This post is about fitting a curve through a set of points. This is called regression: It is also the classic problem of coming up with a generalization from a discrete training data set in machine learning. We have a set of points that are observations at specific places and we want to make a system that predicts what the likely observations should be at all places within the domain of interest. We use the given observations (a training set) to train a model and then when we get more observations (a test set) we can evaluate how much error there is in our Continue reading
The hypothesis that all ravens are black is logically equivalent to the statement that all non black things are non ravens, and this is supported by the observation of a white shoe.
This is a paraphrasing of a famous paradox due to Hempel. There is a lot of fairly impenetrable discussion on the Wikipedia page about this paradox, some of which I believe to be incorrect, and so I include a readable resolution based on a Bayesian perspective here, and I also relate this issue to our ability to know the truth Continue reading