A Dichotomy in Machine Knowledge

TL;DR

This paper demonstrates a fundamental limitation in machines with basic logical and knowledge axioms, showing they cannot simultaneously know their factivity and their own G"odel number.

Contribution

It establishes a dichotomy in machine knowledge, revealing a theoretical boundary in self-knowledge capabilities.

Findings

Machines cannot know both their factivity and their G"odel number simultaneously.

The result is a fundamental limitation in formal models of self-knowledge.

Highlights a logical boundary in knowledge systems.

Abstract

We show that a machine, which knows basic logic and arithmetic and basic axioms of knowledge, and which is factive (knows nothing false), can either know that it is factive, or know its own Goedel number, but not both.