[Paper Review] Algorithmic Randomness and Probabilistic Laws

Jeffrey A. Barrett, Eddy Keming Chen|arXiv (Cornell University)|Mar 2, 2023

Philosophy and Theoretical Science16 citations

TL;DR

The paper compares two algorithmic-randomness-based notions of probabilistic laws—generative chance* and probabilistic* constraining laws—and argues that the constraining variant offers benefits for non-Humean governance and Humean best-system accounts, while highlighting underdetermination issues.

ABSTRACT

We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a nonstandard notion of chance. The second, a probabilistic* constraining law, impose relative frequency and randomness constraints that every physically possible world must satisfy. The constraining notion removes a major obstacle to a unified governing account of non-Humean laws, on which laws govern by constraining physical possibilities; it also provides independently motivated solutions to familiar problems for the Humean best-system account (the Big Bad Bug and the zero-fit problem). On either approach, probabilistic laws are tied more tightly to corresponding sets of possible worlds: some histories permitted by traditional probabilistic laws are now ruled out as physically impossible. Consequently, the framework avoids one variety of empirical underdetermination while bringing to light others that are typically overlooked.

Motivation & Objective

• Motivate the use of algorithmic randomness to characterize probabilistic laws.
• Distinguish between generative chance* and probabilistic* constraining laws.
• Argue the advantages of probabilistic* constraining laws for governing and coherence with best-system analyses.

Proposed method

• Define Martin-Löf and Schnorr randomness as bases for star-laws.
• Formulate L* as a probabilistic* constraining law using randomness constraints.
• Discuss the alternative of chance* and compare conceptual implications.

Experimental results

Research questions

• RQ1 How can algorithmic randomness constrain the set of physically possible world histories?
• RQ2 What are the relative advantages of probabilistic* constraining laws versus generative chance* laws?
• RQ3 How do star-laws interact with non-Humean governing accounts and Humean best-system theories?

Key findings

• L* constraining laws tightly connect probabilistic claims with the set of possible worlds, ruling out maverick histories.
• L* supports a unified governing account and offers solutions to issues in non-Humean and Humean accounts (Big Bad Bug and best-system fit).
• There are underdeterminations introduced by different algorithmic randomness notions (Martin-Löf vs Schnorr) and by choosing chance* versus probabilistic* formulations.
• Lstar as a constraining law eliminates certain physically impossible sequences, aligning with a minimal primitivism view of laws.
• Lstar reduces underdetermination compared to traditional probabilistic laws, but introduces new computational underdetermination.