Deduction is the process of deriving conclusions from logical premises without resort to empirical evidence. Deductive reasoning is the primary method of reasoning used in mathematical proof, whereas, inductive reasoning, or reasoning from specific empirical facts to more general conclusions, is the method most often practiced in the natural sciences. In a deductive mathematical system, certain undefined terms, definitions, and "self-evident" assumptions called axioms or postulates are stated, after which theorems or propositions of the system are derived, based only upon what has been previously assumed or proved. The Greek philosopher, Aristotle (384-322 B.C.) laid the foundation for deductive argument with his method of the syllogism. Syllogistic reasoning, in which conclusions are derived from stated premises, dominated deductive logic for nearly 2000 years after Aristotle. Modern logicians give less emphasis to syllogistic reasoning, but the symbolic logic developed during the 20th century remains deductive in requiring rigorous arguments...