Induction, Algorithmic Learning Theory, and Philosophy

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Michèle Friend, Norma B. Goethe, Valentina S. Harizanov
Springer Science & Business Media, Aug 21, 2007 - Philosophy - 290 pages
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

INTRODUCTION TO THE PHILOSOPHY AND MATHEMATICS OF ALGORITHMIC LEARNING THEORY
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
HOW TO DO THINGS WITH AN INFINITE REGRESS
198
TRADEOFFS
219
TWO WAYS OF THINKING ABOUT INDUCTION
233
BETWEEN HISTORY AND LOGIC
259
Index
279
Copyright

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