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

Forside
Macmillan and Company, 1887 - 786 sider

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The Process of Inference
9
Numerical meaning of Logical Conditions
10
Deduction and Induction
11
Symbolic Expression of Logical Inference
13
Expression of Identity and Difference
14
General Formula of Logical Inference
17
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
CHAPTER III
36
Propositions
39
Simple Identities 3 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
PAGE 1
64
CHAPTER V
66
Expression of the Alternative Relation
67
Nature of the Alternative Relation
68
4
69
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
PAGE 29
93
The Logical Slate
95
Fourth Example
101
The Order of Premises
107
31
119
CHAPTER VII
121
OBSERVATION
126
Induction of Simple Identities
127
SECTION
130
14
135
The Inverse Logical Problem involving Three Classes
137
32
142
Distinction between Perfect and Imperfect Induction
146
THE VARIETY OF NATURE OR THE DOCTRINE OF COMBINATIONS AND PERMUTATIONS 1 The Variety of Nature
173
36
177
Calculation of Number of Combinations
180
PAGE
183
220
184
Connexion between the Arithmetical Triangle and the Logical Alphabet
189
Possible Variety of Nature and
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
37
208
17
230
Observation
232
21
238
CHAPTER XII
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
46
254
General Solution of the Inverse Problem
255
Rules of the Inverse Method
257
Fortuitous Coincidences
261
Summary of the Theory of Inductive Inference
265
242
267
THE EXACT MEASUREMENT OF PHENOMENA SECTION PAGE 1 The Exact Measurement of Phenomena
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
22
297
Comparative Use of Measuring Instruments
299
Systematic Performance of Measurements
300
The Pendulum
302
Attainable Accuracy of Measurement
303
CHAPTER II
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
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 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
Terms
360
On the Average or Fictitious Mean
363
The Precise Mean Result
365
50
367
Determination of the Zero Point
368
Determination of Maximum Points
371
Rejection of the Mean Result
389
Method of Least Squares 3 3
391
Works upon the Theory of Probability
394
Detection of Constant Errors
396
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
203
408
Apparent Sequence of Events
409
Negative Arguments from NonObservation
411
CHAPTER XIX
416
Experiment 2 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
446
Periodic Variations
447
Combined Periodic Changes
450
Principle of Forced Vibrations
451
Integrated Variations
452
QUANTITATIVE INDUCTION
483
Quantitative Induction
485
Probable Connexion of Varying Quantities 3 Empirical Mathematical Laws
487
Discovery of Rational Formulæ
489
The Graphical Method
492
Interpolation and Extrapolation
495
53
496
Illustrations of Empirical Quantitative Laws
499
Simple Proportional Variation 499
501
CHAPTER XXIII
504
The Use of Hypothesis
508
Requisites of a good Hypothesis
510
Possibility of Deductive Reasoning 504 510
511
244
524
CHAPTER XXV
551
Discordance of Theory and Experiment
558
Agreement of Distinct Modes of Measurement
564
55
569
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
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
673
675
724
701
The Tree of Porphyry
702
Does Abstraction imply Generalisation?
704
Discovery of Marks or Characteristics
708
Diagnostic Systems of Classification
710
Index Classifications
714
Classification in the Biological Sciences
718
Classification by Types
722
Natural Genera and Species
724
416
726
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 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 INDEX
765
205
771
57
772
419
773
59
774
67
775
68
776
439
777
257
779
76
780
265
781
441
785
447
786
Twofold meaning of General Names
2
Abstract Terms
3
Substantial Terms
4
Conformity with Facts
5
Experimentum Crucis
6
Descriptive Hypotheses
7
MODERN LANGUAGES
13
888888
21
24
24
27
27
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