Again: I'm no expert in probability theory, but I can very confidently say that probability is not a mathematical theory. Probability theory is a theory, but probability is something else. I'd prefer not to be the one to make the change, though. --Larry Sanger
Probability theory is certainly a mathematical theory. It is formally a branch of measure theory, and its foundations are as solid as any other branch of mathematics. As a one-line description, probability theory deals with objects known as Random Variables, which are functions mapping from an event P:E -> [0,1]. Now, the application of probability theory gets into some really sticky business, i.e., one must define what probability actually means. Applied probability isn't just Statistics, but must be founded a priori on some particular notion of reality. In particular, the concepts of aleatory and epistemic probability seem to cause much confusion.
There are philosophical concepts of probability which do not match or fit the mathematical theory of probability. My usage is perhaps too informal, but is conditioned by the topic residing in the Mathematics hierarchy as distinct from Philosophy. --Dick Beldin
It seems to me an article about probability ought to acknowledge the morass of senses that exist in ordinary language, philosophy, and mathematics. --LMS
I have renamed all of Dick's pages so that the ones that should have (IMHO) lower-case titles do have lower-case titles. I have also moved the internal links from the beginning of the articles to the end of the articles, for consistency with other Wikipedia articles. What remains to be done now is to change all the Upper Case links to lower case ones, so that we can bypass all the redirection pages that I've created. I would do the latter myself, but it's dinnertime. :-) --LMS