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If you’re interested in learning a bit more about Aquinas’ philosophy, Jennifer Frey recommends the following two books: Herbert McCabe, On Aquinas Etienne Gilson, Wisdom and Love in Saint Thomas Aquinas Matt Teichman ...

In our latest episode, Frey sketches out Aquinas’ “exemplary method of philosophy,” the ‘quaestio format.’ With this format, Aquinas models a core pedagogical technique of the universities of his time—quaestiones disputatae (lit: questions debated). For this technique, students would take up sides of an issue, articulated as a question, and offer arguments for each side. The master (think professor) would then evaluate the arguments and adjudicate. That Aquinas structures many of his texts around this technique (especially his magnum opus, the Summa Theologica) indicates that he is concerned with students reading his texts acquiring not only the content of the view Aquinas himself supports, but also the proper method for thinking through an issue and arriving at a view—one which engages with contrary arguments and show the superiority of one’s own view to such arguments. As Frey points out the in episode, this pedagogical value of Aquinas’ writing is not restricted to his own students; philosophers today can gain much from a close study of Aquinas’ method. ...

Subscribe to Elucidations:       This month we’re joined by Jennifer Frey, Harper Schmidt Fellow and Collegiate Assistant Professor in the Humanities at the University of Chicago. Click here to listen to our conversation. In this episode, we begin with an overview of Thomas Aquinas, one of the most prolific philosophers ever. (It is sometimes said that he wrote, on average, about 10,000 words per day.) Frey points out that whereas today it is common to think of philosophy as a set of specialized subdisciplines, Aquinas’ approach was to pursue philosophy as a unified discipline, under the assumption that one can’t have a fully developed ethics (for example) without thinking through the difficult issues in metaphysics. ...

In Episode 47, Baltag and Matt briefly discuss what they call the ‘KK principle,’ or the ‘principle of positive introspection.’ The basic formulation of this principle is: (KK): If I know that p, then I know that I know that p. (Where ‘p’ is some proposition.) For example, if I know that 2+2=4, then I know that I know that 2+2=4. A close cousin of the ‘KK principle’ is what we’ll call the ‘K-not-K principle,’ or the principle of negative introspection. The basic formulation of this principle is: ...

Subscribe to Elucidations:       In our latest episode, we talk some epistemology with Alexandru Baltag, Associate Professor of Logic at the Institute for Logic, Language, and Computation in Amsterdam. Click here to listen to our conversation. Knowledge may seem straightforward at first. But try to give an exact definition of what it is, and you’ll soon find that it’s more difficult than you would have thought. Maybe it’s just belief. No, wait–if I believe something false, that probably can’t count as knowledge. Maybe it’s true belief. But I may believe something for the wrong reason, or for no reason at all. So maybe it’s true belief that’s supported by good evidence. Oh, my; it seems there are famous counterexamples to that definition as well. ...

In the Veltman episode on normality (46), Matt mentions the “No True Scotsman Fallacy,” in its relationship to statements of normality. I’d like to sketch out what the fallacy is just a bit more fully, and further highlight how it brings out the problem of how we falsify normality claims. The basic idea behind the No True Scotsman Fallacy is that one can make a generalization of some sort (from the offensive ‘All Greeks are lazy’ to the more benign ‘Bears normally hibernate’), and then protect this generalization from any counterexample by claiming that it isn’t a real counterexample. But by doing so, the person making the assertion has made a contingent statement into a logically necessary statement, illegitimately. That is, ‘All Greeks are lazy’ could turn out to be either true or false until we go out, find some Greeks, and check (and quickly discover our error). But if the person who has made the assertion systematically rejects any example that undermines the generalization (‘That’s not a real Greek person.’), then it seems that the statement could never be falsified—it’s logically true. But “All Greeks are lazy” is obviously not a logical truth; it’s not a truth at all! In essence, the person who makes the ‘No True Scotsman’ move is perpetually moving the goalposts, preventing us from ever convincing her that that she made a false claim. ...

Subscribe to Elucidations:       This month, we talk with Frank Veltman, Professor of Logic and Philosophy at the Institute for Logic, Language, and Computation in Amsterdam. Click here to listen to our conversation. Most of our everyday reasoning involves the notion of things normally being one way rather than another. But sometimes, this gets us into trouble. Statements of prejudice and bigotry, for instance, usually make recourse to the idea of normality. Imagine I’m xenophobe, and I say, ‘Greek people are normally lazy.’ Now, clearly that’s an offensive thing to say because it shows that I’m buying into a harmful stereotype. But to make matters worse, on top of being offensive, it’s difficult to try to refute. Why? Because whenever someone tries to give me a counterexample–a Greek person who isn’t lazy–I can just reply that that counterexample doesn’t matter, because I was only saying that they’re normally lazy. Not that you couldn’t find me the odd Greek person here or there who wasn’t. ...

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 ...