Orders of combinations, 194.

Original research, 574.

Oscillation, centre of, 364.

Ostensive instances, 608.

Ozone, 663.

π, value of, 234, 529.

Pack of cards, arrangement of, 241.

Paley on design, 762, 763.

Parallax, of stars, 344;

of sun, 560.

Parallel forces, 652.

Paralogism, 62.

Parity of reasoning, 268.

Partial identities, 40, 55, 57, 111;

induction of, 130.

Particular quantity, 56.

Particulars, reasoning from, 227.

Partition, 29.

Pascal, 176;

arithmetical machine, 107;

arithmetical triangle, 182;

binomial formula, 182;

error in probabilities, 213;

barometer, 519.

Passive state of steel, 659.

Pedesis, or molecular movement of microscopic particles, 406, 612.

Peirce, Professor, 23;

on rejection of observations, 391.

Pendulum, 290, 302, 315;

faults of, 311;

vibrations, 453, 454;

cycloidal, 461.

Perfect induction, 146, 149.

Perigon, 306.

Permutations, 173, 178;

distinction from combinations, 177.

Personal error, 347.

Photometry, 288.

Physiology, exceptions in, 666.

Planets, conjunctions of, 181, 187, 657;

discovery of, 412;

motions, 457;

perturbations of, 657;

classification, 683;

system of, 748.

Plants, classification of, 678.

Plateau’s experiments, 427.

Plato on science, 595.

Plattes, Gabriel, 434, 438.

Pliny on tides, 451.

Plumb-line, divergence of, 461.

Plurality, 29, 156.

Poinsot, on probability, 214.

Poisson, on principle of the inverse method, 244;

work on Probability, 395;

Newton’s rings, 470;

simile of ballot box, 524.

Polarisation, 653;

discovery of, 530.

Pole-star, 652;

observations of, 366.

Poles, of magnets, 365;

of battery, 421.

Political economy, 760.

Porphyry, on the Predicables, 698;

tree of, 702.

Port Royal logic, 22.

Positive philosophy, 760, 768.

Pouillet’s pyrheliometer, 337.

Powell, Baden, 623;

on planetary motions, 660.

Power, definition of, 224.

Predicables, 698.

Prediction, 536, 739;

in science of light, 538;

theory of undulations, 540;

other sciences, 542;

by inversion of cause and effect, 545.

Premises, order of, 114.

Prime numbers, 123, 139;

formula for, 230.

Principia, Newton’s, 581, 583.

Principle, of probability, 200;

inverse method, 242;

forced vibrations, 451;

approximation, 471;

co-existence of small vibrations, 476;

superposition of small effects, 476.

Probable error, 555.

Probability, etymology of, 197;

theory of, 197;

principles, 200;

calculations, 203;

difficulties of theory, 213;

application of theory, 215;

in induction, 219;

in judicial proceedings, 216;

works on, 394;

results of law, 656.

Problems, to be worked by reader, 126;

inverse problem of two classes, 135;

of three classes, 137.

Proclus, commentaries of, 232.

Proctor, R. A., star-drifts, 248.

Projectiles, theory of, 466.

Proper names, 27.

Properties, generality of, 600;

uniform, 603;

extreme instances, 607;

correlation, 681.

Property, logical, 699;

peculiar, 699.

Proportion, simple, 501.

Propositions, 36;

negative, 43;

conversion of, 46;

twofold meaning, 47;

disjunctive, 66;

equivalence of, 115;

identical, 119;

tautologous, 119.

Protean verses, 175.

Protoplasm, 524, 764.

Prout’s law, 263, 464.

Provisional units, 323.

Proximate statements, 144.

Pyramidal numbers, 185.

Pythagoras, on duality, 95;

on the number seven, 262, 624.

Quadric variation, 474.

Qualitative, reasoning, 48;

propositions, 119.

Quantification of predicate, 41.

Quantitative, reasoning, 48;

propositions, 119;

questions, 278;

induction, 483.

Quantities, continuous, 274;

incommensurable, 275.

Quaternions, 160, 634.

Quetelet, 188;

experiment on probability, 208;

on mean and average, 363;

law of error, 378, 380;

verification of law of error, 385.

Radian, 306.

Radiant matter, 642.

Radiation of heat, 430.

Radiometer, 435.

Rainbow, theory of, 526, 533.

Rainfall, variation of, 430.

Ramean tree, 703, 704.

Ramsden’s balance, 304.

Rankine, on specific heat of air, 557;

reconcentration of energy, 751.

Rational formulæ, 489.

Rayleigh, Lord, on graphical method, 495.

Reasoning, arithmetical, 167;

numerically definite, 168;

geometrical, 458.

Recorde, Robert, 15.

Reduction, of syllogisms, 85;

ad absurdum, 415;

of observations, 552, 572.

Reflection, total, 650.

Refraction, atmospheric, 340, 356, 500;

law of, 501;

conical, 540;

double, 585.

Regnault, dilatation of mercury, 342;

measurement of heat, 350;

exact experiment, 397;

on Boyle’s law, 468, 471;

latent heat of steam, 487;

graphical method, 494;

specific heat of air, 557.

Reid, on bifurcate classification, 697.

Reign of law, 741, 759.

Rejection of observations, 390.

Relation, sign of, 17;

logic of, 22;

logical, 35;

axiom of, 164.

Repetition, method of, 287, 288.

Representative hypotheses, 524.

Reproduction, modes of, 730.

Reservation of judgment, 592.

Residual effects, 558;

phenomena, 560, 569.

Resisting medium, 310, 523, 570.

Resonance, 453.

Reusch, on substitution, 21.

Reversal, method of, 354.

Revolution, quantity of, 306.

Robertson, Prof. Croom, 27, 101.

Robison, electric curves, 446.

Rock-salt, 609.

Rœmer, divided circle, 355;

velocity of light, 535.

Roscoe, Prof., photometrical researches, 273;

solubility of salts, 280;

constant flame, 441;

absorption of gases, 499;

vanadium, 528;

atomic weight of vanadium, 392, 649.

Rousseau on geometry, 233.

Rules, of inference, 9, 17;

indirect method of inference, 89;

for calculation of combinations, 180;

of probabilities, 203;

of inverse method, 257;

for elimination of error, 353.

Rumford, Count, experiments on heat, 343, 350, 467.

Ruminants, Cuvier on, 683.

Russell, Scott, on sound, 541.

Sample, use of, 9.

Sandeman, on perigon, 306;

approximate arithmetic, 481.

Saturn, motions of satellites, 293;

rings, 293.

Schehallien, attraction of, 369, 566.

Schottus, on combinations, 179.

Schwabe, on sun-spots, 452.

Science, nature of, 1, 673.

Selenium, 663, 670.

Self-contradiction, 32.

Senior’s definition of wealth, 75.

Senses, fallacious indications of, 276.

Seven, coincidences of number, 262;

fallacies of, 624.

Sextus, fatality of name, 264.

Sieve of Eratosthenes, 82, 123, 139.

Similars, substitution of, 17.

Simple identity, 37, 111;

inference of, 58;

contrapositive, 86;

induction of, 127.

Simple statement, 143.

Simplicity, law of, 33, 58, 72.

Simpson, discovery of property of chloroform, 531.

Simultaneity of knowledge, 34.

Singular names, 27;

terms, 129.

Siren, 10, 298, 421.

Slate, the logical, 95.

Smeaton’s experiments, on water-wheels, 347;

windmills, 401, 441.

Smee, Alfred, logical machines, 107.

Smell, delicacy of, 437.

Smithsonian Institution, 329.

Smyth, Prof. Piazzi, 452.

Socrates, on the sun, 611.

Solids, 602.

Solubility of salts, 279.

Some, the adjective, 41, 56.

Sorites, 60.

Sound, observations on, 356;

undulations, 405, 421;

velocity of, 571;

classification of sounds, 732.

Space, relations of, 220.

Species, 698;

infima, 701;

natural, 724.

Specific gravities, 301;

heat of air, 557.

Spence, on boiling point, 546.

Spencer, Herbert, nature of logic, 4, 7;

sign of equality, 15;

rhythmical motion, 448;

abstraction, 705;

philosophy of, 718, 761, 762.

Spectroscope, 437.

Spectrum, 583.

Spiritualism, 671.

Spontaneous generation, 432.

Standards of measurement, 305;

the bar, 312;

terrestrial, 314;

pendulum, 315;

provisional, 318;

natural system, 319.

Stars, discs of, 277;

motions of, 280, 474;

variations of, 281;

approach or recess, 298;

standard stars, 301;

apparent diameter, 390;

variable, 450;

proper motions, 572;

Bruno on, 639;

new, 644;

pole-star, 652;

conflict with wandering stars, 748.

Stas, M., his balance, 304;

on atomic weights, 464.

Statements, kinds of, 144.

Statistical conditions, 168.

Stevinus, on inclined plane, 622.

Stewart, Professor Balfour, on resisting medium, 570;

theory of exchanges, 571.

Stifels, arithmetical triangle, 182.

Stokes, Professor, on resistance, 475;

fluorescence, 664.

Stone, E. J., heat of the stars, 370;

temperature of earth’s surface, 452;

transit of Venus, 562.

Struve on double stars, 247.

Substantial terms, 28.

Substantives, 14.

Substitution of similars, 17, 45, 49, 104, 106;

anticipations of, 21.

Substitutive weighing, 345.

Sui generis, 629, 728.

Sulphur, 670.

Summum genus, 93, 701.

Sun, distance, 560;

variations of spots, 452.

Superposition, of small effects, 450;

small motions, 476.

Swan, W., on sodium light, 430.

Syllogism, 140;

moods of, 55, 84, 85, 88, 105, 141;

numerically definite, 168.

Symbols, use of, 13, 31, 32;

of quantity, 33.

Synthesis, 122;

of terms, 30.

Table-turning, 671.

Tacit knowledge, 43.

Tacquet on combinations, 179.

Tait, P. G., 375;

theory of comets, 571.

Talbot on the spectrum, 429.

Tartaglia on projectiles, 466.

Tastes, classification of, 732.

Tautologous propositions, 119.

Teeth, use in classification, 710.

Temperature, variations of, 453.

Tension of aqueous vapour, 500.

Terms, 24;

abstract, 27;

substantial, 28;

collective, 29;

synthesis of, 30;

negative, 45.

Terrot, Bishop, on probability, 212.

Test experiments, 347, 433.

Tetractys, 95.

Thales, predicted eclipse, 537.

Theory, results of, 534;

facts known by, 547;

quantitative, 551;

of exchanges, 571;

freedom of forming, 577;

of evolution, 761.

Thermometer, differential, 345;

reading of, 390;

change of zero, 390.

Thermopile, 300.

Thomas, arithmetical machine, 107.

Thomson, Archbishop, 50, 61.

Thomson, James, prediction by, 542;

on gaseous state, 654.

Thomson, Sir W., lighthouse signals, 194;

size of atoms, 195;

tides, 450;

capillary attraction, 614;

magnetism, 665;

dissipation of energy, 744.

Thomson and Tait, chronometry, 311;

standards of length, 315;

the crowbar, 460;

polarised light, 653.

Thomson, Sir Wyville, 412.

Thunder-cloud, 612.

Tides, 366, 450, 476, 541;

velocity of, 298;

gauge, 368;

atmospheric, 367, 553.

Time, 220;

definition of, 307.

Todhunter, Isaac, History of the Theory of Probability, 256, 375, 395;

on insoluble problems, 757.

Tooke, Horne, on cause, 226.

Torricelli, cycloid, 235;

his theorem, 605;

on barometer, 666.

Torsion balance, 272, 287.

Transit of Venus, 294, 348, 562.

Transit-circle, 355.

Tree of Porphyry, 702;

of Ramus, 703.

Triangle, arithmetical, 93, 182.

Triangular numbers, 185.

Trigonometrical survey, 301;

calculations of, 756.

Trisection of angles, 414.

Tuning-fork, 541.

Tycho Brahe, 271;

on star discs, 277;

obliquity of earth’s axis, 289;

circumpolar stars, 366;

Sirius, 390.

Tyndall, Professor, on natural constants, 328;

magnetism of gases, 352;

precaution in experiments, 431;

use of imagination, 509;

on Faraday, 547;

magnetism, 549, 607;

scope for discovery, 753.

Types, of logical conditions, 140, 144;

of statements, 145;

classification by, 722.

Ueberweg’s logic, 6.

Ultimate statements, 144.

Undistributed, attribute, 40;

middle term, 64, 103.

Undulations, of light, 558;

analogy in theory of, 635.

Undulatory theory, 468, 520, 538, 540;

inconceivability of, 510.

Unique objects, 728.

Unit, definition of, 157;

groups, 167;

of measurement, 305;

arcual, 306;

of time, 307;

space, 312;

density, 316;

mass, 317;

subsidiary, 320;

derived, 321;

provisional, 323;

of heat, 325;

magnetical and electrical units, 326, 327.

Unity, law of, 72.

Universe, logical, 43;

infiniteness of, 738;

heat-history of, 744, 749;

possible states of, 749.

Uranus, anomalies of, 660.

Vacuum, Nature’s abhorrence of, 513.

Vapour densities, 548.

Variable, variant, 440, 441, 483.

Variation, linear, elliptic, &c., 474;

method of, 439.

Variations, logical, 140;

periodic, 447;

combined, 450;

integrated, 452;

simple proportional, 501.

Variety, of nature, 173;

of nature and art, 190;

higher orders of, 192.

Velocity, unit of, 321.

Venn, Rev. John, logical problem by, 90;

on Boole, 155;

his work on Logic of Chance, 394.

Venus, 449;

transits of, 294.

Verses, Protean, 175.

Vibrations, law of, 295;

principle of forced, 451;

co-existence of small, 476.

Vital force, 523.

Voltaire on fossils, 661.

Vortices, theory of, 513, 517.

Vulcan, supposed planet, 414.

Wallis, 124, 175.

Water, compressibility of, 338;

properties of, 610.

Watt’s parallel motion, 462.

Waves, 599, 635;

nature of, 468;

in canals, 535;

earthquake, 297.

Weak arguments, effect of, 211.

Wells, on dew, 425.

Wenzel, on neutral salts, 295.

Whately, disjunctive propositions, 69;

probable arguments, 210.

Wheatstone, cipher, 124;

galvanometer, 286;

revolving mirror, 299, 308;

kaleidophone, 445;

velocity of electricity, 543.

Whewell, on tides, 371, 542;

method of least squares, 386.

Whitworth, Sir Joseph, 304, 436.

Whitworth, Rev. W. A., on Choice and Chance, 395.

Wilbraham, on Boole, 206.

Williamson, Professor A. W., chemical unit, 321;

prediction by, 544.

Wollaston, the goniometer, 287;

light of moon, 302;

spectrum, 429.

Wren, Sir C., on gravity, 581.

X, the substance, 523.

Yard, standard, 397.

Young, Dr. Thomas, tension of aqueous vapour, 500;

use of hypotheses, 508;

ethereal medium, 515.

Zero point, 368.

Zodiacal light, 276.

Zoology, 666.

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СНОСКИ:

1 С тех пор как вышеизложенное было написано, г-н Харли зачитал отчет о логическом наследии Стэнхоупа на Дублинском собрании (1878 г.) Британской ассоциации. Статья будет напечатана в Mind. (Примечание добавлено в ноябре 1878 г.)

2 Leibnitii Opera Philosophica quæ extant. Erdmann, Pars I. Berolini, 1840, стр. 94.

3 Erdmann, стр. 102.

4 Ibid. стр. 98.

5 Erdmann, стр. 100.

6 Пятое издание, 1860, стр. 158.

7 Раздел 120.

8 См. его «Замечания о математическом анализе логики Буля». Отчет о 36-м собрании Британской ассоциации, Труды секций, стр. 3–6.

9 Лекции Гамильтона, том IV, стр. 319.

10 Ibid. стр. 326.

11 Чистая логика, или логика качества в отрыве от количества; с замечаниями о системе Буля и о связи логики и математики. Лондон, 1864, стр. 3.

12 La Philosophie Positive, май-июнь 1877 г., том XVIII, стр. 456.

13 Inventum Novum Quadrati Logici и др., Gissæ Hassorum, 1714, 8vo.

14 См. Систему логики Убервега и др., перевод Линдси, стр. 302.

15 С тех пор как вышеизложенное было написано, М. Лиар переиздал это изложение как одну главу интересного и удивительно ясного отчета о прогрессе логической науки в Англии. После краткого, но ясного введения, рассматривающего взгляды Гершеля, Милля и других относительно индуктивной логики, М. Лиар последовательно описывает логические системы Джорджа Бентама, Гамильтона, Де Моргана, Буля и ту, что содержится в настоящей работе. Название книги следующее: Les Logiciens Anglais Contemporains. Par Louis Liard, Professeur de Philosophie à la Faculté des Lettres de Bordeaux. Paris: Librairie Germer Baillière. 1878. (Примечание добавлено в ноябре 1878 г.)

16 Spectator, 19 сентября 1874 г., стр. 1178. Вторая часть обзора появилась в том же журнале 26 сентября 1874 г., стр. 1204.

17 Mind: ежеквартальный обзор психологии и философии. № II. Апрель 1876 г. Том I, стр. 206.

18 Части этой работы уже были опубликованы в моих статьях под названием «Философия Джона Стюарта Милля проверена», напечатанных в Contemporary Review за декабрь 1877 г., том XXXI, стр. 167, и за январь и апрель 1878 г., том XXXI, стр. 256, и том XXXII, стр. 88. (Примечание добавлено в ноябре 1878 г.)

19 Mind, том I, стр. 222.

20 Fortnightly Review, новая серия, апрель 1875 г., стр. 480. Лекция переиздана Обществом воскресных лекций, стр. 24.

21 Слова сэра У. Томсона следующие (Cambridge Mathematical Journal, ноябрь 1842 г., том III, стр. 174): «Когда x отрицательно, представленное состояние не может быть результатом какого-либо возможного распределения температуры, которое существовало ранее». В предложении нет ограничения законами теплопроводности, но, поскольку вся статья рассматривает результаты теплопроводности в твердом теле, можно, несомненно, понимать, что существует негласное ограничение. См. также вторую статью по этому вопросу в том же журнале за февраль 1844 г., том IV, стр. 67, где снова нет выраженного ограничения.

22 Стр. 25–26. Скобки стоят в оригинале и показывают исправления профессора Тейта в дословных отчетах о его лекциях. Предмет снова рассматривается на стр. 168–9.

23 Теория тепла, 1871, стр. 245.

24 Чувства и интеллект, второе издание, стр. 5, 325 и др.

25 Макс Мюллер, Лекции по науке о языке, вторая серия, том II, стр. 63; или шестое издание, том II, стр. 67. Взгляд на этимологическое значение «интеллекта» приведен выше со ссылкой на авторитет профессора Макса Мюллера. Он, по-видимому, противоположен обычному мнению, согласно которому латинское intelligere означает выбирать между, видеть разницу между, различать, вместо того чтобы объединять.

26 Хартли о человеке, том I, стр. 359.

27 Принципы психологии, второе издание, том II, стр. 86.

28 Чистая логика, или логика качества в отрыве от количества, 1864, стр. 10, 16, 22, 29, 36 и др.

29 Брюстер, Трактат о новых философских инструментах, стр. 273. Об этом методе см. также Уэвелл, Философия индуктивных наук, том II, стр. 355; Томлинсон, Philosophical Magazine, четвертая серия, том XL, стр. 328; Тиндаль в книге Юманса «Современная культура», стр. 16.

30 Формальная логика, стр. 38.

31 Литература Европы Халлама, первое издание, том II, стр. 444.

32 Очерк новой системы логики, Лондон, 1827, стр. 133 и др.

33 Исследование законов мышления, стр. 27 и др.

34 Формальная логика, стр. 82, 106. В своей более поздней работе, «Силлабус новой системы логики», он прекратил использование знака.

35 Принципы психологии, второе издание, том II, стр. 54, 55.

36 Чистая логика, или логика качества, стр. 14.

37 Чистая логика, стр. 18, 19.

38 Система логики Убервега, перевод Линдси, стр. 442–446, 571, 572. Предвосхищения принципа подстановки, которые можно найти в работах Лейбница, Рейша и, возможно, других немецких логиков, будут отмечены в предисловии ко второму изданию.

39 Подстановка подобных (1869), стр. 9.

40 Логика Пор-Рояля, перевод Спенсера Бейнса, стр. 212–219. Часть III, гл. X и XI.

41 Описание нотации для логики отношений, являющейся результатом расширения концепций исчисления логики Буля. Ч. С. Пирс. Мемуары Американской академии, том IX. Кембридж, США, 1870.

42 О силлогизме № IV и о логике отношений. Огастес Де Морган. Труды Кембриджского философского общества, том X, часть II, 1860.

43 Наблюдения над законами мышления Буля. Р. Лесли Эллис; передано преподобным Робертом Харли, F.R.S. Отчет Британской ассоциации, 1870. Отчет секций, стр. 12. Также: О законах мышления Буля. Преподобный Роберт Харли, F.R.S., там же, стр. 14.

44 Элементарные уроки логики Джевонса, стр. 41–43; Чистая логика, стр. 6. См. также Дж. С. Милль, Система логики, книга I, гл. II, раздел 5, и Элементы логики Шеддена, Лондон, 1864, стр. 14 и др. Профессор Робертсон возражает (Mind, том I, стр. 210), что я путаю единичные и собственные имена; если так, то это потому, что я придерживаюсь мнения, что те же замечания применимы к собственным именам, которые, как мне кажется, логически не отличаются от единичных имен.

45 Профессор Робертсон критиковал мое введение «субстанциальных терминов» (Mind, том I, стр. 210) и возражает, возможно, справедливо, что это различие, если оно действительно, является экстралогическим. Я склонен думать, однако, что доктрина терминов, строго говоря, по большей части экстралогична.

46 Математический анализ логики, Кембридж, 1847, стр. 17. Исследование законов мышления, Лондон, 1854, стр. 31.

47 Чистая логика, стр. 15.

48 «Velut si dicam, Sol, Sol, Sol, non tres soles effecerim, sed uno toties prædicaverim».

49 Книга I, часть IV, раздел 5.

50 Законы мышления, стр. 29. В предисловии ко второму изданию указано, что Лейбниц был знаком с законами простоты и коммутативности.

51 Первая аналитика, I, гл. XXVII, 3.

52 Британская энциклопедия, восьмое издание, ст. «Логика», раздел 37, примечание. Репринт 8vo, стр. 79.

53 Де Морган, О корне любой функции. Труды Кембриджского философского общества, 1867, том XI, стр. 25.

54 Силлабус предложенной системы логики, §§ 122, 123.

55 Элементарные уроки логики, стр. 86.

56 Очерк законов мышления, § 87.

57 Трактат по натурфилософии, том I, стр. 161.

58 Трактат по натурфилософии, том I, стр. 6.

59 Плоская аналитическая геометрия Тодхантера, гл. II, стр. 11–14.

60 Объяснение этого и других технических терминов старой логики можно найти в моих «Элементарных уроках логики», шестое издание, 1876; Macmillan.

61 Элементарные уроки логики, стр. 67, 79.

62 Чистая логика, стр. 19.

63 Очерк необходимых законов мышления, пятое издание, стр. 161.

64 Олдрич Мансела, стр. 103, и Prolegomena Logica, стр. 221.

65 Элементы логики, книга II, гл. IV, раздел 4.

66 Олдрич, Artis Logicæ Rudimenta, стр. 104.

67 Исследование философии сэра У. Гамильтона, стр. 452–454.

68 Чистая логика, стр. 76, 77.

69 Чистая логика, стр. 65. См. также критику этого пункта Де Морганом в Athenæum, № 1892, 30 января 1864 г., стр. 155.

70 Законы мышления Буля, стр. 106. Чистая логика Джевонса, стр. 69.

71 О силлогизме, № III, стр. 12. Труды Кембриджского философского общества, том X, часть I.

72 См. Хорсли, Философские труды, 1772, том LXII, стр. 327. Монтюкла, История математики, том I, стр. 239. Пенни-циклопедия, статья «Эратосфен».

73 Евклид, книга X, предложение 117.

74 Philosophical Magazine, декабрь 1852 г.; четвертая серия, том IV, стр. 435, «О косвенном доказательстве».

75 Philosophical Magazine, декабрь 1852 г., стр. 437.

76 Mind; ежеквартальный обзор психологии и философии; октябрь 1876 г., том I, стр. 487.

77 Уэвелл, История индуктивных наук, том I, стр. 222.

78 Формальная логика, стр. 124. Как указал мне профессор Крум Робертсон, вторая и третья посылки могут быть сведены в одно суждение, D = De BC ꖌ DE bc.

79 Стр. 55–59, 81–86.

80 См. его работу под названием «Процесс мышления, адаптированный к словам и языку, вместе с описанием реляционных и дифференциальных машин». Также Философские труды, [1870] том 160, стр. 518.

81 Философские труды [1870], том 160, стр. 497. Труды Королевского общества, том XVIII, стр. 166, 20 января 1870 г. Nature, том I, стр. 343.

82 Силлабус предложенной системы логики, §§ 57, 121 и др. Формальная логика, стр. 66.