Embracing undecidability: Cognitive needs and theory evaluation

TL;DR

This paper discusses the inherent limits of knowledge imposed by logical and physical undecidability, emphasizing the importance of accepting these limits in scientific theory evaluation and understanding.

Contribution

It highlights the significance of undecidability in scientific theories and advocates for acknowledging cognitive and formal system limitations in evaluating physical theories.

Findings

Undecidability affects the evaluation of physical theories.

Scientists often behave as if they can know the truth despite limits.

Acceptance of limits can prevent cognitive mistakes in science.

Abstract

There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things get even harder. We want to compare the results of our mathematical theories to observations, and that means the use of inductive methods. While we can demonstrate how an ideal probabilistic induction should work, the requirements of such a method include a few infinities. Furthermore, it would not be even enough to be able to compute those methods and obtain predictions. There are cases where underdeterminacy might be unavoidable, such as the interpretation of quantum mechanics or the current status of string theory. Despite that, scientists still behave as if they were able to know the truth. As it becomes clear that such behavior can cause severe cognitive mistakes, the need to accept our limits, both our natural human limits and the limits of the tools we have created, become apparent. This essay will discuss how we must accept that knowledge is almost only limited to formal systems. Moreover, even in those, there will always be undecidable propositions. We will also see how those questions influence the evaluation of current theories in physics.