Description

ILCLI Seminar.  Manolo Martínez (Logos - UB): "The “Algorithmic Best System” Approach to Laws" November 28, 2025

November 28, 2025. 15:00.

Venue: Carlos Santamaria Zentroa, room 4.

Abstract:

The Best-System Approach [BSA] (Lewis 1999; Cohen and Callender 2009; Loewer 1996) is one of the main approaches to the metaphysics of laws. In this tradition, a “system” is a deductive system: a set of axioms and theorems derived from them. We want to set things up in such a way that the axioms can be reasonably identifies with the laws of that world, and the derived theorems with the rest of truths.

The Best System Approach to this desideratum is to make the axioms optimally trade off (balance) strength and simplicity. Strength: something like how many theorems can be derived from the axioms. Simplicity: something like very few, syntactically simple axioms. Balance: something like judiciously trading off strength and simplicity.
BSA is an impressive modeling feat. It promises to recover something close to the laws described by scientists, without extravagant ontological commitments; and it is claimed to recapitulate how working scientists go about discovering laws. But it is not without problems: The above characterizations of strength, simplicity and balance are impressionistic at best. We want to be more explicit. Also, it is often claimed that BSA has a language problem: different languages (using different predicates) will deem different systems best. It looks as if BSA doesn’t have the resources to distinguish between laws and initial conditions (Woodward 2014). Finally, it is unclear that it has the resources to accommodate special-science and ceteris paribus laws.
In this paper I explore an algorithmic development of BSA [ABSA]. Instead of thinking of the end product of the system to be truths about the world, I will take it to be data about the world. Instead of thinking of systems as sets of axioms I will think of them as algorithms. Instead of thinking of the production of truths from axioms as a matter of deductive inference, I will think of the production of data from algorithms as the output of running a program.
This rethinking of BSA raw materials should help in three ways: It affords the formulation of formally perspicuous notions of simplicity, strength, and balance. It shows the ABSA version of the language problem to be not very threatening at all: language changes at most introduce a finite supplementary overhead to the complexity of systems. It has the resources to at least sketch approaches to the other worries: laws vs initial conditions can be mapped (imperfectly, perhaps, but it’s a start) onto the two codes in a structure-function approach to complexity; and algorithmic rate-distortion theory can be used to shed light on the status of special-science laws.