Philosophical Applications of Computational Learning Theory: Chomskyan Innateness and Occam's Razor Contents Preface V 1 Introduction to Computational Learning Theory 1 2 Application to Language Learning 19 3 Kolmogorov Complexity and Simplicity 45

List of Symbols 97 Bibliography 99 Index of Names 107 Index of Subjects 109 iv CONTENTS Preface What is learning? Learning is what makes us adapt to changes and threats, and what allows us to cope with a world in ux. In short, learning is what keeps us alive. Learning has strong links to almost any other topic in philosophy: scientiic inference, knowledge, truth, reasoning (logic), language, anthropology, behaviour (ethics), good taste (aesthetics), and so on. Accordingly, it can be seen as one of the quintessential philosophical topics|an appropriate topic for a graduation thesis! Much can be said about learning, too much to t in a single thesis. Therefore this thesis is restricted in scope, dealing only with computational learning theory (often abbreviated to COLT). Learning seems so simple: we do it every day, often without noticing it. Nevertheless, it is obvious that some fairly complex mechanisms must be at work when we learn. COLT is the branch of Artiicial Intelligence that deals with the computational properties and limitations of such mechanisms. The eld can be seen as the intersection of Machine Learning and complexity theory. COLT is a very young eld|the publication of Valiant's seminal paper in 1984 may be seen as its birth|and it appears that virtually none of its many interesting results are known to philosophers. Some philosophical work has referred to complexity theory (for instance Che86]) and some has referred to Machine Learning (for instance Tha90]), but as far as I know, thus far no philosophical use has been made of the results that have sprung from COLT. For instance, at the time of writing of this thesis, the Philosopher's Index, a database containing most major publications in philosophical journals or books, contains no entries whatsoever that refer to COLT or to its main model, the model of PAC learning; there is hardly any reference to Kolmogorov complexity, either. Stuart Russell devotes two pages to PAC learning Rus91, pp. 43{44] and James McAllister devotes one page to Kolmogorov complexity as a quantitative measure of simplicity McA96, pp. 119{120], but both do not provide more than a sketchy and superrcial explanation. As its title already indicates, the present thesis tries to make contact between COLT and philosophy. The aim of the thesis is threefold. The rst and most shallow goal is to obtain a degree in philosophy for its author. The second goal is to take a …