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The Logic of Reliable Inquiry : Logic and Computation in Philosophy - Kevin T. Kelly

The Logic of Reliable Inquiry

Logic and Computation in Philosophy

Hardcover Published: 4th January 1996
ISBN: 9780195091953
Number Of Pages: 448

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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.

Introductionp. 3
Reliable Inquiryp. 11
Background Assumptionsp. 11
Methods and Data Streamsp. 11
Data Protocolsp. 14
Truth and Global Underdeterminationp. 16
The Philosophy of Global Underdeterminationp. 19
The Philosophy of Local Underdeterminationp. 24
Scientific Realism, Probability, and Subjunctivesp. 30
The Logic of Reliable Inquiryp. 35
The Demons of Passive Observationp. 38
Introductionp. 38
Decidability with a Deadlinep. 42
Decidability, Verifiability, and Refutability with Certaintyp. 48
Verification, Refutation, and Decision in the Limitp. 51
Decision with n Mind Changesp. 64
Gradual Verification, Refutation, and Decisionp. 66
Optimal Background Assumptionsp. 69
Exercisesp. 71
Topology and Ideal Hypothesis Assessmentp. 74
Introductionp. 74
Basic Topological Conceptsp. 74
The Baire Spacep. 78
Restricted Topological Spacesp. 83
A Characterization of Bounded Sample Decidabilityp. 83
Characterizations of Certain Assessmentp. 85
Characterizations of Limiting Assessmentp. 88
Efficient Data Usep. 96
A Characterization of n-Mind-Change Decidabilityp. 103
A Demon-Oriented Characterization of n-Mind-Change Decidabilityp. 108
Characterizations of Gradual Assessmentp. 113
The Levels of Underdeterminationp. 115
Exercisesp. 117
Reducibility and the Game of Sciencep. 121
Introductionp. 121
Ideal Inductive Methods as Continuous Operators on the Baire Spacep. 122
Assessment as Reductionp. 124
Ideal Transcendental Deductions as Cnt-Completeness Theoremsp. 127
Inductive Demons as Continuous Counterreductionsp. 128
Science as a Limiting Gamep. 130
Exercisesp. 136
The Demons of Computabilityp. 138
Introductionp. 138
Church Meets Humep. 138
Programs as Reliable Methodsp. 140
The Arithmetical Hierarchyp. 143
Uncomputability and Diagonalizationp. 144
The Demons of Uncomputabilityp. 146
Some Disanalogiesp. 155
Exercisesp. 157
Computers in Search of the Truthp. 158
Ideal Epistemology and Computabilityp. 158
Computation as Internalized Inductive Inquiryp. 160
The Arithmetical Hierarchy over the Baire Spacep. 162
Universal Relations and Hierarchy Theoremsp. 165
Characterization Theoremsp. 169
Data-Minimal Computable Methodsp. 173
The Empirical Irony of Cognitive Sciencep. 175
The Computable Assessment of Uncomputable Theoriesp. 176
Ideal Norms and Computational Disastersp. 183
Computable Inquiryp. 186
Exercisesp. 187
So Much Time, Such Little Brainsp. 190
Introductionp. 190
Finite State Automatap. 191
Regular Setsp. 193
Scientific Automatap. 194
Scientific Automata and Certaintyp. 194
Scientific Automata in the Limitp. 195
Limiting Regular Expressionsp. 203
[omega]-Expressionsp. 206
The Inductive Power of Indeterminismp. 208
Primitive Recursionp. 212
The Empirical Irony of Cognitive Science Revisitedp. 214
Exercisesp. 216
The Logic of Ideal Discoveryp. 217
Introductionp. 217
Basic Definitionsp. 219
Assessment as Discoveryp. 222
Conjectures and Refutationsp. 222
A Complete Architecture for Discoveryp. 226
Data-Minimal Limiting Discoveryp. 230
Discovery with Bounded Mind Changesp. 233
A Characterization of Almost Stable Identification in the Limitp. 234
Unstable Identification in the Limitp. 240
Gradual Identificationp. 241
Exercisesp. 244
Computerized Discoveryp. 246
Introductionp. 246
Computable Hypothesis Enumerationsp. 246
Characterizationp. 252
Function Identificationp. 253
Cognitive Science Revisitedp. 258
Exercisesp. 259
Predictionp. 260
Introductionp. 260
Ideal Extrapolationp. 260
Computable Extrapolationp. 262
Exercisesp. 267
Inquiry Concerning First-Order Theoriesp. 269
Introductionp. 269
Logical Hypothesis Assessment from Complete, True Datap. 270
Truth and Underdeterminationp. 272
Quantifier Prefix Complexityp. 273
An Examplep. 274
Data Complexityp. 276
Theories and Axiomatizationsp. 287
Theory Discoveryp. 292
Discovery and Vocabularyp. 296
Exercisesp. 301
Probability and Reliabilityp. 302
Introductionp. 302
Conditionalizationp. 303
Probabilistic Reliabilityp. 317
Countable Additivityp. 321
Probabilistic Reliability without Countable Additivityp. 327
Probabilistic Mathematics and Nonprobabilistic Sciencep. 330
Probabilistic Theoriesp. 333
Conclusionp. 337
Proofs of Propositions 13.18 and 13.20p. 338
Exercisesp. 345
Experiment and Causal Inferencep. 347
Introductionp. 347
Systemsp. 348
Causation and Manipulationp. 352
Variable Causationp. 358
Experimental Methodsp. 362
The Course of Experimental Inquiryp. 363
Hypothesis Correctness and Background Knowledgep. 364
Experimental Reliabilityp. 365
Dreaming and the Principle of Plenitudep. 366
Weakened Assumptions and Global Underdeterminationp. 371
Exercisesp. 374
Relativism and Reliabilityp. 376
Introductionp. 376
Relativism, Truth, and Interpersonal Agreementp. 380
Relativistic Reliabilismp. 383
Functional vs. Metaphysical Relativismp. 385
Causal vs. Semantic Relativismp. 386
Acts, Scientists, and Worlds-in-Themselvesp. 387
Transcendental Background Knowledgep. 389
The Course of Relativistic Inquiryp. 389
Relativistic Hypothesis Assessmentp. 390
Relativistic Hypothesis Assessment as Nonrelativistic Discoveryp. 392
Relativistic Theory Discoveryp. 393
Whiggish Relativismp. 396
Exercisesp. 397
Closing Conversationp. 398
Referencesp. 413
Indexp. 419
Index of Symbolsp. 432
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780195091953
ISBN-10: 0195091957
Series: Logic and Computation in Philosophy
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 448
Published: 4th January 1996
Country of Publication: US
Dimensions (cm): 23.55 x 16.0  x 3.51
Weight (kg): 0.85

Earn 343 Qantas Points
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