Undecidability and unpredictability: not limitations, but triumphs of science

TL;DR

The paper challenges the view that undecidability and unpredictability are fundamental limitations of science, proposing instead that they reflect the nature of real patterns and structure, leading to a more optimistic scientific outlook.

Contribution

It introduces a structural notion of 'real patterns' as fundamental, replacing traditional metaphysical views and reframing undecidability as undifferentiation of structure rather than limitation.

Findings

Undecidability reflects structural undifferentiation, not epistemic limitations.

Modern physics supports a worldview focusing on patterns over things.

This perspective fosters an optimistic view of scientific knowledge.

Abstract

It is a widespread belief that results like G\"odel's incompleteness theorems or the intrinsic randomness of quantum mechanics represent fundamental limitations to humanity's strive for scientific knowledge. As the argument goes, there are truths that we can never uncover with our scientific methods, hence we should be humble and acknowledge a reality beyond our scientific grasp. Here, I argue that this view is wrong. It originates in a naive form of metaphysics that sees the physical and Platonic worlds as a collection of things with definite properties such that all answers to all possible questions exist ontologically somehow, but are epistemically inaccessible. This view is not only a priori philosophically questionable, but also at odds with modern physics. Hence, I argue to replace this perspective by a worldview in which a structural notion of `real patterns', not `things' are regarded as fundamental. Instead of a limitation of what we can know, undecidability and unpredictability then become mere statements of undifferentiation of structure. This gives us a notion of realism that is better informed by modern physics, and an optimistic outlook on what we can achieve: we can know what there is to know, despite the apparent barriers of undecidability results.