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

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Macmillan and Company, 1883 - 786 sider

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The Process of Inference
9
The Five Predicables
10
Deduction and Induction
11
CHAPTER III
12
Symbolic Expression of Logical Inference
13
Expression of Identity and Difference
14
Propositions
15
Index Classifications
16
General Formula of Logical Inference
17
The Propagating Power of Similarity
20
Anticipations of the Principle of Substitution
21
The Logic of Relatives
22
CHAPTER II
24
Simple Identities
37
Partial Identities
40
Limited Identities
42
Negative Propositions
43
Conversion of Propositions
46
Twofold Interpretation of Propositions
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
62
CHAPTER V
66
Expression of the Alternative Relation
67
Nature of the Alternative Relation
68
BOOK II
69
Terms
71
Symbolic Expression of the Law of Duality
73
Various Forms of the Disjunctive Proposition
74
Inference by Disjunctive Propositions
76
6
81
Second Example
99
The Order of Premises
107
CHAPTER VII
117
NUMBER VARIETY AND PROBABILITY CHAPTER VIII
153
The Nature of Number
156
Of Numerical Abstraction
158
Concrete and Abstract Number
159
Analogy of Logical and Numerical Terms
160
Principle of Mathematical Inference
162
Reasoning by Inequalities
165
Arithmetical Reasoning
167
Numerically Definite Reasoning
168
Numerical meaning of Logical Conditions
171
CHAPTER IX
173
Distinction of Combinations and Permutations
177
Calculation of Number of Combinations
180
The Arithmetical Triangle
182
Connexion between the Arithmetical Triangle and the Logical Alphabet
189
Possible Variety of Nature and Art
190
Higher Orders of Variety
192
CHAPTER X
197
Fundamental Principles of the Theory
200
Rules for the Calculation of Probabilities
203
The Logical Alphabet in questions of Probability
205
SECTION PAGE
206
61
214
CHAPTER XI
218
Distinction of Inductive and Deductive Results
226
Geometrical Reasoning
233
CHAPTER XII
240
The Theory of Probability in Astronomy
247
Simple Illustration of the Inverse Problem
253
Fortuitous Coincidences
261
Division of the Subject 3 Continuous quantity
274
The Fallacious Indications of the Senses
276
Complexity of Quantitative Questions
278
The Methods of Accurate Measurement 7 Conditions of Accurate Measurement
282
Measuring Instruments
284
The Method of Repetition
287
Measurements by Natural Coincidence
292
Modes of Indirect Measurement
296
12 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
Provisional Units
323
Theory of Dimensions
325
Natural Constants
328
Mathematical Constants 15 Physical Constants 16 Astronomical Constants 17 Terrestrial Numbers 18 Organic Numbers 19 Social Numbers
329
ANALYSIS OF QUANTITATIVE PHENOMENA SECTION PAGE 1 Analysis of Quantitative Phenomena
335
Illustrations of the Complication of Effects
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
The Mean and the Average
360
On the Average or Fictitious Mean
363
5 The Precise Mean Result
365
Determination of the Zero Point
368
Determination of Maximum Points
371
CHAPTER XVII
374
Establishment of the Law of Error
375
Herschels Geometrical Proof
377
Laplaces and Quetelets Proof of the Law
378
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
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 Experiment
437
CHAPTER XX
439
The Variable and the Variant
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
THEORY OF APPROXIMATION
456
CHAPTER XXII
483
Discovery of Rational Formulæ
489
Interpolation and Extrapolation
495
Simple Proportional Variation
501
134
505
Requisites of a good Hypothesis
510
Descriptive Hypotheses 518
522
274
523
CHAPTER XXIV
525
Empirical Knowledge
526
Overlooked Results of Theory
534
Predicted Discoveries
536
Predictions in the Science of Light
538
Predictions from the Theory of Undulations
540
Prediction in other Sciences
542
Prediction by Inversion of Cause and Effect
545
Facts known only by Theory
547
CHAPTER XXV
551
Empirical Measurements
552
Quantities indicated by Theory but Empirically Measured
553
Explained Results of Measurement
554
Quantities determined by Theory and verified by Measurement
555
Quantities determined by Theory and not verified
556
Discordance of Theory and Experiment
558
Accordance of Measurements of Astronomical Distances
560
Selection of the best Mode of Measurement
563
Agreement of Distinct Modes of Measurement
564
Residual Phenomena
569
CHAPTER XXVI
574
Error of the Baconian Method
576
Freedom of Theorising
577
The Newtonian Method the True Organum
581
Candour and Courage of the Philosophic Mind
586
The Philosophic Character of Faraday 687
587
Reservation of Judgment
592
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
278
614
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
282
637
Analogy in Astronomy
638
Failures of Analogy
641
CHAPTER XXIX
644
Imaginary or False Exceptions
647
Apparent but Congruent Exceptions
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
ᏢᎪᏩᎬ 673
675
Classification in the Biological Sciences
718
Classification by Types
722
Natural Genera and Species
724
Unique or Exceptional Objects
728
Limits of Classification
730
BOOK VI
735
The Meaning of Natural
737
Infiniteness of the Universe
738
The Indeterminate Problem of Creation
740
Hierarchy of Natural Laws
742
The Ambiguous Expression Uniformity 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
288
772
Substantial Terms PAGK 1
774
5
775
6
776
20
778
300
779
21
780
752
781
22
782
759
783
315
784
25 27 28
785

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