One of the more interesting things I've learned in my life is that our best account of epistemology is that rational beliefs are governed by the probability axioms. Furthermore, there is a specific way in a rational agent updates her beliefs given new evidence---Bayesian conditionalization. Of course there is disagreement on this. At this point… Continue reading Paper Review: Philosophy and the practice of Bayesian statistics

## Paper Review: The Idea of a Scientific Philosophy

Often when someone learns I am studying philosophy of science I get a confused look in response. Even worse is when I use the term mathematical philosophy (see here, the top of page 1 for my favourite definition of mathematical philosophy), which often gets the response "math and philosophy, aren't those opposites?!" I've developed a… Continue reading Paper Review: The Idea of a Scientific Philosophy

## Paper Review: Unified dynamics for microscopic and macroscopic systems

In the wake of the quantum measurement problem there is a constellation of competing theories of quantum mechanics. Any adequate solution to the measurement problem must make predictions that agree with the observed quantum statistics. In particular, the theory must explain why small particles exhibit counter-intuitive behaviour and why this seems to go away at… Continue reading Paper Review: Unified dynamics for microscopic and macroscopic systems

## Paper Review: Subject and Object

One way to think about the quantum measurement is to think about the conflict between subjective and objective probability. We looked at some of Everett's earlier thoughts along these lines last week. As I mentioned in that post, later on in one version of his thesis he provided a much cleaner account of the measurement… Continue reading Paper Review: Subject and Object

## Paper Review: Objective versus Subjective Probability

Hugh Everett III proposed his many worlds (or as he preferred to call it, relative state) formulation of quantum mechanics back in the mid 50s in order to solve the quantum measurement problem. Although it took a while for the theory to gain traction, it (or some form of it) is one of the more… Continue reading Paper Review: Objective versus Subjective Probability

## Paper Review: Nonconglomerability for Countably Additive Measures that are not κ-additive

Probability plays a central role in this blog---many of my posts focus on where probability makes contact with philosophy and physics. However, there is also of course the mathematical theory of probability. The mathematics and the;philosophy interact in many ways, often technical results in the mathematics can be important for our work as philosophers. For… Continue reading Paper Review: Nonconglomerability for Countably Additive Measures that are not κ-additive

## Paper Review: Evolution and Disagreements Between Dynamics

Evolutionary game theory promises to provide a unifying mathematical framework for a breadth of sciences from biology and economics to anthropology and social epistemology. I endorse this project. In evolutionary game theory the mathematics of dynamical systems are used to represent and reason about various processes of change, such as change in gene frequencies within… Continue reading Paper Review: Evolution and Disagreements Between Dynamics

## Paper Review: Knowledge

A number of my posts have looked at the tight connection between rationality and probability. One of the pioneers of this kind of work was Frank Plumpton Ramsey, who made major contributions to mathematics, economics, psychology, and philosophy before passing away at the young age of 26. Ramsey was also a friend of the influential… Continue reading Paper Review: Knowledge

## Paper Review: The measurement theory of Everett and de Broglie’s pilot wave

I've written before on this blog about quantum mechanics. We've looked at a questionable interpretation of a recent experiment, the way in which quantum mechanics is radically nonlocal, and certain theoretical constructs needed for the thought experiments used in physics. One of the main reasons why quantum physics fascinates people is because the phenomenon themselves… Continue reading Paper Review: The measurement theory of Everett and de Broglie’s pilot wave

## Paper Review: The Regression of the Unstructural

What is the nature of meaning? This is one of the core questions on which the Vienna Circle, a group of early 20th century philosophers, took a stance. The kind of bumper sticker version of their answer is that a sentence only has meaning if it can be empirically verified (or tested, or confirmed, or… Continue reading Paper Review: The Regression of the Unstructural