## Induction, Algorithmic Learning Theory, and PhilosophyMichèle Friend, Norma B. Goethe, Valentina S. Harizanov The idea of the present volume emerged in 2002 from a series of talks by Frank Stephan in 2002, and John Case in 2003, on developments of algorithmic learning theory. These talks took place in the Mathematics Department at the George Washington University. Following the talks, ValentinaHarizanovandMichèleFriendraised thepossibility ofanexchange of ideas concerning algorithmic learning theory. In particular, this was to be a mutually bene?cial exchange between philosophers, mathematicians and computer scientists. Harizanov and Friend sent out invitations for contributions and invited Norma Goethe to join the editing team. The Dilthey Fellowship of the George Washington University provided resources over the summer of 2003 to enable the editors and some of the contributors to meet in Oviedo (Spain) at the 12th International Congress of Logic, Methodology and Philosophy of Science. The editing work proceeded from there. The idea behind the volume is to rekindle interdisciplinary discussion. Algorithmic learning theory has been around for nearly half a century. The immediate beginnings can be traced back to E.M. Gold’s papers: “Limiting recursion” (1965) and “Language identi?cation in the limit” (1967). However, from a logical point of view, the deeper roots of the learni- theoretic analysis go back to Carnap’s work on inductive logic (1950, 1952). |

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### Contents

1 | |

INDUCTIVE INFERENCE SYSTEMS FOR LEARNING CLASSES OF ALGORITHMICALLY GENERATED SETS AND STRUCTURES | 27 |

DEDUCTION INDUCTION AND BEYOND IN PARAMETRIC LOGIC | 55 |

HOW SIMPLICITY HELPS YOU FIND THE TRUTH WITHOUT POINTING AT IT | 111 |

INDUCTION OVER THE CONTINUUM | 144 |

LOGICALLY RELIABLE INDUCTIVE INFERENCE | 157 |

SOME PHILOSOPHICAL CONCERNS ABOUT THE CONFIDENCE IN CONFIDENT LEARNING | 179 |

### Other editions - View all

Induction, Algorithmic Learning Theory, and Philosophy Michèle Friend,Norma B. Goethe,Valentina S. Harizanov No preview available - 2007 |

Induction, Algorithmic Learning Theory, and Philosophy Michèle Friend,Norma B. Goethe,Valentina S. Harizanov No preview available - 2007 |

Induction, Algorithmic Learning Theory, and Philosophy Michèle Friend,Norma B Goethe,Valentina S. Harizanov No preview available - 2010 |

### Common terms and phrases

algorithmic learning theory anomaly answer argument assumptions Bayesian Borel Borel sets bound c.e. sets Carnap’s Ce(k classical compactness complexity computable functions concept confident learning conjecture consider convergence correct countable deductive consequence defined Definition empirical enumeration equivalent EX-learnable from text example first-order logic forcible formal learning theory given Glymour grammar Harizanov Hence hierarchy Hume’s hypothesis ideals identifier inductive inference inductive reasoning infinite informant input stream inquiry Kelly language learnable learner learning function lemma limit logical consequence marbles mathematical method methodological mind changes natural numbers nonnull ordinal notion of logical Ockham’s razor output parameters parametric logic philosophical philosophy of science positively classifiable possible knowledge base presupposition Proof Proposition Putnam question ravens are black refuted regress reliable retractions scientific scientist sentences sequence solution stalwart Stephan strategy structures subset Theorem true truth Turing machine uniformitarianism uniquely simplest vector space well-formed formula