Induction, Algorithmic Learning Theory, and Philosophy

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).

Only book to combine philosophy essays with technical essays on algorithmic learning theory Invaluable for the reflective computer scientist or the mathematician/logician interested in modelling learning Deepens the argument and debate about mathematically modelling learning No-one with a serious interest in the philosophy of science can afford to ignore this development Refracts the classical problem of induction into a spectrum of new insights and questions

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This is the first book to collect essays from philosophers, mathematicians and computer scientists working at the exciting interface of algorithmic learning theory and the epistemology of science and inductive inference. Readable, introductory essays provide engaging surveys of different, complementary, and mutually inspiring approaches to the topic, both from a philosophical and a mathematical viewpoint.

Building upon this base, subsequent papers present novel extensions of algorithmic learning theory as well as bold, new applications to traditional issues in epistemology and the philosophy of science. The volume is vital reading for students and researchers seeking a fresh, truth-directed approach to the philosophy of science and induction, epistemology, logic, and statistics.

Contenu
to the Philosophy and Mathematics of Algorithmic Learning Theory.- to the Philosophy and Mathematics of Algorithmic Learning Theory.- Technical Papers.- Inductive Inference Systems for Learning Classes of Algorithmically Generated Sets and Structures.- Deduction, Induction, and beyond in Parametric Logic.- How Simplicity Helps You Find the Truth without Pointing at it.- Induction over the Continuum.- Philosophy Papers.- Logically Reliable Inductive Inference.- Some Philosophical Concerns about the Confidence in 'Confident Learning'.- How to Do Things with an Infinite Regress.- Trade-Offs.- Two Ways of Thinking about Induction.- Between History and Logic.