The Logic of Reliable Inquiry

by Kevin T. Kelly

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. This approach answers such important questions as whether there are computable methods more reliable than Bayesian updating or Popper's method of conjectures and refutations. Finally, Kelly clarifies the relationship between the resulting framework and other standard issues in the philosophy of science, such as probability, causation, and relativism. His work is a major contribution to the literature and will be essential reading for scientists, logicians, and philosophers

Product Details

ISBN-13:	9780195091953
Publisher:	Oxford University Press
Publication date:	01/04/1996
Series:	Logic and Computation in Philosophy
Edition description:	New Edition
Pages:	448
Product dimensions:	9.27(w) x 6.30(h) x 1.38(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