The Principles of Science: A Treatise on Logic and Scientific Method, المجلدات 1-2

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Macmillan, 1874 - 480 من الصفحات
 

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المحتويات

Expression of Identity and Difference
18
General Formula of Logical Inference
21
The Propagating Power of Identity
24
Anticipations of the Principle of Substitution
25
The Logic of Relatives
27
CHAPTER II
29
Twofold Meaning of General Names
31
Abstract Terms
33
Substantial Terms
34
Collective Terms
35
Synthesis of Terms
36
Symbolic Expression of the Law of Contradiction
38
Certain Special Conditions of Logical Symbols
39
SECTION PAGE 1 Propositions
43
Simple Identities
44
Partial Identities
47
Limited Identities
51
Negative Propositions
52
Conversion of Propositions
55
Twofold Interpretation of Propositions
57
CHAPTER IV
59
Immediate Inference
60
Inference with Two Simple Identities
61
Inference with a Simple and a Partial Identity
64
Inference of a Partial from Two Partial Identities
66
On the Ellipsis of Terms in Partial Identities
69
Inference of a Simple from Two Partial Identities
70
Inference of a Limited from Two Partial Identities
71
Miscellaneous Forms of Deductive Inference
72
Fallacies
74
CHAPTER XVin OBSERVATION PAGE
77
CHAPTER V
79
Expression of the Alternative Relation
81
Laws of the Disjunctive Relation
85
Symbolic Expression of the Law of Duality
87
Various Forms of the Disjunctive Proposition
89
Inference by Disjunctive Propositions
90
CHAPTER VI
93
THE INDIRECT METHOD OF INFERENCE 1 The Indirect Method of Inference
95
Simple Illustrations
97
Employment of the Contrapositive Proposition
99
Contrapositive of a Simple Identity
101
Miscellaneous Examples of the Method
103
Abbreviation of the Process
105
The Logical Abecedarium
107
The Logical Slate
110
Abstraction of Indifferent Circumstances
112
SECTION PACE 10 Illustrations of the Indirect Method
113
Fallacies analysed by the Indirect Method
118
The Logical Abacus
119
The Logical Machine
123
The Order of Premises
131
The Equivalency of Propositions
132
The Nature of Inference
136
CHAPTER VII
139
Induction
143
Induction an Inverse Operation 3 Induction of Simple Identities
146
Induction of Partial Identities
149
Complete Solution of the Inverse or Inductive Logical Pro blem
154
SECTION 1
157
The Inverse Logical Problem involving Three Terms 7 Distinction between Perfect and Imperfect Induction
164
Transition from Perfect to Imperfect Induction
168
BOOK II
172
PRINCIPLES OF NUMBER 1 Principles of Number
173
The Nature of Number 3 Of Numerical Abstraction
177
Concrete and Abstract Numbers
178
Analogy of Logical and Numerical Terms
180
Principle of Mathematical Inference
183
Reasoning by Inequalities
186
Arithmetical Reasoning
188
Numerically Definite Reasoning
190
THE VARIETY OF NATURE OR THE DOCTRINE OF COMBINATIONS AND PERMUTATIONS 1 The Variety of Nature
195
Distinction of Combinations and Permutations
200
Calculation of Number of Combinations
204
The Arithmetical Triangle
206
SECTION PAGE 5 Connexion between the Arithmetical Triangle and the Logical Abecedarium
214
Possible Variety of Nature and Art
216
Higher Orders of Variety
219
CHAPTER X
224
Fundamental Principles of the Theory
228
Rules for the Calculation of Probabilities
231
Employment of the Logical Abecedarium in questions of Probability
234
Comparison of the Theory with Experience
236
Probable Deductive Arguments
239
Difficulties of the Theory
243
CHAPTER XI
250
PHILOSOPHY OF INDUCTIVE INFERENCE 1 Philosophy of Inductive Inference
251
The Relation of Cause and Effect
253
Fallacious Use of the Term Cause
254
Confusion of Two Questions
256
Definition of the Term Cause
257
Distinction of Inductive and Deductive Results
260
On the Grounds of Inductive Inference
262
Illustrations of the Inductive Process
263
Geometrical Reasoning
268
Discrimination of Certainty and Probability in the Inductive Process
271
CHAPTER XII
276
Principle of the Inverse Method
279
Simple Applications of the Inverse Method
281
Application of the Theory of Probabilities in Astronomy
285
Statement of the General Inverse Problem
289
Simple Hlustration of the Inverse Problem
292
General Solution of the Inverse Problem
295
Rules of the Inverse Method
297
Fortuitous Coincidences
302
Summary of the Theory of Inductive Inference
307
METHODS OF MEASUREMENT CHAPTER XIII
313
Division of the Subject
318
The Fallacious Indications of the Senses
320
Complexity of Quantitative Questions
323
The Methods of Accurate Measurement
328
Measuring Instruments
330
The Method of Repetition
336
Measurements by Natural Coincidence
341
Modes of Indirect Measurement
345
Comparative Use of Measuring Instruments
349
Systematic Performance of Measurements
351
The Pendulum
352
Attainable Accuracy of Measurement
354
UNITS AND STANDARDS OF MEASUREMENT 1 Units and Standards of Measurement
357
Standard Unit of Time 3
359
The Unit of Space and the Bar Standard 305
365
The Terrestrial Standard
367
The Pendulum Standard
369
Unit of Density
371
Unit of Mass
372
Subsidiary Units
374
Derived Units
375
Provisionally Independent Units
377
Natural Constants and Numbers
380
Mathematical Constants
381
Physical Constants
383
Astronomical Constants
384
Terrestrial Numbers
385
Social Numbers
386
CHAPTER XV
387
Illustrations of the Complication of Effects
388
Methods of Eliminating Error
391
SECTION PAGE 4 Method of Avoidance of Error
393
Differential Method
398
Method of Correction
400
Method of Compensation
406
Method of Reversal
410
CHAPTER XVI
414
Several Uses of the Mean Result
416
The Significations of the Terms Mean and Average
418
On the Fictitious Mean or Average Result
422
The Precise Mean Result
424
Determination of the Zero Point by the Method of Means
428
Weighted Observations
449
The Probable Error of Mean Results
451
The Rejection of the Mean Result
454
Method of Least Squares
458
Works upon the Theory of Probability and the Law of Error
459
Detection of Constant Errors 400
460
Distinction of Observation and Experiment 2
2
Mental Conditions of Correct Observation 4
4
Instrumental and Sensual Conditions of Correct Observation 7
7
External Conditions of Correct Observation 10 13
10
Apparent Sequence of Events 7 Negative Arguments founded on the NonObservation of 16
16
CHAPTER XIX
22
Experiment 26
26
Simplification of Experiments 33
33
Removal of Usual Conditions 37
35
Interference of Unsuspected Conditions 43
37
Blind or Test Experiments 45
43
Negative Results of Experiment 48
45
Limits of Experiment CHAPTER XX
48
METHOD OF VARIATIONS 1 Method of Variations 50 51
50
175
51
Measurement of the Variable 55
53
Maintenance of Similar Conditions 57
55
Collective Experiments 61
57
Periodic Variations 63
61
Combined Periodic Changes 65
63
Principle of Forced Vibrations 67
67
THEORY OF APPROXIMATION SECTION PAGE 1 Theory of Approximation 72
72
Substitution of Simple Hypotheses 74
74
Approximation to Exact Laws 79
79
Successive Approximations to Natural Conditions 84
84
Discovery of Hypothetically Simple Laws 90
90
Mathematical Principles of Approximation 92
92
Approximate Independence of Small Effects 96
96
Four Meanings of Equality 102
102
Arithmetic of Approximate Quantities 103
103
CHAPTER XXII
105
Probable Connexion of Varying Quantities 106
106
Empirical Mathematical Laws 110
110
Discovery of Rational Formulae 113
113
The Graphical Method 116
116
Interpolation and Extrapolation 120
120
Illustrations of Empirical Quantitative Laws 125
125
Simple Proportional Variation 127
127
CHAPTER XXIII
131
Requisites of a good Hypothesis 138
138
The First RequisitePossibility of Deductive Reasoning 140
140
The Second RequisiteConsistency with Established Laws of Nature 143
143
The Third RequisiteConformity with Facts 146
146
Experiraentum Crucis 148
148
Descriptive Hypothesis 153
154
CHAPTER XXIV
157
Empirical Knowledge 158
158
Accidental Discovery 162
162
Empirical Observations subsequently explained 166
166
Overlooked Results of Theory 168
168
Predicted Discoveries 171
171
Predictions in the Science of Light 173
173
Predictions from the Theory of Undulations 176
176
178
178
180
180
Prediction by Inversion of Cause and Effect 181
181
183
183
Facts known only by Theory 185
185
186
186
188
188
ACCORDANCE OF QUANTITATIVE THEORIES AND EXPERIMENTS SECTION PAGE 1 Accordance of Quantitative Theories and Experiments ...
189
190
190
Quantities indicated by Theory but Empirically Measured 192
192
Explained Results of Measurement 193
193
Quantities determined by Theory and verified by Measurement 194
194
Quantities determined by Theory and not verified 196
196
Discordance of Theory and Experiment 198
198
Accordance of Measurements of Astronomical Distances 201
201
Selection of the best Mode of Measurement 204
204
Agreement of Distinct Modes of Measurement 206
206
Residual Phenomena 212
212
CHARACTER OF THE EXPERIMENTALIST 1 Character of the Experimentalist 217
217
Nature of Genius 219
219
Error of the Baconian Method 220
220
Freedom of Theorizing 221
221
The Newtonian Method the True Organum 226
226
Candour and Courage of the Philosophic Mind 232
232
The Philosophic Character of Faraday 234
234
Reservation of Judgment 239
239
BOOK V
242
Distinction of Generalization and Analogy 244
244
Two Meanings of Generalization 246
246
Value of Generalization 248
248
Comparative Generality of Physical Properties 249
249
Uniform Properties of all Matter 254
254
Variable Properties of Matter 258
258
Extreme Instances of Properties 259
259
The Detection of Continuity 262
262
The Law of Continuity 268
268
Failure of the Law of Continuity 273
273
Negative Arguments on the Principle of Continuity 276
276
Tendency to Hasty Generalization 278
278
CHAPTER XXVIII
283
Analogy as a Guide in Discovery 286
286
Analogy in the Mathematical Sciences 288
288
Analogy in the Theory of Undulations 293
293
Use of Analogy in Astronomy 297
297
Failures of Analogy 302
302
CHAPTER XXIX
306
Imaginary or False Exceptions 309
309
Apparent but Congruent Exceptions 313
313
Singular Exceptions 316
316
Divergent Exceptions 320
320
Accidental Exceptions 324
324
Novel and Unexplained Exceptions 328
328
Limiting Exceptions 331
331
Real Exceptions to Supposed Laws 336
336
Unclassed Exceptions 338
338
CHAPTER XXX
344
Classification involving Induction 346
346
Multiplicity of Modes of Classification 348
348
Natural and Artificial Systems of Classification 351
351
Correlation of Properties 353
353
Classification in Crystallography 359
359
Classification an Inverse and Tentative Operation 364
364
Symbolic Statement of the Theory of Classification 367
367
Bifurcate Classification 371
371
The Five Predicates 375
375
Summun Genus and Infima Species 379
379
The Tree of Porphyry 381
381
Does Abstraction imply Generalization I 389
389
Discovery of Marks or Characteristics 394
394
Diagnostic Systems of Classification 396
396
Index Classifications 400
400
Classification in the Biological Sciences 405
405
Classification by Types 411
411
Natural Genera and Species 414
414
Unique or Exceptional Objects 418
418
Limits of Classification 421
421
BOOK VI
427
The Meaning of Natural Law 429
429
Infiniteness of the Universe 431
431
The Indeterminate Problem of Creation 433
433
Hierarchy of Natural Laws 436
436
The Ambiguous ExpressionUniformity of Nature 440
440
Possible States of the Universe 444
444
Speculations on the Reconcentration of Energy 446
446
The Divergent Scope for New Discovery 449
449
The Infinite Incompleteness of the Mathematical Sciences 451
451
The Reign of Law in Mental and Social Phenomena 457
457
The Theory of Evolution 460
460
Possibility of Divine Interference 464
464
Conclusion
466

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الصفحة 106 - Whatever phenomenon varies in any manner, whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation.
الصفحة 360 - Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external...
الصفحة 457 - Veniet tempus quo ista quae nunc latent in lucem dies extrahat et longioris aevi diligentia. Ad inquisitionem tantorum aetas una non sufficit, ut tota caelo vacet ; quid quod tarn paucos annos inter studia ac vitia non aequa portione dividimus?
الصفحة 75 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
الصفحة 235 - I have long held an opinion, almost amounting to conviction, in common I believe with many other lovers of natural knowledge, that the various forms under which the forces of matter are made manifest have one common origin; or, in other words, are so directly related and mutually dependent, that they are convertible, as it were, one into another, and possess equivalents of power in their action.
الصفحة 469 - Now among the most unquestionable rules of Scientific Method is that first law that whatever phenomenon is, is. We must ignore no existence whatever ; we may variously interpret or explain its meaning and origin, but if a phenomenon does exist it demands some kind of explanation.
الصفحة 222 - The world little knows how many of the thoughts and theories which have passed through the mind of a scientific investigator have been crushed in silence and secrecy by his own severe criticism and adverse examination; that in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realized.
الصفحة 361 - Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
الصفحة 241 - The philosopher should be a man willing to listen to every suggestion, but determined to judge for himself. He should not be biased by appearances, have no favourite hypothesis, be of no school, and in doctrine have no master. He should not be a respecter of persons, but of things. Truth should be his primary object. If to these qualities he adds industry, he may indeed hope to walk within the veil of the temple of nature.
الصفحة 145 - That it is the glory of God to conceal a thing, but the glory of a king to search it out.

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