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 ‘Logic’ 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’ [...]
Self-referential multiple choice quiz
Posted in Logic on March 2, 2009 | Leave a Comment »
The solution is unique, and can be found by progressive elimination of impossible answer choices (or by trial and error). Post the solution in the combox.
1) The number of questions whose answer is a vowel is:
a) 4
b) 1
c) 3
d) 5
e) 2
2) The answer to question 5 is:
a) B
b) C
c) D
d) E
e) A
3) The most number [...]
Puzzle Update
Posted in Logic on October 8, 2008 | 1 Comment »
Joseph posted a couple of interesting variants on my logic puzzle in the comments. I’ve reproduced them here, with my answers in white (select the text to read them). I particularly like the second one, which looks especially crazy at first.
1.
A: You don’t, and cannot know, what your number is.
B: I don’t know whether or [...]
Logic puzzle
Posted in Logic on October 4, 2008 | 9 Comments »
This is a puzzle I made up based on a generic category of logic puzzle (usually called “induction” puzzles, I believe).
Two men, A and B, sit facing each other. A third man, C, puts on the heads of A and B a hat marked with a number, so that A can see B’s number and [...]
