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9780195091953
The Logic of Reliable Inquiry available in Hardcover
- ISBN-10:
- 0195091957
- ISBN-13:
- 9780195091953
- Pub. Date:
- 06/28/1997
- Publisher:
- Oxford University Press, USA
- ISBN-10:
- 0195091957
- ISBN-13:
- 9780195091953
- Pub. Date:
- 06/28/1997
- Publisher:
- Oxford University Press, USA
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Overview
There are many proposed aims for scientific inquiry - to explain or predict events, to confirm or falsify hypotheses, or to find hypotheses that cohere with our other beliefs in some logical or probabilistic sense. This book is devoted to a different proposal - that the logical structure of the scientist's method should guarantee eventual arrival at the truth, given the scientist's background assumptions. Interest in this methodological property, called "logical reliability", stems from formal learning theory, which draws its insights not from the theory of probability, but from the theory of computability. Kelly first offers an accessible explanation of formal learning theory, then goes on to develop and explore a systematic framework in which various standard learning-theoretic results can be seen as special cases of simpler and more general considerations. Finally, Kelly clarifies the relationship between the resulting framework and other standard issues in the philosophy of science, such as probability, causation, and relativism. Extensively illustrated with figures by the author, The Logic of Reliable Inquiry assumes only introductory knowledge of basic logic and computability theory. It is a major contribution to the literature and will be essential reading for scientists, statiticians, psychologists, linguists, logicians, and philosophers.
Product Details
ISBN-13: | 9780195091953 |
---|---|
Publisher: | Oxford University Press, USA |
Publication date: | 06/28/1997 |
Series: | Logic and Computation in Philosophy Series |
Edition description: | New Edition |
Pages: | 448 |
Product dimensions: | 6.50(w) x 9.56(h) x 1.14(d) |
Lexile: | 1440L (what's this?) |
Table of Contents
1. | Introduction | 3 |
2. | Reliable Inquiry | 11 |
1. | Background Assumptions | 11 |
2. | Methods and Data Streams | 11 |
3. | Data Protocols | 14 |
4. | Truth and Global Underdetermination | 16 |
5. | The Philosophy of Global Underdetermination | 19 |
6. | The Philosophy of Local Underdetermination | 24 |
7. | Scientific Realism, Probability, and Subjunctives | 30 |
8. | The Logic of Reliable Inquiry | 35 |
3. | The Demons of Passive Observation | 38 |
1. | Introduction | 38 |
2. | Decidability with a Deadline | 42 |
3. | Decidability, Verifiability, and Refutability with Certainty | 48 |
4. | Verification, Refutation, and Decision in the Limit | 51 |
5. | Decision with n Mind Changes | 64 |
6. | Gradual Verification, Refutation, and Decision | 66 |
7. | Optimal Background Assumptions | 69 |
8. | Exercises | 71 |
4. | Topology and Ideal Hypothesis Assessment | 74 |
1. | Introduction | 74 |
2. | Basic Topological Concepts | 74 |
3. | The Baire Space | 78 |
4. | Restricted Topological Spaces | 83 |
5. | A Characterization of Bounded Sample Decidability | 83 |
6. | Characterizations of Certain Assessment | 85 |
7. | Characterizations of Limiting Assessment | 88 |
8. | Efficient Data Use | 96 |
9. | A Characterization of n-Mind-Change Decidability | 103 |
10. | A Demon-Oriented Characterization of n-Mind-Change Decidability | 108 |
11. | Characterizations of Gradual Assessment | 113 |
12. | The Levels of Underdetermination | 115 |
13. | Exercises | 117 |
5. | Reducibility and the Game of Science | 121 |
1. | Introduction | 121 |
2. | Ideal Inductive Methods as Continuous Operators on the Baire Space | 122 |
3. | Assessment as Reduction | 124 |
4. | Ideal Transcendental Deductions as Cnt-Completeness Theorems | 127 |
5. | Inductive Demons as Continuous Counterreductions | 128 |
6. | Science as a Limiting Game | 130 |
7. | Exercises | 136 |
6. | The Demons of Computability | 138 |
1. | Introduction | 138 |
2. | Church Meets Hume | 138 |
3. | Programs as Reliable Methods | 140 |
4. | The Arithmetical Hierarchy | 143 |
5. | Uncomputability and Diagonalization | 144 |
6. | The Demons of Uncomputability | 146 |
7. | Some Disanalogies | 155 |
8. | Exercises | 157 |
7. | Computers in Search of the Truth | 158 |
1. | Ideal Epistemology and Computability | 158 |
2. | Computation as Internalized Inductive Inquiry | 160 |
3. | The Arithmetical Hierarchy over the Baire Space | 162 |
4. | Universal Relations and Hierarchy Theorems | 165 |
5. | Characterization Theorems | 169 |
6. | Data-Minimal Computable Methods | 173 |
7. | The Empirical Irony of Cognitive Science | 175 |
8. | The Computable Assessment of Uncomputable Theories | 176 |
9. | Ideal Norms and Computational Disasters | 183 |
10. | Computable Inquiry | 186 |
11. | Exercises | 187 |
8. | So Much Time, Such Little Brains | 190 |
1. | Introduction | 190 |
2. | Finite State Automata | 191 |
3. | Regular Sets | 193 |
4. | Scientific Automata | 194 |
5. | Scientific Automata and Certainty | 194 |
6. | Scientific Automata in the Limit | 195 |
7. | Limiting Regular Expressions | 203 |
8. | [omega]-Expressions | 206 |
9. | The Inductive Power of Indeterminism | 208 |
10. | Primitive Recursion | 212 |
11. | The Empirical Irony of Cognitive Science Revisited | 214 |
12. | Exercises | 216 |
9. | The Logic of Ideal Discovery | 217 |
1. | Introduction | 217 |
2. | Basic Definitions | 219 |
3. | Assessment as Discovery | 222 |
4. | Conjectures and Refutations | 222 |
5. | A Complete Architecture for Discovery | 226 |
6. | Data-Minimal Limiting Discovery | 230 |
7. | Discovery with Bounded Mind Changes | 233 |
8. | A Characterization of Almost Stable Identification in the Limit | 234 |
9. | Unstable Identification in the Limit | 240 |
10. | Gradual Identification | 241 |
11. | Exercises | 244 |
10. | Computerized Discovery | 246 |
1. | Introduction | 246 |
2. | Computable Hypothesis Enumerations | 246 |
3. | Characterization | 252 |
4. | Function Identification | 253 |
5. | Cognitive Science Revisited | 258 |
6. | Exercises | 259 |
11. | Prediction | 260 |
1. | Introduction | 260 |
2. | Ideal Extrapolation | 260 |
3. | Computable Extrapolation | 262 |
4. | Exercises | 267 |
12. | Inquiry Concerning First-Order Theories | 269 |
1. | Introduction | 269 |
2. | Logical Hypothesis Assessment from Complete, True Data | 270 |
3. | Truth and Underdetermination | 272 |
4. | Quantifier Prefix Complexity | 273 |
5. | An Example | 274 |
6. | Data Complexity | 276 |
7. | Theories and Axiomatizations | 287 |
8. | Theory Discovery | 292 |
9. | Discovery and Vocabulary | 296 |
10. | Exercises | 301 |
13. | Probability and Reliability | 302 |
1. | Introduction | 302 |
2. | Conditionalization | 303 |
3. | Probabilistic Reliability | 317 |
4. | Countable Additivity | 321 |
5. | Probabilistic Reliability without Countable Additivity | 327 |
6. | Probabilistic Mathematics and Nonprobabilistic Science | 330 |
7. | Probabilistic Theories | 333 |
8. | Conclusion | 337 |
9. | Proofs of Propositions 13.18 and 13.20 | 338 |
10. | Exercises | 345 |
14. | Experiment and Causal Inference | 347 |
1. | Introduction | 347 |
2. | Systems | 348 |
3. | Causation and Manipulation | 352 |
4. | Variable Causation | 358 |
5. | Experimental Methods | 362 |
6. | The Course of Experimental Inquiry | 363 |
7. | Hypothesis Correctness and Background Knowledge | 364 |
8. | Experimental Reliability | 365 |
9. | Dreaming and the Principle of Plenitude | 366 |
10. | Weakened Assumptions and Global Underdetermination | 371 |
11. | Exercises | 374 |
15. | Relativism and Reliability | 376 |
1. | Introduction | 376 |
2. | Relativism, Truth, and Interpersonal Agreement | 380 |
3. | Relativistic Reliabilism | 383 |
4. | Functional vs. Metaphysical Relativism | 385 |
5. | Causal vs. Semantic Relativism | 386 |
6. | Acts, Scientists, and Worlds-in-Themselves | 387 |
7. | Transcendental Background Knowledge | 389 |
8. | The Course of Relativistic Inquiry | 389 |
9. | Relativistic Hypothesis Assessment | 390 |
10. | Relativistic Hypothesis Assessment as Nonrelativistic Discovery | 392 |
11. | Relativistic Theory Discovery | 393 |
12. | Whiggish Relativism | 396 |
13. | Exercises | 397 |
16. | Closing Conversation | 398 |
References | 413 | |
Index | 419 | |
Index of Symbols | 432 |
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