Uncertainty, incompleteness, chance, and design

TL;DR

This paper discusses the fundamental limitations of scientific knowledge due to indeterminacy and undecidability, suggesting that questions about finality in nature are beyond scientific resolution.

Contribution

It offers a philosophical reflection on how physical indeterminacy and mathematical incompleteness challenge the scope of scientific inquiry.

Findings

Physical reality is intrinsically undetermined in many respects.

Mathematical truths can be undecidable, affecting our understanding of randomness.

Questions of finality in nature are outside scientific scope.

Abstract

The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincar\'e's nonlinear dynamics and Heisenberg's uncertainty principle leads to a world picture where physical reality is, in many respects, intrinsically undetermined. On the other hand, G\"odel's incompleteness theorems reveal us the existence of mathematical truths that cannot be demonstrated. More recently, Chaitin has proved that, from the incompleteness theorems, it follows that the random character of a given mathematical sequence cannot be proved in general (it is 'undecidable'). I reflect here on the consequences derived from the indeterminacy of the future and the undecidability of randomness, concluding that the question of the presence or absence of finality in nature is fundamentally outside the scope of the scientific method.