Physics and science: the art of taking a stance about undecidable questions

TL;DR

This paper explores the historical and philosophical significance of undecidable questions in science, arguing that addressing such questions is integral to scientific progress and involves a form of invalid induction.

Contribution

It offers a historical and philosophical analysis showing that resolving undecidable questions is a core aspect of scientific practice and discusses implications for mathematics and philosophy of mind.

Findings

Undecidability is a long-standing aspect of scientific inquiry.

Resolving undecidable questions often involves invalid induction.

The role of mathematics and philosophy in addressing undecidability is significant.

Abstract

In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this existential crisis may appear to be new, we develop the view that it has a long history and that, in fact, providing closure to undecidable questions is a defining feature of scientific practice and development. We support our claim with historical and contemporary examples and suggest that the crux of many instances of undecidability in science is a form of invalid induction. Finally, we use our thesis to discuss the place of mathematics in the sciences, and to assess whether or not certain perspectives in the philosophy of mind might provide us with closure.