Fundamental Nomic Vagueness

TL;DR

This paper explores the concept of fundamental nomic vagueness, where some laws of nature are inherently vague, affecting the expressibility of physical theories and using the Past Hypothesis as a case study.

Contribution

It introduces the idea of fundamental nomic vagueness, characterizes its features, and proposes a quantum theory of time's arrow to resolve related philosophical dilemmas.

Findings

Vague fundamental laws admit borderline lawful worlds.

Such vagueness prevents complete mathematical expressibility of physical theories.

A new quantum theory of time's arrow dissolves the dilemma between vagueness and arbitrariness.

Abstract

If there are fundamental laws of nature, can they fail to be exact? In this paper, I consider the possibility that some fundamental laws are vague. I call this phenomenon 'fundamental nomic vagueness.' I characterize fundamental nomic vagueness as the existence of borderline lawful worlds and the presence of several other accompanying features. Under certain assumptions, such vagueness prevents the fundamental physical theory from being completely expressible in the mathematical language. Moreover, I suggest that such vagueness can be regarded as 'vagueness in the world.' For a case study, we turn to the Past Hypothesis, a postulate that (partially) explains the direction of time in our world. We have reasons to take it seriously as a candidate fundamental law of nature. Yet it is vague: it admits borderline (nomologically) possible worlds. An exact version would lead to an untraceable arbitrariness absent in any other fundamental laws. However, the dilemma between fundamental nomic vagueness and untraceable arbitrariness is dissolved in a new quantum theory of time's arrow.