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The Nature of Mathematical Knowledge
The Origin and Influence of Logical Systems
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abstract addition angle arithmetic associative postulate assumptions Boolean algebra Boolean ring Chapter commutative postulate complete complex numbers concepts congruent considered consistency consistency proof Corollary deductive Definition distributive postulate Einstein equal equation equivalent Euclid Euclidean geometry example Exercises false field postulates finite finite geometry fundamental rule given Hence idempotent idempotent field idempotent postulate illustration implies integers interpretation inverse postulate lattice laws Lobachevskian logical system mathematicians matics method modulo systems multiplication natural numbers Newton's non-Euclidean geometries number system operations opposite converse ordered field parallel parallel postulate partially ordered partially ordered system plane geometry point of view positive integers possible postulates of Set Principia Mathematica principles proof properties propositional function prove q is true rational numbers real numbers reasoning relation Riemannian Riemannian geometry right distributive rule of inference satisfied scientific set of postulates statements straight line symbols Theorem theory tion truth undefined terms unity element