Axioms
There are two kinds of axioms, 1) conventions that are taken as true that should be avoided because they cannot be tested, and 2) hypotheses. Proof in the theory of probability was built on four axioms developed in the late 17th century:
- The probability of a hypotheses is a non-negative real number: ;
- The probability of necessary truth equals one: ;
- If two hypotheses h1 and h2 are mutually exclusive, then the sum of their probabilities is equal to the probability of their disjunction: ;
- The conditional probability of h1 given h2 is equal to the unconditional probability of the conjunction h1 and h2, divided by the unconditional probability of h2 where that probability is positive, where .
The preceding axioms provide the statistical proof and basis for the laws of randomness, or objective chance from where modern statistical theory has advanced. Experimental data, however, can never prove that the hypotheses (h) is true, but relies on an inductive inference by measuring the probability of the hypotheses relative to the empirical data. The proof is in the rational demonstration of using the logic of inference, math, testing, and deductive reasoning of significance.
Read more about this topic: Statistical Proof
Famous quotes containing the word axioms:
““I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.””
—Henry Brooks Adams (1838–1918)
“The axioms of physics translate the laws of ethics. Thus, “the whole is greater than its part;” “reaction is equal to action;” “the smallest weight may be made to lift the greatest, the difference of weight being compensated by time;” and many the like propositions, which have an ethical as well as physical sense. These propositions have a much more extensive and universal sense when applied to human life, than when confined to technical use.”
—Ralph Waldo Emerson (1803–1882)