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The founder or earliest-known expositor of the field of logic, [[Aristotle]], set down some requirements he observed for rigorous proofs (in addition to the ordinary rules of deduction used for less rigorous proofs by means of the well-known [[syllogism]]).

The founder or earliest-known expositor of the field of logic, [[Aristotle]], set down some requirements he observed for rigorous proofs (in addition to the ordinary rules of deduction used for less rigorous proofs by means of the well-known [[syllogism]]).

The form of thinking productive of knowledge that we call "deduction", Aristotle called "analytics" (from leading away, loosening out—subtracting a middle term in the argument, and arranging premises so this is possible by taking into account the preservation of the truth-bearing chain of a series of syllogisms), and in his book ''Posterior Analytics'' written in the mid-fourth century B.C. ("posterior" meaning "after" as in ''after'' insuring the logical patterns by which the different qualities and quantities of propositions are correctly accounted), he exposits upon what makes a sound, and not merely valid, argument.  This extends from the bearing the coordination and quality of the premises has upon it down to the conclusion itself.

The form of thinking productive of knowledge that we call "deduction", Aristotle called "analytics" (from leading away, loosening out—subtracting a middle term in the argument, and arranging premises so this is possible by taking into account the preservation of the truth-bearing chain of a series of syllogisms), and in his book ''Posterior Analytics'' written in the mid-fourth century B.C. ("posterior" meaning "after" as in ''after'' insuring the logical patterns by which the different qualities and quantities of propositions are correctly accounted), he exposits upon what makes a sound, and not merely valid, argument.  This extends from this bearing the coordination and quality of the premises has upon it down to the conclusion itself.

Aristotle used the subject-predicate type of propositional relationships, the kind usually learned about today beginning in elementary school which may differ from more modern attempts at organized logic.

Aristotle used the subject-predicate type of propositional relationships, the kind usually learned about today beginning in elementary school which may differ from more modern attempts at organized logic.