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In the first part of this post, we talked about the motivations behind the epistemic interpretation of probability. Now, let’s take a look at one of the core mathematical theorems employed by those who subscribe to such an interpretation: Bayes’ Theorem (which is mentioned by Fitleson in Ep. 31). Before introducing Bayes’ Theorem, it is important to get clear on one last concept: conditional probability. The basic idea behind conditional probabilities is that we offer the probability that some event occurs, given that something else is true. It’s helpful to think about this once again in a gambling analogy. Let’s say that we want to bet on whether the Philadelphia Phillies will win the World Series next year. I might only wish to make a bet on this if one of their star players (say, Ryan Howard) is not injured this year. So we might make bets conditional on Ryan Howard not becoming injured—if Howard is injured, the bet is simply off. Referencing another of our blog posts, we say that conditional probabilities restrict the set of possible worlds we are considering (say, those possible worlds in which Ryan Howard is not injured for the 2013 season), and compute the probabilities from this restricted set of possible worlds. ...

Two recent episodes (Fitelson, Ep. 31; Vasudevan, Ep. 45) have mentioned ‘epistemic interpretations’ of probability and Bayes’ Theorem. For Fitleson, Bayes’ Theorem provides a model for inductive reasoning, and he is concerned with deviations from this model (as in the ‘base rate fallacy’ and ‘Linda cases’). Vasudevan takes epistemic interpretations of probability as the historical response to the apparent tension between determinism and our intuitions about chance events like the flip of a coin—a response which he ultimately rejects. Bayes’ Theorem and the epistemic interpretation of probability are intimately related, as one view in the philosophy of probability, Bayesianism, uses Bayes’ Theorem to represent changes in our beliefs in light of new evidence, which assumes an epistemic interpretation of probability. In the first part of this post, let’s take a look at some of the basic ideas and motivations behind the epistemic interpretation. In the second, we will look at some of the ‘mathematical machinery’ the Bayesian, who assumes an epistemic interpretation of probability, employs. ...

Please join me in welcoming our new blogger, Phil Yaure! He will be with us for the next few months to talk about the various philosophical topics that come up during our interviews. Coming up is an introduction to the Bayesian interpretation of probability. Matt Teichman ...

Subscribe to Elucidations:       This month, we talk with Anubav Vasudevan (Assistant Professor of Philosophy at the University of Chicago) about whether there’s any conflict between objective probability and determinism. Click here to listen to our conversation. Suppose I say there’s a 50/50 chance that when I toss a coin, it will land heads. Is that statement objectively true or false? Am I describing a physical fact about the coin, the air, and the tabletop? Or is it just a subjective statement about how _certain _I am that the coin will land heads? Maybe, when I say there’s a 50/50 chance that the coin will land heads, all I’m saying is that I have no particular reason to place a bet on one particular outcome over the other. For all I know, either outcome is equally likely. On the one model, when I talk about probabilities, I’m describing physical facts about the way the world works. On the other, when I talk about probabilities, I’m describing my own ignorance. ...

To learn more about the topics we discussed during our last episode, check out these two papers by Joëlle Proust: Epistemic agency and metacognition: an externalist view, Proceedings of the Aristotelian Society, 2008, CVIII, 3, 241-268. Metacognition and mindreading: one or two functions? in: M. Beran, J. Brandl, J. Perner & J. Proust (Eds.), The Foundations of Metacognition. Oxford: Oxford University Press. (2012), 234-251. Those of you who have access to Philosophy Compass can also look at Proust’s survey article. ...

Subscribe to Elucidations:       This month we talk some philosophy of mind with Joëlle Proust, Professor of Philosophy at the École Normale Supérieure and member of the Jean Nicod Institute. Click here to listen to our conversation. You’re on your way to the supermarket to pick up the ingredients for a delicious vegetable stew. Upon arriving, you discover that you mistakenly left the shopping list on your dresser. Oh, no! You haven’t got time to go all the way back home, pick up the list, and return to the grocery store. Should you try to think back and recall the entire list, or should you just forget about the whole thing and get take-out? In order to make this decision, one of the things you’ll have do is determine whether you’ll be able to remember the whole thing. Whether you give up or try to mentally reconstruct the list will depend on how you evaluate your ability to remember things. That’s metacognition, in a nutshell: it’s what happens any time we evaluate our ability to perform some sort of mental task. ...

If you’d like to hear more about some of the philosophical ideas that Al-Kindi was responding to in the work we discussed during our last episode, you really can’t find a better resource than Peter Adamson’s own History of Philosophy podcast. To learn about Aristotle’s arguments for the eternity of the universe, check out this interview with Richard Sorabji. For a great introduction to Plotinus’ influential idea that the ultimate explanatory principle behind the universe has to be completely unified, check out this episode. ...

For those of you who would like to follow up on our discussion of Al-Kindi’s philosophy, a great place to start is Peter Adamson’s Stanford Encylopedia entry on Al-Kindi. If you’re looking to go into a bit more depth, Adamson’s monograph is a riveting read! And finally, if you’d like to look at some of Al-Kindi’s own writings, take a look at this new collection of translations. Matt Teichman ...

Subscribe to Elucidations:       This month, we sit down with Peter Adamson, Professor of Philosophy at Ludwig Maximilians Universität in Munich and King’s College, London. Click here to listen to our conversation with him. Al-Kindi may not be required reading for undergraduate philosophy majors these days, but the role he played in the history of philosophy was pivotal. Working in the ninth century, he was one of the first philosophers to try to unify the ancient Greek philosophical tradition with the tenets of Islam. ...

Before we began recording our previous episode, our guest turned the tables and interviewed me! Click here to listen to our conversation about a number of topics, including filmmaking, avant-garde cinema, interdisciplinary work, podcasting, and the illusion of philosophical depth. Matt Teichman ...