Originally Posted by wphamilton

Mathematics is a discussion, where one or both persons can learn something. If you want an intellectual contest play Chess or Go. I don't "argue" about math, but I don't mind explaining basic concepts if someone is truly interested.

The prediction says that, without knowing other information, you have a 14.3% chance of eventually dying from heart trouble. This simple datum by itself is of limited utility, except that the individual may realize that with such a high probability for one of many possible causes of death, he can take measures to reduce that number for his own case. He would be best served to survey the medical literature for statistical analysis of specific causes of heart disease, and having taken such measures consider other probable health risks.

The more information you know about the individual, along with associated statistical information, the better and more specific your probabilities become. You're getting sidetracked by wanting certainties, and wanting to reason from specific individual details which are unknowable from a particular data set. A quick general overview. Detailed information, combined with some silogisms, are fundamentals of deductive logic, and you derive some certainty thereby. Within the parameters of your space, or construct. You are essentially demanding that I provide a deductive conclusion about an element of the data set from general knowledge of the data set, and obviously that's not possible, but it's an error to presume that this means that probability is not predictive.

You can still use deductive logic with probability, but it's not a simple boolean statement but rather uses the probabilistic equivalents (of and, or, not etc) and results in a probability and confidence range. So, as with set theory, group theory or any other branch you don't actually give up boolean logic and deductive reasoning, but it does apply in different ways and you must interpret the conclusions within the particular system. Is that more clear?