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

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Macmillan, 1924 - Logic - 786 pages

From inside the book

Contents

The Process of Inference
9
Measurements by Natural Coincidence
10
Deduction and Induction
11
Comparative Use of Measuring Instruments
12
Symbolic Expression of Logical Inference
13
Expression of Identity and Difference
14
Attainable Accuracy of Measurement
15
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
SECTION
27
Collective Terms
29
Synthesis of Terms
30
Symbolic Expression of the Law of Contradiction
31
Terms
32
CHAPTER III
36
Propositions 2 Simple Identities
38
Partial Identities
40
Limited Identities
42
Negative Propositions
43
Conversion of Propositions
46
Twofold Interpretation of Propositions
47
CHAPTER
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 10 Fallacies
60
Twofold meaning of General Names 3 Abstract Terms 4 Substantial Terms
64
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 VI
81
Simple Illustrations
83
Employment of the Contrapositive Proposition
84
Contrapositive of a Simple Identity
86
Miscellaneous Examples of the Method
88
Mr Venns Problem
90
Abbreviation of the Process
91
The Logical Alphabet
94
66
95
Abstraction of Indifferent Circumstances
97
Illustrations of the Indirect Method
98
Second Example
99
Third Example
100
Fourth Example
101
Fallacies Analysed by the Indirect Method
102
The Logical Abacus
104
The Logical Machine
107
The Order of Premises
114
The Equivalence of Propositions
115
The Nature of Inference
118
CHAPTER VII
121
Induction an Inverse Operation
122
Inductive Problems for Solution by the Reader
126
11
127
Induction of Partial Identities
130
Solution of the Inverse or Inductive Problem involving Two Classes
134
14
135
The Inverse Logical Problem involving Three Classes
137
Professor Clifford on the Types of Compound Statemast in 9 Distinction between Perfect and Imperfect Induction
146
Transition from Perfect to Imperfect Induction
149
NUMBER VARIETY AND PROBABILITY
153
CHAPTER IX
173
67
174
17
179
Calculation of Number of Combinations
180
21
184
22
186
24
187
Connexion between the Arithmetical Triangle and the Logical
189
68
195
CHAPTER X
197
Rules for the Calculation of Probabilities
203
SECTION PAGE 5 Comparison of the Theory with Experience
206
71
208
Probable Deductive Arguments
209
Difficulties of the Theory
213
CHAPTER XI
218
Various Classes of Inductive Truths
219
The Relation of Cause and Effect
220
Fallacious Use of the Term Cause
221
Confusion of Two Questions
222
Definition of the Term Cause
224
Distinction of Inductive and Deductive Results
226
The Grounds of Inductive Inference
228
Illustrations of the Inductive Process
229
Geometrical Reasoning
233
Discrimination of Certainty and Probability
235
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
General Solution of the Inverse Problem
255
Rules of the Inverse Method
257
Fortuitous Coincidences
261
Summary of the Theory of Inductive Inference
265
UNITS AND STANDARDS OF MEASUREMENT TAGE 270 274
274
282
282
302
302
Units and Standards of Measurement
305
Standard Unit of Time 305
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
THE METHOD OF MEANS 1 The Method of Means
357
Several Uses of the Mean Result
359
The Mean and the Average
360
On the Average or Fictitious Mean
363
The Precise Mean Result
365
Determination of the Zero Point
368
Determination of Maximum Points 357 359 360 363 365 368
371
CHAPTER XVII
374
The Law of Error THE LAW OF ERROR 2 Establishment of the Law of Error
375
Herschels Geometrical Proof
377
Laplaces and Quetelets Proof of the
378
Logical Origin of the Law of Error 6 Verification of the Law of Error
383
25
385
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
27
429
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
CHAPTER XXI
456
Substitution of Simple Hypotheses
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
Descriptive Hypotheses
522
EMPIRICAL KNOWLEDGE EXPLANATION AND PREDICTION 1 Empirical Knowledge Explanation and Prediction
525
Empirical Knowledge
527
Accidental Discovery
529
Empirical Observations subsequently Explained
532
Overlooked Results of Theory
534
Predicted Discoveries 7 Predictions in the Science of Light PAGE 525 526 529 532 534
536
312
539
Predictions from the Theory of Undulations 538
540
Prediction in other Sciences
542
Prediction by Inversion of Cause and Effect
545
Facts known only by Theory 542 545
547
CHAPTER XXV
551
Empirical Measurements
552
Quantities indicated by Theory but Empirically Measured
553
Explained Results of Measurement 551 552
554
Quantities determined by Theory and not verified
556
Discordance of Theory and Experiment
558
Selection of the best Mode of Measurement
563
Agreement of Distinct Modes of Measurement 11 Residual Phenomena
564
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
587
Reservation of Judgment 574
592
599
600
Negative Arguments on the Principle of Continuity 619
621
Analogy 2 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 627 629 631 635 638
641
CHAPTER XXIX
644
76
649
Divergent Exceptions
655
Accidental Exceptions
658
Novel and Unexplained Exceptions
661
Limiting Exceptions 9 Real Exceptions to Supposed Laws
666
Unclassed Exceptions
668
CHAPTER XXX
673
Classification involving Induction
675
Multiplicity of Modes of Classification
677
Natural and Artificial Systems of Classification
679
577
681
Classification in Crystallography
685
586
687
Classification an Inverse and Tentative Operation
689
Symbolic Statement of the Theory of Classification
692
Bifurcate Classification
694
The Five Predicables
698
Summum Genus and Infima Species
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
Unique or Exceptional Objects
728
Limits of Classification
730
BOOK VI
735
The Meaning of Natural Law
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
765
Conclusion
766
592
772
INDEX
773
647
774
374
776
375
777
377
778
378
779
314
780
315
782
396
783
320
785
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Page 593 - 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 favorite 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 be added industry, he may indeed hope to walk within the veil of the temple of nature.
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