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

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Macmillan and Company, 1877 - 786 Seiten
 

Inhalt

The Process of Inference
9
Prediction by Inversion of Cause and Effect
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
CHAPTER II
24
Twofold meaning of General Names
25
Abstract Terms
27
Substantial Terms
28
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
THE INDIRECT METHOD OF INFERENCE PAGE
64
CHAPTER V
66
Expression of the Alternative Relation 3 Nature of the Alternative Relation
67
BOOK II
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
102
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
PAGE
93
The Logical Slate
95
Abstraction of Indifferent Circumstances
97
Illustrations of the Indirect Method
98
Second Example
99
Third Example
100
Fourth Example 15 Fifth 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
CHAPTER VII
117
Induction an Inverse Operation
122
Inductive Problems for Solution by the Reader
126
Induction of Simple Identities
127
Induction of Partial Identities
130
Solution of the Inverse or Inductive Problem involving
134
The Inverse Logical Problem involving Three Classes
137
Professor Clifford on the Types of Compound Statement in volving Four Classes
143
Distinction between Perfect and Imperfect Induction
146
Transition from Perfect to Imperfect Induction
149
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
29
169
Numerical meaning of Logical Conditions
171
CHAPTER IX
173
Distinction of Combinations and Permutations
177
Calculation of Number of Combinations
180
30
181
The Arithmetical Triangle
182
32
186
Connexion between the Arithmetical Triangle and the Logical Alphabet
189
Possible Variety of Nature and Art
190
36
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
37
208
BOOK III
210
CHAPTER XI
218
Definition of the Term Cause
224
47
230
146
232
Geometrical Reasoning
233
CHAPTER XII
240
49
250
The Theory of Probability in Astronomy
253
51
258
Fortuitous Coincidences
261
METHODS OF MEASUREMENT CHAPTER XIII
270
Division of the Subject 274 3 Continuous quantity
274
The Fallacious Indications of the Senses
276
Complexity of Quantitative Questions
278
The Methods of Accurate Measurement 282 7 Conditions of Accurate Measurement
282
Measuring Instruments
284
The Method of Repetition
287
Measurements by Natural Coincidence
292
Modes of Indirect Measurement 12 Comparative Use of Measuring Instruments 13 Systematic Performance of Measurements 14 The Pendulum 15 A...
296
CHAPTER XIV
305
Units and Standards of Measurement
311
Standard Unit of Time 3 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
335
Analysis of Quantitative Phenomena
337
Illustrations of the Complication of Effects 3 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
The Precise Mean Result
365
Determination of the Zero Point
368
Rejection of the Mean Result
389
Method of Least Squares
391
Works upon the Theory of Probability
394
Detection of Constant Errors
396
INDUCTIVE INVESTIGATION CHAPTER XVIII
399
Distinction of Observation and Experiment
400
Mental Conditions of Correct Observation
402
PAGE 335
404
Instrumental and Sensual Conditions of Correct Observation 5 External Conditions of Correct Observation
407
Apparent Sequence of Events
409
Negative Arguments from NonObservation
411
344
415
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
Method of Variations 2 The Variable and the Variant 3 Measurement of the Variable 4 Maintenance of Similar Conditions
443
Collective Experiments
446
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
305
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
501
CHAPTER XXIII
504
Requisites of a good Hypothesis
510
Possibility of Deductive Reasoning 511
511
Consistency with the Laws of Nature
514
Conformity with Facts
516
Experimentum Crucis
518
Descriptive Hypotheses
522
525
526
Accordance of Quantitative Theories
551
Empirical Measurements
552
Quantities indicated by Theory but Empirically Measured
553
Accordance of Measurements of Astronomical Distances 4 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
Agreement of Distinct Modes of Measurement 11 Residual Phenomena
564
55
569
CHARACTER OF THE EXPERIMENTALIST
574
Character of the Experimentalist 2 Error of the Baconian Method
581
Candour and Courage of the Philosophic Mind
586
The Philosophic Character of Faraday
587
Reservation of Judgment
592
SECTION PAGE 1 Generalisation
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
346
620
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
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
Correlation of Properties
681
350
684
Classification in Crystallography
685
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 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
149
765
Conclusion
766
57
772
INDEX
773
59
774
67
775
68
776
P 312
777
74
780
315
782
396
783
333
785
447

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Seite 458 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Seite 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.
Seite 484 - Whatever phenomenon varies in any manner, whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation.
Seite 308 - Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external...
Seite 592 - ... says the same scientist; and further quotes the noble words of Faraday —"occasionally, and frequently the exercise of the judgment ought to end in absolute reservation. It may be very distasteful and a great fatigue to suspend a conclusion, but as we are not infallible, so we ought to be cautious.
Seite 758 - ... recorded, vows unredeemed, promises unfulfilled, perpetuating in the united movements of each particle, the testimony of man's changeful will.
Seite 308 - 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.
Seite xxxi - I have very imperfectly succeeded in expressing my strong conviction that before a rigorous logical scrutiny the Eeign of Law will prove to be an unverified hypothesis, the Uniformity of Nature an ambiguous expression, the certainty of our scientific inferences to a great extent a delusion.
Seite 126 - That it is the glory of God to conceal a thing, but the glory of a king to search it out.
Seite 621 - Each Seed includes a Plant: that Plant, again, Has other Seeds, which other Plants contain: Those other Plants have all their Seeds; and Those, More Plants, again, successively inclose. Thus, ev'ry single Berry that we find, Has, really, in itself whole Forests of its Kind, Empire and Wealth one Acorn may dispense, By Fleets to sail a thousand Ages hence: Each Myrtle-Seed includes a thousand Groves, Where future Bards may warble forth their Loves.

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