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''Reductio ad absurdum'' (Latin: "reduction to absurdity"; ''pl.'': ''reductiones ad absurdum''), also known as ''argumentum ad absurdum'' (Latin: "argument to absurdity", ''pl.'': ''argumenta ad absurdum''), is a common form of argument which seeks to demonstrate that a statement is true by showing that a false, untenable, or absurd result follows from its denial, or in turn to demonstrate that a statement is false by showing that a false, untenable, or absurd result follows from its acceptance. First recognized and studied in classical Greek philosophy (the Latin term derives from the Greek "''εις άτοπον απαγωγή''" or ''eis atopon apagoge'', "reduction to the impossible", for example in Aristotle's ''Prior Analytics''),〔 this technique has been used throughout history in both formal mathematical and philosophical reasoning, as well as informal debate. The "absurd" conclusion of a ''reductio ad absurdum'' argument can take a range of forms: * The Earth cannot be flat, otherwise we would find people falling off the edge. * Society must have laws, otherwise there would be chaos. * There is no smallest positive rational number, because if there were, then it could be divided by two to get a smaller one. The first example above argues that the denial of the assertion would have a ridiculous result; it would go against the evidence of our senses. The second argues that denial of the assertion would be untenable: unpleasant or unworkable for society. The third is a mathematical proof by contradiction, arguing that the denial of the premise would result in a logical contradiction (there is a "smallest" number and yet there is a number smaller than it). ==Greek philosophy== This technique is used throughout Greek philosophy, beginning with Presocratic philosophers. The earliest Greek example of a ''reductio'' argument is supposedly in fragments of a satirical poem attributed to Xenophanes of Colophon (c.570 – c.475 BC). Criticizing Homer's attribution of human faults to the gods, he says that humans also believe that the gods' bodies have human form. But if horses and oxen could draw, they would draw the gods with horse and oxen bodies. The gods can't have both forms, so this is a contradiction. Therefore the attribution of other human characteristics to the gods, such as human faults, is also false. The earlier dialogs of Plato (424 – 348 BC), relating the debates of his teacher Socrates, raised the use of ''reductio'' arguments to a formal dialectical method (''Elenchus''), now called the ''Socratic method'' which is taught in law schools. Typically Socrates' opponent would make an innocuous assertion, then Socrates by a step-by-step train of reasoning, bringing in other background assumptions, would make the person admit that the assertion resulted in an absurd or contradictory conclusion, forcing him to abandon his assertion. The technique was also a focus of the work of Aristotle (384 – 322 BC).〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Reductio ad absurdum」の詳細全文を読む スポンサード リンク
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