推論の検証についての数学教育的考察

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All dogs have two legs. All two legged animals are carnivorous. Therefore, all dogs are carnivorous. Here the argument is valid and the conclusion is true, but both premises are false! (Introduction to Finite Mathematics, P. 30) The diagonal lines of a rhombus meet at right angles. The diagonal lines of this quadrangle don't meet at right angles. Therefore this quadrangle is not rhombus. Here the argument is valid and premises and conclusion are true. Why are those arguments valid ? We shall consider the checking of arguments and that mathematics educational guidance. Therefore we know that a true conclusion is neither necessary nor suficient for the validity of the argument.
名古屋女子大学の論文
1992-03-05