Kolmogorov Complexity and Information Content

TL;DR

This paper examines the concept of Kolmogorov complexity, clarifying debates about whether program size truly measures a string's information content, addressing criticisms from philosophical and logical perspectives.

Contribution

It provides a detailed analysis of the philosophical and logical issues surrounding Kolmogorov complexity and its interpretation as a measure of information content.

Findings

Clarifies subtle issues in the interpretation of Kolmogorov complexity.

Addresses criticisms from logicians and philosophers.

Reevaluates the objectivity of program-size complexity as information measure.

Abstract

In this paper, we revisit a central concept in Kolmogorov complexity in which one would equate program-size complexity with information content. Despite the fact that Kolmogorov complexity has been widely accepted as an objective measure of the information content of a string, it has been the subject of many criticisms including the fundamental one directed by logicians and philosophers towards the statistical and semantical theories of information, which is about confusing an object and its name. In this paper, we clarify a number of subtle issues that are at the center of this debate.