• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.123-135
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• 2008

This study analysed the schemata which are requisite to understand and prove examples of mathematical induction, and examined students' construction of the schemata. We verified that the construction of implication-valued function schema and modus ponens schema needs function schema and proposition-valued function schema, and needs synthetic coordination for successive mathematical induction schema. Given this background, we establish $1{\sim}4$ levels for students' understanding of the mathematical induction. Further, we analysed cognitive difficulties of students who studying mathematical induction in connection with these understanding levels.

• Korean Journal of Logic
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• v.3
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• pp.27-51
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• 2000

이글의 기본적인 목적은 2치를 포함한 다치 논리 체계들간의 관계를 검토하는 데 있다. 이를 위하여 여기서는 명제를 대상으로 한 형식 의미 해석체계들 간에 고러해야 할 의미론적 확장 개념을 분명히 하였다. 구체적으로 다음의 두 작업이 수행되었다 첫째로 2치와 다치 논리 또는 다치 논리들간에 적용될 만한 의미론적 확장 개념을 의미해석의 바탕을 이루는 진리치 함수와 진리연산에 맞게 정의하였다. 둘째로 정의의 적합성을 확장, 비확장 사례 증명을 통해 예증해 보였다.

• Korean Journal of Logic
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• v.16 no.3
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• pp.347-380
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• 2013

In this paper I will try to show how Wittgenstein criticized Frege's theory of meaning. Frege's theory of meaning can be compressed as sense-reference theory. Frege distinguishes between sense and reference on all the linguistic expressions. In particular, he regards that a sentence has sense and reference. This distinction was raised from, so to speak, the problem of identity sentences. Wittgenstein's "fundamental thought" of Tractatus Logico-Philosophicus is the key of his direct criticism of Frege's sense-reference theory. That is, it is an attack on Frege's thought that the reference of a sentence is a truth value and truth values are "objects themselves" (in Frege's meaning). According to Wittgenstein, such an object does not exist and according to his picture theory, the function of a name and that of a proposition are fundamentally different. By the way, Frege can reply justly to this criticism that it is insufficient. In short, Frege's 'sense' and 'reference' etc, are the technical terms. Hence Wittgenstein's decisive criticism of Frege's theory consists in accusing his theory of logical flaws. There is an another route to the sense and reference of a sentence which Frege introduces. In discourses of judgement stroke and content stroke in his Begriffsshrift and in those of horizontal stroke since his "Function and Concept", Frege deals with the sense and reference of a sentence. Wittgenstein criticize that the sense of a complex sentence such as ~p would by no means be determined by Frege's determination.