The Logical Foundations of Probability

The logical foundations of probability revolve around how we reason about uncertainty and make consistent judgments based on available information. It treats probability as a measure of our degrees of belief or confidence in the truth of a statement, given what we know. Instead of viewing probability as just chance, it emphasizes rational coherence—ensuring our beliefs are logically consistent and follow set principles. This approach allows us to update beliefs when new evidence appears (using methods like Bayes' theorem) and to quantify uncertainty in a clear, systematic way based on logic and evidence rather than chance alone.