Uncomputability: the problem of induction internalized

  title={Uncomputability: the problem of induction internalized},
  author={Kevin T. Kelly},
  journal={Theor. Comput. Sci.},

Ockham's razor, empirical complexity, and truth-finding efficiency

Ockham’s Razor, Empirical Complexity, and Truth-finding Efficiency

The nature of empirical simplicity and its relationship to scientific truth are long-standing puzzles. In this paper, empirical simplicity is explicated in terms of empirical effects, which are defined

Ockham's Razor, Truth, and Information

How to Do Things with an Infinite Regress

  • Kevin T. Kelly
  • Philosophy
    Induction, Algorithmic Learning Theory, and Philosophy
  • 2007
This paper explains how to assess the methodological worth of a methodological regress by solving for the strongest sense of single-method performance that can be achieved given that such a regress exists.

How To Do Things With an Infinte Regress

Scientific methods may be viewed as procedures for converging to the true answer to a given empirical question. Typically, such methods converge to the truth only if certain empirical presuppositions

Mechanizing Induction

The Foundations of Solomonoff Prediction

R.J. Solomonoff’s theory of Prediction assembles notions from information theory, confirmation theory and computability theory into the specification of a supposedly all-encompassing objective method

A New Solution to the Puzzle of Simplicity

It is demonstrated that always choosing the simplest theory compatible with experience, and hanging onto it while it remains simplest, is both necessary and sufficient for efficiency.

How Simplicity Helps You Find the Truth without Pointing at it

  • Kevin T. Kelly
  • Philosophy
    Induction, Algorithmic Learning Theory, and Philosophy
  • 2007
It is demonstrated, for a broad range of cases, that the Ockham strategy of favoring the simplest hypothesis, together with the strategy of never dropping the simplest hypotheses until it is no longer simplest, uniquely minimizes reversals of opinion and the times at which the reversals occur prior to convergence to the truth.

Introduction to the Philosophy and Mathematics of Algorithmic Learning Theory

The purpose of this volume is to bolster discussion among mathematicians and philosophers, both to encourage the development of new and more philosophically relevant theoretical results and to bring existing results to a wider philosophical audience.



Efficient Convergence Implies Ockman's Razor

This note argues, on the basis of computational learning theory, that a fixed simplicity bias is necessary if inquiry is to converge to the rightanswer efficiently, whatever the right answer might be.

Church’s Thesis and Hume’s Problem

We argue that uncomputability and classical scepticism are both reflections of inductive underdetermination, so that Church’s thesis and Hume’s problem ought to receive equal emphasis in a balanced

Means-Ends Epistemology

  • O. Schulte
  • Philosophy
    The British Journal for the Philosophy of Science
  • 1999
This paper describes the corner-stones of a means-ends approach to the philosophy of inductive inference, establishes a hierarchy of means- ends notions of empirical success, and discusses a number of issues, results and applications of means.

On the Role of Procrastination in Machine Learning

Hierarchies of classes of learnable phenomena (represented by sets of recursive functions) isomorphic to the structure of the constructive ordinals are revealed, indicating a potential advantage of procrastination as a learning technique.

An Incorrect Theorem

In the fourth edition of Hilbert-Ackermann's Grundzüge der Theoretischen Logik (Springer-Verlag: Berlin-Göttingen-Heidelberg 1959) the following assertion is “proved” (p. 131): Ein Ausdruck, der

Elements of Scientific Inquiry

A Priori Knowledge

A44 priori" has been a popular term with philosophers at least A since Kant distinguished between a priori and a posteriori knowledge. Yet, despite the frequency with which it has been used in

Limiting recursion

  • E. Gold
  • Mathematics
    Journal of Symbolic Logic
  • 1965
A class of problems is called decidable if there is an algorithm which will give the answer to any problem of the class after a finite length of time. The purpose of this paper is to discuss the

The Logic of Reliable Inquiry

This chapter discusses Reliable Inquiry, Continuity, Reducibility, and the Game of Science, which aims to clarify the role of faith in the development of science.

Computability: An Introduction to Recursive Function Theory

The author explains how theorems such as Godel's incompleteness theorem and the second recursion theorem can be applied to the problem of computable functions.