The Study on Formation Process of Statistical Concepts: Based on the Negation Theory

Abstract

　　 The purpose of this paper is to elucidate the way of the concept formation that is inherent to the statistics domain, in other words, the process forming statistical concepts as methodological knowledge.  For achieving this purpose, three tasks are worked on.  At first, the characteristic of statistics is made clear.  Then, the difficulty in forming concepts is revealed. Finally, the formation process of statistical concepts is explained.

　　 One of the characteristic of statistics is that it makes uncertainty targeted for consideration.  But, It characterizes statistics plainly further that statistics are methodological knowledge.  Based on this characteristic of statistics, statistical concepts must be formed as the solution while solving a problem with the uncertainty statistically.  The difficulty of the statistical concept formation is not abstraction but generalization.  In this paper, as approach for this difficulty, the negation theory is paid the attention to.  It is three stages in a process of the concept formation based on the negation theory.  At first, the extension of concept A, which can solve problem P, is limited by an appearance of problem Q.  This is the stage of limiting extension.  Then, concept B which can solve problem Q is constructed.  Concept B overcomes a shortcoming of denied concept A.  It is the stage of revealing intension. In the last stage, two concepts are reconstructed.  The relation between concept A and concept B are made clear.