Basic Concepts of Logic and Formal Systems
Formalization or axiomatization is an outgrowth of the broader goals of scientific systematization. Euclid systematized geometry by showing how a great many statements known to be true about geometrical figures could be logically derived from a small set of principles assumed to be true, called the axioms. Newton systematized mechanics by showing how the known laws of motion, both planetary and terrestrial, could be derived from three basic statements. In both cases, the initial assumptions had the status of true statements, ‘self-evident’ in the Euclidean system, empirically discovered truths in the Newtonian system. In both cases the system was concerned with particular objects, points and lines in the one case, physical objects in the other.
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