Last post on probability for now. This one doesn’t involve propositions or questions of ignorance vs. knowledge, just straightforward mathematics. The point is to illustrate how counterintuitive conditional probabilities can be.
Suppose in a given population there are an equal number of males and females. This population is subject to a disease, which I’ll call Bayesitis. [...]
Archive for the ‘Probability’ Category
Mathematical puzzle
Posted in Logic, Mathematics, Probability on March 21, 2009 | 9 Comments »
Propositional evidence part III: Applying the lesson learned
Posted in Logic, Mathematics, Probability on March 18, 2009 | 3 Comments »
This post is a thought experiment. As is evident from the number of comments on the first Bayes’s theorem post below, it has sparked quite a debate. I’d like to step into my opponent’s shoes for a moment and think about this debate from the point of view that I’m seeing presented.
<tongue in cheek>
Suppose I [...]
Propositional evidence part II: Raspberries
Posted in Logic, Mathematics, Probability on March 17, 2009 | 4 Comments »
In the combox of the last post, we have an interesting example in which it seems that some random person’s assertion in fact constitutes zero evidence. I’d like to analyze that example in more detail.
Here’s the scenario. You’re sitting in front of your computer. Some random guy instant messages you, saying, “You’re eating raspberries.” Does [...]
Bayes’ theorem and propositional evidence
Posted in Logic, Mathematics, Probability, tagged Cur in his scholis eos philosophiam non docent? on March 15, 2009 | 46 Comments »
Suppose I want to evaluate the probability, given the state of my knowledge, of a certain proposition X. I say that learning the additional fact that some random guy entirely unknown to me, John Smith, asserts that X is true should increase my assessment of the probability that X is true.
Reductio: We know from Bayes’ [...]
Probability and Evidence, Part III
Posted in Philosophy / Theology, Probability on July 19, 2008 | 2 Comments »
To wrap up the previous two posts, I have a few thoughts on the common invocation of the principle that “extraordinary claims require extraordinary evidence.” We have already seen that this principle doesn’t do what its common proponents would like it to do, for the reason that extraordinary claims constitute extraordinary evidence. However, there is [...]
Probability and Evidence, Part II
Posted in Philosophy / Theology, Probability on July 5, 2008 | 1 Comment »
I didn’t realize until I came to WordPress to write this post that my last post was more than a week ago! I had originally intended to write this last Friday or Saturday. All future statements about forthcoming blog posts should be taken in the same general vein as the Scriptural statement “Behold, I am [...]
