One central notion in mathematics is cardinality (I've given an intuitive of cardinality in this post). In particular, there are different types of infinity, with some being larger than others. The smallest infinity is the cardinality of the natural numbers. We say that any set with such a cardinality is countable, since its elements can… Continue reading Paper Review: Is the Dream Solution of the Continuum Hypothesis Attainable?
Many arguments for the existence of God face the gap problem. In general, the gap problem is the problem of moving from some premiss of the form "there is a being with some perfections" to a conclusion of the form "there is a being with all perfections". Justin Mooney, following an approach by T. Ryan… Continue reading Paper Review: From a Cosmic Fine-Tuner to a Perfect Being
The standard Bayesian story goes something like this: probabilities represent a rational agent's degrees of belief. When the agent learns something new she conditions on it, meaning that she updates her probabilities according to Bayes' rule. Importantly, the interpretation of the probability function is that it represents the agent's degrees of belief about how likely… Continue reading Paper Review: New Semantics for Bayesian Inference: The Interpretive Problem
We're taught in school something like the following: DNA is the blueprint for an organism. We can sharpen up this kind of idea using ideas from information theory. In particular, biologists tend to say things like "DNA transmits information" or "DNA sequences are coded instructions". However, some philosophers of biology have claimed that when biologists… Continue reading Paper Review: The Transmission Sense of Information
Is it rational for me to want to have a child if I cannot know what it will be like to have a child? Laurie Paul, in her book Transformative Experience, argues that this question poses a significant problem for traditional theories of decision-making. Paul holds that many major life decisions are ones in which… Continue reading Can one rationally choose to have a child?
Last week I reviewed Kadane and Larkey's paper. In short, the main claim of their paper was that since the solution concepts used in game theory do not depend on the beliefs of the players they are irrelevant to game theory. Haranyi wrote a response to this paper, which it what I will review today.… Continue reading Paper Review: Subjective Probability and the Theory of Games: Comments on Kadane and Larkey’s Paper
Game theory is the study of the strategic interaction of rational agents. Decision theory is the study of the decision making of a rational agent. Clearly there is something similar about these two fields. What, exactly, is the relationship though? Do they study different aspects of rational action, or do they overlap? If they overlap,… Continue reading Paper Review: Subjective Probability and the Theory of Games