The Principles of Science: A Treatise on Logic and Scientific Method

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Macmillan, 1887 - 786 páginas

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Contenido

Bifurcate Classification
9
The Five Predicables
10
Summum Genus and Infima Species
11
The Tree of Porphyry
12
Does Abstraction imply Generalisation
13
Discovery of Marks or Characteristics
14
Diagnostic Systems of Classification
15
Index Classifications
16
General Formula of Logical Inference
17
Classification by Types
18
Natural Genera and Species
19
The Propagating Power of Similarity
20
Anticipations of the Principle of Substitution
21
The Logic of Relatives
22
SECTION
27
Collective Terms
29
Synthesis of Terms
30
Symbolic Expression of the Law of Contradiction
31
Certain Special Conditions of Logical Symbols
32
30
33
CHAPTER III
36
36
37
Propositions
39
Simple Identities 3 Partial Identities
40
Limited Identities
42
Negative Propositions
43
Conversion of Propositions
46
Twofold Interpretation of Propositions 42 43 46
47
CHAPTER IV
49
Immediate Inference
50
Inference with Two Simple Identities
51
Inference with a Simple and a Partial Identity
53
Inference of a Partial from Two Partial Identities
55
On the Ellipsis of Terms in Partial Identities 7 Inference of a Simple from Two Partial Identities
58
Inference of a Limited from Two Partial Identities
59
Miscellaneous Forms of Deductive Inference
60
Fallacies 49 50 51 53 55 57 58 59 60 62 1
62
PAGE
64
CHAPTER V
66
Expression of the Alternative Relation
67
Nature of the Alternative Relation
68
Laws of the Disjunctive Relation
71
Symbolic Expression of the Law of Duality
73
Various Forms of the Disjunctive Proposition
74
Inference by Disjunctive Propositions
76
CHAPTER VII
117
Inductive Problems for Solution by the Reader
126
14
135
The Inverse Logical Problem involving Three Classes
137
Professor Clifford on the Types of Compound Statement
143
Transition from Perfect to Imperfect Induction
149
NUMBER VARIETY AND PROBABILITY
153
CHAPTER IX
173
67
174
20
179
Calculation of Number of Combinations
180
21
184
22
186
CHAPTER II
187
TERMS
189
68
195
CHAPTER X
197
24
203
BOOK III
210
PHILOSOPHY OF INDUCTIVE INFERENCE
218
Philosophy of Inductive Inference 2 Various Classes of Inductive Truths 3 The Relation of Cause and Effect 4 Fallacious Use of the Term Cause
221
Confusion of Two Questions
222
Definition of the Term Cause
224
Distinction of Inductive and Deductive Results 8 The Grounds of Inductive Inference
228
Illustrations of the Inductive Process
229
71
230
Geometrical Reasoning
232
Discrimination of Certainty and Probability 218 219 220 221 222 224 226 228 229
235
THE INDUCTIVE OR INVERSE APPLICATION OF THE THEORY OF PROBABILITY
240
Principle of the Inverse Method
242
Simple Applications of the Inverse Method
244
The Theory of Probability in Astronomy
247
The General Inverse Problem
250
Simple Illustration of the Inverse Problem
253
General Solution of the Inverse Problem
255
Rules of the Inverse Method
257
Summary of the Theory of Inductive Inference
265
METHODS OF MEASUREMENT CHAPTER XIII
270
Division of the Subject
274
The Fallacious Indications of the Senses
276
Complexity of Quantitative Questions
278
The Methods of Accurate Measurement
282
Measuring Instruments
284
The Method of Repetition
288
Measurements by Natural Coincidence
292
Modes of Indirect Measurement
296
Comparative Use of Measuring Instruments
299
Systematic Performance of Measurements
300
The Pendulum
302
Attainable Accuracy of Measurement
303
CHAPTER XIV
305
Standard Unit of Time
307
The Unit of Space and the Bar Standard
312
The Terrestrial Standard
314
The Pendulum Standard
315
Unit of Density
316
Unit of Mass
317
Natural System of Standards
319
Subsidiary Units
320
Derived Units
321
11 Provisional Vuits
323
Theory of Dimensions
325
Natural Constants
328
Mathematical Constants
330
Physical Constants
331
Astronomical Constants
332
Terrestrial Numbers
333
Social Numbers
334
ANALYSIS OF QUANTITATIVE PHENOMENA SECTION PAGE 1 Analysis of Quantitative Phenomena
335
Illustrations of the Complication of Etfects
336
Methods of Eliminating Error
339
Method of Avoidance of Error
340
Differential Method
344
Method of Correction
346
Method of Compensation
350
Method of Reversal
354
CHAPTER XVI
357
Several Uses of the Mean Result
359
Terms
360
Logical Origin of the Law of Error
383
The Probable Mean Result
385
The Probable Error of Results
386
Rejection of the Mean Result
389
240
390
Method of Least Squares 3 3
391
Works upon the Theory of Probability
394
Detection of Constant Errors
396
CHAPTER XVIII
399
Distinction of Observation and Experiment
400
Mental Conditions of Correct Observation
402
Instrumental and Sensual Conditions of Correct Observation
404
External Conditions of Correct Observation
407
Apparent Sequence of Events
409
Negative Arguments from NonObservation
411
CHAPTER XIX
416
Exclusion of Indifferent Circumstances
419
Simplification of Experiments
422
Failure in the Simplification of Experiments
424
Removal of Usual Conditions
426
Interference of Unsuspected Conditions
428
Blind or Test Experiments
433
Negative Results of Experiment
434
Limits of Experinient
437
CHAPTER XX
439
The Variable and the Variaut
440
Measurement of the Variable
441
Maintenance of Similar Conditions
443
Collective Experiments
445
Periodic Variations
447
Combined Periodic Changes
450
Principle of Forced Vibrations
451
Integrated Variations
452
CHAPTER XXI
456
THEORY OF APPROXIMATION SECTION PAGE 1 Theory of Approximation
457
Substitution of Simple Mypotheses
458
Approximation to Exact Laws
462
Successive Approximations to Natural Conditions
465
Discovery of Hypothetically Simple Laws
470
Mathematical Principles of Approximation
471
Approximate Independence of Small Effects
475
Four Meanings of Equality
479
Arithmetic of Approximate Quantities
481
CHAPTER XXII
483
Probable Connexion of Varying Quantities
484
Empirical Mathematical Laws
487
Discovery of Rational Formulæ
489
The Graphical Method
492
Interpolation and Extrapolation
495
Illustrations of Empirical Quantitative Laws
499
Simple Proportional Variation
501
CHAPTER XXIII
504
Requisites of a good Hypothesis
510
Possibility of Deductive Reasoning
511
Consistency with the Laws of Nature
514
Conformity with Facts
516
Experimentum Crucis
518
Descriptire Hypotheses
522
244
524
73
543
CHAPTER XXV
551
Discordance of Theory and Experiment
558
Agreement of Distinct Modes of Measurement
564
CHAPTER XXVI
574
The Newtonian Method the True Organum
581
The Philosophic Character of Faraday
587
GENERALISATION ANALOGY AND CLASSIFICATION CHAPTER XXVII
594
Distinction of Generalisation and Analogy
596
Two Meanings of Generalisation
597
Value of Generalisation
599
Comparative Generality of Properties
600
Uniform Properties of all Matter
603
Variable Properties of Matter
606
Extreme Instances of Properties
607
The Detection of Continuity
610
The Law of Continuity
615
Failure of the Law of Continuity
619
Negative Arguments on the Principle of Continuity
621
Tendency to Hasty Generalisation
623
CHAPTER XXVIII
627
Analogy as a Guide in Discovery
629
Analogy in the Mathematical Sciences
631
Analogy in the Theory of Undulations
635
Analogy in Astronomy
638
Failures of Analogy
641
CHAPTER XXIX
644
Imaginary or False Exceptions
645
76
649
Singular Exceptions
652
Divergent Exceptions
655
Accidental Exceptions
658
Novel and Unexplained Exceptions
661
Limiting Exceptions
663
Real Exceptions to Supposed Laws
666
Unclassed Exceptions
668
673
675
CHAPTER XXXI
735
The Meaning of Natural
737
Infiniteness of the Universe
738
The Indeterminate Problem of Creation
740
Hierarchy of Natural Laws
742
The ambiguous ExpressionUniformity of Nature
745
Possible States of the Universe
749
Speculations on the Reconcentration of Energy
751
The Divergent Scope for New Discovery
752
Infinite Incompleteness of the Mathematical Sciences
754
The Reign of Law in Mental and Social Phenomena
759
The Theory of Evolution
761
Possibility of Divine Interference 14 Conclusion
765
Twofold meaning of General Names 3 Abstract Terms
771
250
772
253
774
257
779
742
780
265
781
759
783
Substantial Terms
784
Fundamental Principles of the Theory
2
MODERN LANGUAGES
13
25
21
27
27
28
28
22
49
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