Abstract
At first the author suppose that if a structure-mapping consist between two things, the source system of one side thing act on forming the target system of the another thing. In this paper the author urged as followings (1)〜(6). (1) revalued "counting" based on epistemological viewpoint. (2) suggested that there are degree of difficulty in situations which form the cardinal number concept. (3) poited out that the order number system is analogy to the cardinal number system. (4) showed that there are two different recognition, that is, "these do exist" and "these have equal quantity", in recognizing counting objects. (5) showed that there are two ways as followings for generalizating "counting". (1) expand the domain of count objects. (2) transform "exist" and "equal qantity" in (4) to "equal value". (6) indicated that epistemological obstacle occure on (5)(2).
