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

Cover
 

Was andere dazu sagen - Rezension schreiben

Es wurden keine Rezensionen gefunden.

Inhalt

The Nature of Inference
16
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
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
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
109
The Logical Slate
110
Abstraction of Indifferent Circumstances
112
Analogy
124
INDUCTION
139
139
140
Induction 2 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
The Inverse Logical Problem involving Three Terms
157
Distinction between Perfect and Imperfect Induction
164
Transition from Perfect to Imperfect Induction 154 157 164
168
BOOK II
172
SEOTION PAGE
207
Connexion between the Arithmetical Triangle and the Logical Abecedarium
214
Possible Variety of Nature and
216
Higher Orders of Variety 214 216
219
CHAPTER X
224
Fundamental Principles of the Theory
228
Rules for the Calculation of Probabilities
231
Employment of the Logical Abecedarium in questions
234
Probability
235
Comparison of the Theory with Experience
236
Probable Deductive Arguments
239
Difficulties of the Theory 234 236 239
243
CHAPTER XI
250
PHILOSOPHY OF INDUCTIVE INFERENCE 1 Philosophy of Inductive Inference 2 Various Classes of Inductive Truths
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
271
251 253 254 256 257 260 262 263 268 271 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 Illustration of the Inverse Problem
292
4
293
General Solution of the Inverse Problem
295
Rules of the Inverse Method
297
Fortuitous Coincidences
302
Summary of the Theory of Inductive Inference
307
THE EXACT MEASUREMENT OF PHENOMENA SECTION PAGE 1 The Exact Measurement of Phenomena
313
7
315
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
CHAPTER XIV
357
Standard Unit of Time
359
The Unit of Space and the Bar Standard
365
The Terrestrial Standard
367
10
368
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
Method of Avoidance of Error
393
Differential Method
398
Method of Correction
400
Method of Compensation
406
Method of Reversal PAGE 393 398 400 406
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
Determination of Maximum Points 414 416 418 422 424 428
431
CHAPTER XVII
434
434
435
The Law of Error
452
Principles of Number
1
The Nature of Number
2
Of Numerical Abstraction
3
Concrete and Abstract Numbers
4
Analogy of Logical and Numerical Terins
5
Principle of Mathematical Inference
6
Reasoning by Inequalities
7
Arithmetical Reasoning
8
Numerically Definite Reasoning
9
The Probable Error of Mean Results
10
The Rejection of the Mean Result
11
Method of Least Squares
12
Works upon the Theory of Probability and the Law of Error
13
Detection of Constant Errors
14
CHAPTER XX
50
The Variable and the Variant
51
Measurement of the Variable
53
Maintenance of Similar Conditions
55
Collective Experiments
57
Periodic Variations
61
Combined Periodic Changes
63
Principle of Forced Vibrations
65
Integrated Variations
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
286 288
91
Mathematical Principles of Approximation 92
92
Approximate Independence of Small Effects 96
96
Four Meanings of Equality 102
102
50
103
CHAPTER XXII
105
Probable Connexion of Varying Quantities 106
106
Empirical Mathematical Laws 110
110
Discovery of Rational Formula 113
113
The Graphical Method 116
116
Interpolation and Extrapolation 120
120
53
122
Illustrations of Empirical Quantitative Laws 125
125
Simple Proportional Variation 127
127
CHAPTER XXIII
131
276
135
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
Experimentum 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
297
170
Predicted Discoveries 171
171
172
172
Predictions in the Science of Light 173
173
175
175
Predictions from the Theory of Undulations 176
176
177
177
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
CHAPTER XXIX
189
190
190
Empirical Measurements 190 3 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
279
200
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
443
211
Residual Phenomena 212
212
CHAPTER XXVI
217
Nature of Genius
219
Error of the Baconian Method
220
Freedom of Theorizing
221
The Newtonian Method the True Organum
226
Candour and Courage of the Philosophic Mind
232
The Philosophic Character of Faraday
234
Reservation of Judgment 217 219 220 221 226 232 234 239
239
BOOK V
242
Generalization 2 Distinction of Generalization and Analogy 3 Two Meanings of Generalization 4 Value of Generalization
248
Comparative Generality of Physical Properties
249
55
254
Variable Properties of Matter
258
Extreme Instances of Properties
259
The Detection of Continuity
262
The Law of Continuity
268
Failure of the Law of Continuity
273
Negative Arguments on the Principle of Continuity
276
Tendency to Hasty Generalization
278
281
281
CHAPTER IX
283
285
285
289
289
292
292
295
295
297
297
302
302
EXCEPTIONAL PHENOMENA
306
307
307
Exceptional Phenomena 2 Imaginary or False Exceptions
309
Apparent but congruent Exceptions
313
Singular Exceptions
316
Divergent Exceptions
320
Accidental Exceptions
324
Novel and Unexplained Exceptions
328
Limiting Exceptions
335
Real Exceptions to Supposed Laws
336
Unclassed Exceptions 306 309 313 316 320 324 328 331 336 338
338
CHAPTER XXX
344
THE VARIETY OF NATURE OR THE DOCTRINE OF COMBINATIONS AND PERMUTATIONS
345
Classification involving Induction
346
Multiplicity of Modes of Classification
348
Natural and Artificial Systems of Classification
351
Correlation of Properties
353
Classification in Crystallography
359
Classification an Inverse and Tentative Operation
364
Symbolic Statement of the Theory of Classification
367
Bifurcate Classification
371
The Five Predicables
375
Summun Genus and Infima Species
379
The Tree of Porphyry
381
Does Abstraction imply Generalization
389
Discovery of Marks or Characteristics
394
Diagnostic Systems of Classification
396
Index Classifications
400
Classification in the Biological Sciences
405
Classification by Types
411
Natural Genera and Species
414
Unique or Exceptional Objects
418
Limits of Classification
421
REFLECTIONS ON THE RESULTS AND LIMITS OF SCIENTIFIC METHOD SECTION PAGE 1 Reflections on the Results and Limits of Scientific...
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
444
444
The Variety of Nature 2 Distinction of Combinations and Permutations 3 Calculation of Number of Combinations 4 The Arithmetical Triangle
445
Speculations on the Reconcentration of Energy 446
446
447
447
449
449
451
451
454
454
The Reign of Law in Mental and Social Phenomena 457
457
458
458
459
459
460
460
Possibility of Divine Interference 461
464
Conclusion
466
57
472
364
473
248
474
61
475
63
476
65
478
206
479

Andere Ausgaben - Alle anzeigen

Häufige Begriffe und Wortgruppen

Beliebte Passagen

Seite 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.
Seite 360 - Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external...
Seite 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?
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 145 - That it is the glory of God to conceal a thing, but the glory of a king to search it out.

Bibliografische Informationen