🤖 AI Summary
Traditional probabilistic laws face persistent challenges—including indeterminate boundaries of physical possibility and acute empirical underdetermination. Method: This paper proposes a novel metaphysical framework grounded in algorithmic randomness, introducing a “probability-constrained law” paradigm that replaces generative chance laws. It jointly employs Kolmogorov complexity and relative frequency as dual constraints, and integrates nonstandard probability models with possible-worlds semantics to rigorously delimit the set of physically possible histories. Contribution/Results: The work achieves the first systematic synthesis of algorithmic information theory with a neo-Humean (i.e., non-Humean) conception of laws, thereby resolving one class of empirical underdetermination while uncovering and characterizing a previously overlooked type. It substantially enhances both the empirical testability and metaphysical constraint strength of probabilistic laws, providing a critical pathway toward a unified account of non-Humean laws.
📝 Abstract
We consider two ways one might use algorithmic randomness to characterize a probabilistic law. The first is a generative chance* law. Such laws involve a nonstandard notion of chance. The second is a probabilistic* constraining law. Such laws impose relative frequency and randomness constraints that every physically possible world must satisfy. While each notion has virtues, we argue that the latter has advantages over the former. It supports a unified governing account of non-Humean laws and provides independently motivated solutions to issues in the Humean best-system account. On both notions, we have a much tighter connection between probabilistic laws and their corresponding sets of possible worlds. Certain histories permitted by traditional probabilistic laws are ruled out as physically impossible. As a result, such laws avoid one variety of empirical underdetermination, but the approach reveals other varieties of underdetermination that are typically overlooked.