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: 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: Contribution to discussion on Probability

Probability can seem like a slippery notion. Indeed, though we have an intuitive notion of various aspects of probability, it took a long time for humanity to develop a rigorous formal theory. And even with the mathematics of probability on surer footing, the interpretation of probability -- what does it mean -- is still plagued… Continue reading Paper Review: Contribution to discussion on Probability

Paper Review: The Semantics Latent in Shannon Entropy

One joke about philosophers is that we walk around all day just going, "what does it all mean?" Though it is a joke, some philosophers are concerned with meaning. I don't mean meaning in a kind of ethical, "why are we here?" sense (although some philosophers are concerned with that), but rather what we mean… Continue reading Paper Review: The Semantics Latent in Shannon Entropy

Paper Review: Decision Theory Without Representation Theorems

Decision theory seeks to understand how rational agents should act. More specifically, I am talking about normative decision theory. There is also descriptive decision theory which tries to characterize how people in fact act. For this post (and most of my posts) I will focus on normative decision theory. Importantly, the "should" here is not… Continue reading Paper Review: Decision Theory Without Representation Theorems

Paper Review: Difficulties in the Theory of Personal Probability

Readers of the blog will know that I am a fan of the Bayesian approach to probability. This approach is also sometimes called "personal probability", because it takes probabilities to be the degrees of belief (or credences) of rational agents. We can think of using probability like this as a framework for managing uncertainty in… Continue reading Paper Review: Difficulties in the Theory of Personal Probability

Paper Review: Bell’s Theorem: The Price of Locality

Quantum phenomena--and the theories built to account for them--can be strange. One of the most fundamental and (to some), spooky, things about quantum mechanics is action at a distance. What exactly is action at a distance in quantum mechanics, and what are its implications? This is one of the central questions of Tim Maudlin's book… Continue reading Paper Review: Bell’s Theorem: The Price of Locality