Like other theories, the theory of probability is a representation of probabilistic concepts in formal terms—that is, in terms that can be considered separately from their meaning. These formal terms are manipulated by the rules of mathematics and logic, and any results are interpreted or translated back into the problem domain.
There have been at least two successful attempts to formalize probability, namely the Kolmogorov formulation and the Cox formulation. In Kolmogorov's formulation (see probability space), sets are interpreted as events and probability itself as a measure on a class of sets. In Cox's theorem, probability is taken as a primitive (that is, not further analyzed) and the emphasis is on constructing a consistent assignment of probability values to propositions. In both cases, the laws of probability are the same, except for technical details.
There are other methods for quantifying uncertainty, such as the Dempster-Shafer theory or possibility theory, but those are essentially different and not compatible with the laws of probability as usually understood.
Read more about this topic: Probability
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Famous quotes containing the word theory:
“No theory is good unless it permits, not rest, but the greatest work. No theory is good except on condition that one use it to go on beyond.”
—André Gide (18691951)
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—Oscar Wilde (18541900)
“The theory of rights enables us to rise and overthrow obstacles, but not to found a strong and lasting accord between all the elements which compose the nation.”
—Giuseppe Mazzini (18051872)