# Axiomatic Reasoning and Axiomatic Methods (Coursework Sample)

Axiomatic reasoning has a long history. It has been used in many different ways. Aristotle saw it as part of what he called first philosophy. Euclid applied it to geometry. Archimedes used it in solving statics problems. Ptolemy studied astronomical models by it. Spinoza used it in his conceptual demonstrations, Newton in mechanics and optics, Peano in number theory, Hilbert in geometry and physics, Einstein in gravitation theory, Whitehead and Russell in logic. Many other scientists and philosophers used it in different fields.

There was a common purpose in all the different uses. It was to provide a systematic investigation of the structures that are intended to be characterized by axioms. The struc- tures in question can be mathematical, physical (material), social, legal, pure structures, or what not.

Axiomatic Reasoning and Axiomatic Methods NP1402 (Mathematical Literacy)

Axiomatic reasoning has a long history. It has been used in many different ways. Aristotle saw it as part of what he called first philosophy. Euclid applied it to geometry. Archimedes used it in solving statics problems. Ptolemy studied astronomical models by it. Spinoza used it in his conceptual demonstrations, Newton in mechanics and optics, Peano in number theory, Hilbert in geometry and physics, Einstein in gravitation theory, Whitehead and Russell in logic. Many other scientists and philosophers used it in different fields.

There was a common purpose in all the different uses. It was to provide a systematic investigation of the structures that are intended to be characterized by axioms. The struc- tures in question can be mathematical, physical (material), social, legal, pure structures, or what not.

1 Axiom

1 A formal statement or principle in mathematics, science, etc., from which other statements can be obtained.

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