What probability is about

Just as formal logic is a tool for capturing intuitions about effective ways of reasoning probability is a tool for capturing effective ways of reasoning about uncertainty.  In logic, we are taught to proceed from premises to conclusions. We conclude  that "If every CSE graduate takes the exit exam  before graduating and Emily is a CSE graduate, then Emily must have taken the exam" because this matches the Modus ponens pattern .  The good thing about this is that if we trust Modus ponens and we believe that we have correctly mapped the English description of the conclusion onto the terms of the formula, we know that the argument is valid. Notice that this claim of validity is not affected by the truth or falsity of the premises. Even if Emily never was a CSE student, or even if some CSE students are in fact able to weasel out of taking the exit exam, the argument is still OK. Not, however, especially useful as a way of working out stuff about Emily: if we aren't sure about the assumptions, we can't be sure about the conclusion either. Aristotle hit on the idea of laying out a taxonomy of plausible ways of reasoning, then thinking, in the abstract, about which of these patterns of reasoning actually deliver valid arguments. This is a wonderful idea, because you can rely on the insights about the patterns of reasoning without having to be concerned about the truth or falsity of particular facts.

In the same way that logic is the study of patterns of true/false reasoning, probability is the study of patterns of reasoning in the face of uncertainty.