The Logic of Reliable InquiryThere 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 |
Contents
| 3 | |
| 11 | |
3 The Demons of Passive Observation | 38 |
4 Topology and Ideal Hypothesis Assessment | 74 |
5 Reducibility and the Game of Science | 121 |
6 The Demons of Computability | 138 |
7 Computers in Search of the Truth | 158 |
8 So Much Time Such Little Brains | 190 |
11 Prediction | 260 |
12 Inquiry Concerning FirstOrder Theories | 269 |
13 Probability and Reliability | 302 |
14 Experiment and Causal Inference | 347 |
15 Relativism and Reliability | 376 |
16 Closing Conversation | 398 |
References | 413 |
| 419 | |
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Common terms and phrases
arbitrary arithmetical hierarchy assumptions background knowledge Baire space Borel hierarchy C₁ certainty given chapter characterization clopen sets closed sets computationally bounded conjecture convergence correct hypotheses countable additivity data stream data-minimal datum decidable with certainty define demonic argument denote discovery empirical entails enumeration example fans Figure finite sequence finitely additive given K global underdetermination H is decidable h is verifiable hence hypothesis identifiable inductive problem infinite infinite divisibility initial segment input inquiry learning-theoretic Learnio lemma lh(e limit given limiting relative frequency logical reliability manipulation mind changes starting natural numbers notion open set output paradigm Philo possible prediction primitive recursive primitive recursive functions probabilistic probability measure propensities quantifier recursive function refutable with certainty relation relativism reliabilism result scientist sense skepticism solvable stabilizes stage subset Suppose theorem theory topological truth Turing machine variables verifiable with certainty verifies h