The Principles of science

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Macmillan and Company, 1874 - 480 oldal

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Miscellaneous Forms of Deductive Inference
9
Fallacies
10
The Process of Inference
11
Deduction and Induction
13
CONTENTS
14
Symbolic Expression of Logical Inference
15
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
59
60
66
69
PAGE
77
Disjunctive Propositions
79
Expression of the Alternative Relation 3 Nature of the Alternative Relation CHAPTER V
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
SECTION PAGE 10 Illustrations of the Indirect Method
113
The Indirect Method of Inference
115
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 an Inverse Operation
140
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
168
BOOK II
172
The Nature of Number
175
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
95
191
CHAPTER IX
195
Distinction of Combinations and Permutations
200
Calculation of Number of Combinations
204
The Arithmetical Triangle
206
THEORY OF PROBABILITY 1 Theory of Probability
224
Fundamental Principles of the Theory
228
Rules for the Calculation of Probabilities
231
Employment of the Logical Abecedarium in questions of Probability 231
234
Comparison of the Theory with Experience
236
Probable Deductive Arguments
239
BOOK III
240
Difficulties of the Theory
243
CHAPTER XI
250
Various Classes of Inductive Truths
251
The Relation of Cause and Effect
253
Fallacious Use of the Term Cause
254
Confusion of Two Questions 6 Definition of the Term Cause
257
Distinction of Inductive and Deductive Results 8 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 Illustration 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
CHAPTER XIV
357
Standard Unit of Time
359
The Unit of Space and the Bar Standard
365
The Terrestrial Standard
366
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
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
Determination of Maximum Points
431
THE LAW OF ERROR 1 The Law of Error
435
Herschels Geometrical Proof
437
Laplaces and Quetelets Proof of the Law of Error
438
Derivation of the Law of Error from Simple Logical Prin ciples
443
Verification of the Law of Error
444
Remarks on the General Law of Error
447
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
461
BOOK IV
1
Abstraction of Indifferent Circumstances 2 Simple Illustrations
2
Employment of the Contrapositive Proposition
3
Contrapositive of a Simple Identity
4
Miscellaneous Examples of the Method
5
Abbreviation of the Process
6
The Logical Abecedarium
7
Failure in the Simplification of Experiments 33
33
Removal of Usual Conditions 35
35
Interference of Unsuspected Conditions 37
37
Blind or Test Experiments 43
43
45
45
Limits of Experiment 48
48
CHAPTER XX
50
The Variable and the Variant 51
51
Measurement of the Variable 53
53
Maintenance of Similar Conditions 55
55
Collective Experiments 57
57
Periodic Variations 61
61
Combined Periodic Changes 63
63
Principle of Forced Vibrations 65
65
Integrated Variations 67
67
CHAPTER XXI
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
PAGE 283
91
Mathematical Principles of Approximation 92
92
Approximate Independence of Small Effects 96
96
97
97
99
99
101
101
Four Meanings of Equality 102
102
103
103
CHAPTER XXII
105
Probable Connexion of Varying Quantities 106
106
Empirical Mathematical Laws 110
110
Discovery of Rational Formulæ 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
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 Requisite Conformity with Facts 146
146
Experimentum Crucis 148
148
288
152
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
Predictions in other Sciences 178
178
Prediction by Inversion of Cause and Effect 181
181
Facts known only by Theory 185
185
CHAPTER XXV
189
Empirical Measurements 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
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
Residual Phenomena 212
212
CHAPTER XXVI
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
GENERALIZATION ANALOGY AND CLASSIFICATION CHAPTER XXVII
243
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
281
281
285
285
289
289
292
292
293
293
295
295
297
297
302
302
307
307
309
309
313
313
316
316
320
320
324
324
328
328
331
331
336
336
338
338
CHAPTER XXX
344
Classification 2 Classification involving Induction 344 346 3 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 Predicables 375
375
Summun Genus and Infima Species 379
379
The Tree of Porphyry 381
381
105
387
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
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
Conclusion
466
109
471
405
473
418
474
421
475
110
476

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Népszerű szakaszok

359. oldal - 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.
233. oldal - 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.
145. oldal - That it is the glory of God to conceal a thing, but the glory of a king to search it out.
465. oldal - Scientific method leads us to the inevitable conception of an infinite series of successive orders of infinitely small quantities. If so, there is nothing impossible in the existence of a myriad universes within the compass of a needle's point, each with its stellar systems, and its suns and planets, in number and variety unlimited. Science does nothing to reduce the number of strange things that we may believe. When fairly pursued, it makes large drafts upon our powers of comprehension and belief...
63. oldal - If one part of any system connected either by material ties, or by the mutual attractions of its members, be continually maintained by any cause, whether inherent in the constitution of the system or external to it, in a state of regular periodic motion, that motion will be propagated throughout the whole system, and will give rise, in every member of it, and in every part of each member, to periodic movements executed in eijual periods with that to which they owe their origin, though not necessarily...
161. oldal - Malus, while looking through a prism of calcareous spar at the light of the setting sun reflected from the windows of the Luxembourg palace in...
244. oldal - He that will not eat till he has demonstration that it will nourish him; he that will not stir till he infallibly knows the business he goes about will succeed, will have little else to do but to sit still and perish.
84. oldal - A peer is either a duke, or a marquis, or an earl, or a viscount, or a baron.' If expressed in Professor Boole's symbols, it would be implied that a peer cannot be at once a duke and marquis, or marquis and earl. Yet many peers do possess two or more titles, and the Prince of Wales is Duke of Cornwall, Earl of Dublin, and Baron Renfrew.
272. oldal - not one of the inductive truths which men have established, or think they have established, is really safe from exception or reversal. . . . Euler expresses no more than the truth when he says that it would be impossible to fix on any one thing really existing of which we could have so perfect a knowledge as to put us beyond the reach of mistake.
6. oldal - Whatever is, is." (2) The law of contradiction: "Nothing can both be and not be." (3) The law of excluded middle: "Everything must either be or not be.

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