The Principles of Science: A Treatise on Logic and Scientific Method, 1-2. kötet

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Macmillan, 1874 - 480 oldal

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Tartalomjegyzék

The Logical Abacus
12
Deduction and Induction
13
The Order of Premises
14
Symbolic Expression of Logical Inference
15
The Nature of Inference
16
Expression of Identity and Difference
18
General Formula of Logical Inference
21
The Propagating Power of Identity
24
Anticipations of the Principle of Substitution
25
The Logic of Relatives
27
CHAPTER II
29
SECTION PAGE
33
Propositions
36
Simple Identities
44
Partial Identities
47
Limited Identities
51
Negative Propositions
52
Conversion of Propositions
55
Twofold Interpretation of Propositions
57
CHAPTER IV
59
Immediate Inference
60
Inference with Two Simple Identities
61
Inference with a Simple and a Partial Identity
64
Inference of a Partial from Two Partial Identities
66
On the Ellipsis of Terms in Partial Identities
69
Inference of a Simple from Two Partial Identities
70
Inference of a Limited from Two Partial Identities
71
Miscellaneous Forms of Deductive Inference
72
Fallacies
74
PAGE
77
CHAPTER V
79
Expression of the Alternative Relation 3 Nature of the Alternative Relation
81
Laws of the Disjunctive Relation
85
Symbolic Expression of the Law of Duality
87
Various Forms of the Disjunctive Proposition
89
Inference by Disjunctive Propositions
90
CHAPTER VI
95
95
97
THE INDIRECT METHOD OF INFERENCE
99
PAGE
108
The Indirect Method of Inference
115
INDUCTION
140
Induction
141
OBSERVATION
145
Induction of Simple Identities
146
Induction of Partial Identities
149
Complete Solution of the Inverse or Inductive Logical Pro blem
154
The Inverse Logical Problem involving Three Terms
157
TERMS
161
Distinction between Perfect and Imperfect Induction
164
Transition from Perfect to Imperfect Induction 154 157 164
168
BOOK II
172
The Nature of Number
175
Of Numerical Abstraction
177
Concrete and Abstract Numbers
178
Analogy of Logical and Numerical Terms
180
Principle of Mathematical Inference
183
Reasoning by Inequalities
186
Arithmetical Reasoning
188
Numerically Definite Reasoning
190
183
193
CHAPTER IX
195
Distinction of Combinations and Permutations
200
Calculation of Number of Combinations
204
SECTION PAGE 5 Connexion between the Arithmetical Triangle and the Logical Abecedarium
214
Possible Variety of Nature and
216
Higher Orders of Variety
219
CHAPTER X
224
Fundamental Principles of the Theory
228
Rules for the Calculation of Probabilities
231
Employment of the Logical Abecedarium in questions of Probability
234
Comparison of the Theory with Experience
236
The Arithmetical Triangle
238
Probable Deductive Arguments
239
Difficulties of the Theory
243
CHAPTER XI
250
Various Classes of Inductive Truths
251
The Relation of Cause and Effect
253
Fallacious Use of the Term Cause
254
Distinction of Inductive and Deductive Results
260
On the Grounds of Inductive Inference
262
Illustrations of the Inductive Process
263
206
266
Geometrical Reasoning
268
Discrimination of Certainty and Probability in the Inductive Process
271
CHAPTER XII
276
Principle of the Inverse Method
279
Simple Applications of the Inverse Method
281
Application of the Theory of Probabilities in Astronomy lomy
285
Statement of the General Inverse Problem
289
Simple Illustration of the Inverse Problem
292
General Solution of the Inverse Problem
295
Rules of the Inverse Method
297
Fortuitous Coincidences
302
Summary of the Theory of Inductive Inference
307
METHODS OF MEASUREMENT CHAPTER XIII
313
Division of the Subject
318
The Fallacious Indications of the Senses
320
Complexity of Quantitative Questions
323
The Methods of Accurate Measurement
328
Measuring Instruments
330
The Method of Repetition
336
Measurements by Natural Coincidence
341
Modes of Indirect Measurement
345
Comparative Use of Measuring Instruments
349
Systematic Performance of Measurements
351
The Pendulum
352
Attainable Accuracy of Measurement
354
SECTION
356
CHAPTER XIV
357
Standard Unit of Time 339
359
The Unit of Space and the Bar Standard
365
The Terrestrial Standard
367
Terms
369
Unit of Density
371
Unit of Mass
372
Subsidiary Units
374
Derived Units
375
Provisionally Independent Units
377
Methods of Eliminating Error
391
Several Uses of the Mean Result
416
On the Fictitious Mean or Average Result
422
Determination of the Zero Point by the Method of Means
428
CHAPTER XVII
434
Derivation of the Law of Error from Simple Logical Prin
443
Weighted Observations
449
Method of Least Squares
458
Twofold Meaning of General Names
2
Abstract Terms
3
Substantial Terms
4
Collective Terms
5
Synthesis of Terms
6
Symbolic Expression of the Law of Contradiction
7
Certain Special Conditions of Logical Symbols
8
Abstraction of Indifferent Circumstances
9
EXPERIMENT
22
METHOD OF VARIATIONS
50
CHAPTER XXI
72
101
101
103
103
CHAPTER XXII
105
Discovery of Rational Formulæ
113
Interpolation and Extrapolation
120
Simple Proportional Variation
127
Requisites of a good Hypothesis
138
The Third RequisiteConformity with Facts
146
Descriptive Hypothesis
154
Empirical Knowledge
163
Predicted Discoveries
171
Predictions in other Sciences
178
Facts known only by Theory
185
Accordance of Quantitative Theories and Experiments 189
189
Empirical Measurements 190
190
Quantities indicated by Theory but Empirically Measured 192
192
Explained Results of Measurement 193
193
Quantities determined by Theory and verified by Measurement 194
194
195
195
Quantities determined by Theory and not verified
196
Discordance of Theory and Experiment
198
Accordance of Measurements of Astronomical Distances 201
201
Selection of the best Mode of Measurement 204
204
206
206
Residual Phenomena 212 196 198
215
CHAPTER XXVI
217
Nature of Genius
219
Error of the Baconian Method
220
Freedom of Theorizing
221
The Newtonian Method the True Organum
226
Candour and Courage of the Philosophic Mind
232
The Philosophic Character of Faraday
234
Reservation of Judgment
239
BOOK V
242
Distinction of Generalization and Analogy
244
Two Meanings of Generalization
246
Value of Generalization
248
Comparative Generality of Physical Properties
249
Uniform Properties of all Matter
254
Variable Properties of Matter
258
Extreme Instances of Properties
259
The Detection of Continuity
262
The Law of Continuity
268
Failure of the Law of Continuity
273
Negative Arguments on the Principle of Continui
276
Tendency to Hasty Generalization
278
EXCEPTIONAL PHENOMENA 1 Exceptional Phenomena
306
Imaginary or False Exceptions 3 Apparent but congruent Exceptions 4 Singular Exceptions 5 Divergent Exceptions 6 Accidental Exceptions 7 Novel...
308
Unclassed Exceptions 306 309
309
313
313
316
316
320
320
324
324
328
328
331
331
336
336
338
338
CHAPTER XXX
344
346
346
348
348
351
351
Correlation of Properties
353
153
359
Classification an Inverse and Tentative Operation 8 Symbolic Statement of the Theory of Classification
367
Bifurcate Classification
371
The Five Predicables
375
Summun Genus and Infima Species
379
The Tree of Porphyry Forphyry
381
105
387
Does Abstraction imply Generalization
389
Discovery of Marks or Characteristics
394
Diagnostic Systems of Classification
396
Index Classifications
400
Classification in the Biological Sciences
405
Classification by Types
411
Natural Genera and Species
414
Unique or Exceptional Objects
418
Limits of Classification
421
REFLECTIONS ON THE RESULTS AND LIMITS OF SCIENTIFIC METHOD SECTION PAGE 1 Reflections on the Results and Limits of Scientific...
427
The Meaning of Natural Law 429
429
Infiniteness of the Universe 431
431
The Indeterminate Problem of Creation 433
433
Hierarchy of Natural Laws 436
436
The Ambiguous ExpressionUniformity of Nature 440
440
Possible States of the Universe 444
444
Speculations on the Reconcentration of Energy 446
446
The Divergent Scope for New Discovery 449
449
451
451
The Reign of Law in Mental and Social Phenomena 457
457
The Theory of Evolution 460
460
Possibility of Divine Interference 461
464
Conclusion
466
112
471
353
472
364
473
389
474
394
475
246
477
268
478
418
479

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106. oldal - 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.
360. oldal - Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external...
457. oldal - Veniet tempus quo ista quae nunc latent in lucem dies extrahat et longioris aevi diligentia. Ad inquisitionem tantorum aetas una non sufficit, ut tota caelo vacet ; quid quod tarn paucos annos inter studia ac vitia non aequa portione dividimus?
75. oldal - 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.
235. oldal - I have long held an opinion, almost amounting to conviction, in common I believe with many other lovers of natural knowledge, that the various forms under which the forces of matter are made manifest have one common origin; or, in other words, are so directly related and mutually dependent, that they are convertible, as it were, one into another, and possess equivalents of power in their action.
469. oldal - Now among the most unquestionable rules of Scientific Method is that first law that whatever phenomenon is, is. We must ignore no existence whatever ; we may variously interpret or explain its meaning and origin, but if a phenomenon does exist it demands some kind of explanation.
222. oldal - The world little knows how many of the thoughts and theories which have passed through the mind of a scientific investigator have been crushed in silence and secrecy by his own severe criticism and adverse examination; that in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realized.
361. oldal - 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.
241. oldal - 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 favourite 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 he adds industry, he may indeed hope to walk within the veil of the temple of nature.
145. oldal - That it is the glory of God to conceal a thing, but the glory of a king to search it out.

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