arXiv subjects

Josiah Lopez-Wild

Publications and source records attributed to Josiah Lopez-Wild.

4 recordsLinked to original sources

arXiv2026

Algorithmic Randomness and Physical Typicality

Appeals to typicality are common in physics, but it is often unclear what it means for a physical state to be typical relative to a probability measure, and correspondingly unclear what a law that appeals to typicality asserts. Here we consider how one might characterize physical typicality using ideas from the theory of algorithmic randomness. As a concrete example, we show how taking a physical state to be typical relative to a computable measure when it is Martin-Löf random allows one to formulate the distribution postulate in Bohmian mechanics as a statistical constraining law of the theory. Using a toy model, we show how this constraint guarantees the standard Born statistics for computable experimental protocols. Algorithmic Bohmian mechanics (aBM) thus illustrates how algorithmic randomness may be used to provide precise content to a statistical law.

quant-ph↗

arXiv2026

The Distribution Postulate in Algorithmic Bohmian Mechanics

In order to make the right empirical predictions Bohmian mechanics requires a special statistical boundary condition -- the distribution postulate -- but it is unclear how best to understand this condition. We show how one might use the theory of algorithmic randomness to formulate the distribution postulate as an objective constraining law. The framework requires us to say something about admissible quantum-mechanical states and measurements. In return, algorithmic Bohmian mechanics (aBM) guarantees the standard Born statistics for a collection of canonical quantum experiments in the limit, not just with high probability. The algorithmic distribution postulate provides a sharp typicality condition, clarifies the status of quantum probabilities in the deterministic theory, and provides a concrete example of how notions provided by the theory of algorithmic randomness can aid in specifying the content of a physical law.

quant-ph↗

arXiv2026

At the Edge of Putnam's Program: Limitative Results For Computable Inductive Logics

The task of inductive logic is to develop a formal framework to analyze inductive reasoning. Historically this was accomplished by assigning probabilities to sentences of a logical language. Two natural criteria for such a system are: (i) the underlying language should be rich enough to express scientific hypotheses, and (ii) the probabilities should be, in some sense, accessible. The first criterion suggests that the language should at least contain the language of arithmetic, while the second suggests that probabilities should be computable. We show that these two criteria are in tension with one another. Various natural proposals for an inductive logic result in probabilities that are not arithmetically definable, much less computable. We isolate the assumptions responsible for this result, and search for a weaker inductive logic with more accessible probabilities. The most natural weakening results in probabilities that are arithmetically definable but still are not computable.

math.LO↗

arXiv2021

Cartesian Frames

We introduce a novel framework, the theory of Cartesian frames (CF), that gives powerful tools for manipulating sets of acts. The CF framework takes as its most fundamental building block that an agent can freely choose from a set of available actions. The framework uses the mathematics of Chu spaces to develop a calculus of those sets of actions, how those actions change at various levels of description, and how different agents' actions can combine when agents work in concert. We discuss how this framework might provide an illuminating perspective on issues in decision theory and formal epistemology.

math.CT↗