Abduction As A Mathematical Resoning.

수학적 추론으로서의 가추법

This Study takes Peirce' abduction which is Phenomenology' first reasoning mode, as a part of mathematical reasoning with deduction and induction. Abduction(retroduction, hypothesis, presumption, and originary argument) leads a case through a result and a rule, while deduction leads a result through a rule and a case and induction leads a rule through a case and a result. Polya(1954) involved generalization, specialization, and analogy within induction, but this paper contain analogy in abduction. And metaphors and metonymies are also contained in abduction, in which metaphors are contained in analogy. Metaphors and metonymies are applied to semiosis i.e. the signification of mathematical signs. Semiotic analysis for a student's problem solving showed the semiosis with metaphors and metonimies. Thus, abductions should be regarded as a mathematical reasoning, and we must utilize abductions in mathematical teaming since abductions are thought as a natural reasoning by students.