Definability in the Real Universe

TL;DR

This paper explores the logical and computability aspects of the real universe, emphasizing their physical and epistemological significance in understanding the nature of reality.

Contribution

It connects recent developments in logic and computability theory to foundational questions about the real world and our descriptions of it.

Findings

Highlights the relevance of logical definability to physical reality

Bridges concepts in computability with epistemological questions

Provides a philosophical perspective on mathematical foundations

Abstract

Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and computability theory. "If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics lead me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress." - Paul Dirac, 27 November, 1975. In Paul A. M. Dirac Papers, Florida State University Libraries, Tallahassee, Florida, USA, No. 2/29/17.