axiomatic method

In logic, the procedure by which an entire science or system of theorems is deduced in accordance with specified rules by logical deduction from certain basic propositions (axioms), which in turn are constructed from a few terms taken as primitive.

These terms may be either arbitrarily defined or conceived according to a model in which some intuitive warrant for their truth is felt to exist. The oldest examples of axiomatized systems are Aristotle's syllogistic and Euclidean geometry. Early in the 20th century, Bertrand Russell and Alfred North Whitehead attempted to formalize all of mathematics in an axiomatic manner. Scholars have even subjected the empirical sciences to this method, as in J. H. Woodger's The Axiomatic Method in Biology (1937) and Clark Hull's Principles of Behavior (1943).

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      in logic, a procedure by which an entire system (e.g., a science) is generated in accordance with specified rules by logical deduction from certain basic propositions (axioms or postulates), which in turn are constructed from a few terms taken as primitive. These terms and axioms may either be arbitrarily defined and constructed or else be conceived according to a model in which some intuitive warrant for their truth is felt to exist. The oldest examples of axiomatized systems are Aristotle's syllogistic and Euclid's geometry. Early in the 20th century the British philosophers Bertrand Russell (Russell, Bertrand) and Alfred North Whitehead (Whitehead, Alfred North) attempted to formalize all of mathematics in an axiomatic manner. Scholars have even subjected the empirical sciences to this method, as J.H. Woodger has done in The Axiomatic Method in Biology (1937) and Clark Hull (Hull, Clark L.) (for psychology) in Principles of Behaviour (1943). See also axiom.

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