## Elements of Scientific InquiryOne influential view of science focuses on the credibility that scientists attach to alternative theories and on the evolution of these credibilities under the impact of data. Interpreting credibility as probability leads to the Bayesian analysis of inquiry, which has helped us to understand diverse aspects of scientific practice. Eric Martin and Daniel N. Osherson take as their starting point a different set of intuitions about the variables to be retained in a model of inquiry. They present a theory of inductive logic that is built from the tools of logic and model theory. Their aim is to extend the mathematics of Formal Learning Theory to a more general setting and to provide a more accurate image of empirical inquiry. In particular, their theory integrates recent ideas in the theory of rational belief change. The formal results of their study illuminate aspects of scientific inquiry that are not covered by the Bayesian approach. Exercises appear throughout the text; solutions are provided in an appendix. |

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### Contents

A Numerical Paradigm | 17 |

A FirstOrder Framework for Inquiry | 61 |

Inquiry via Belief Revision | 129 |

A Solutions to Exercises for Chapter 1 | 183 |

B Solutions to Exercises for Chapter 2 | 189 |

Solutions to Exercises for Chapter 3 | 227 |

Solutions to Exercises for Chapter 4 | 243 |

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### Common terms and phrases

a e SEQ assignment h B C Lform Bayesian belief revision binary predicate closure operator cofinitely computable function computable scientist computably solvable consistent contraction function contradiction converges countable substructures define scientist definition denote easy to verify elementarily equivalent environment e finite first-order paradigm following properties formulas full assignment functional languages given Hence implies infinite inquiry L-score least element Lemma length(a Let a e SEQ Let environment Let scientist maxichoice MOD(T U nonempty numerical paradigm order isomorphic Osherson partially isomorphic pow(N problem of form proposition Proposition 31 q Solution r e SEQ range(a range(ct recursive function revision-based scientists satisfy scientist solves scientist that solves sequence Solution to Exercise solvable problem stably strict total order stringent revision function subset suffices to show Suppose that scientist Suppose that Sym Theorem tip-off unary function underlies a computable