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 nomic vagueness. I propose to characterize nomic vagueness as the
existence of borderline lawful worlds. The existence of nomic vagueness raises
interesting questions about the mathematical expressibility and metaphysical
status of fundamental laws.
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 nomic vagueness and untraceable arbitrariness is dissolved in a new
quantum theory of time’s arrow
