• Korean Journal of Logic
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• v.12 no.2
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• pp.59-88
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• 2009

According to David Hume, a deductive demonstration for inductive inference is not possible, because inductive inference is not deductive; and an inductive demonstration for inductive inference is not possible either, because such a demonstration is circular. Thus, on his view, there is no way of justifying inductive inference. Ever since Hume raised this problem of induction, a fair number of philosophers have tried to solve it. Nevertheless there is still no solution which is plausible enough to receive wide endorsement. According to Wilfrid Sellars, we cannot justify inductive inference by any theoretical reasoning; we can vindicate it only by a certain sort of practical reasoning. In this paper, I defend this Sellarsian proposal by developing and explaining it.

• The Journal of Korean Institute for Practical Engineering Education
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• v.5 no.1
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• pp.1-13
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• 2013

For a basic engineering education the confirmation and verification of the deductive Inference was studied and the principle of probability inference was applied. The background of introduction of deductive Inference and its test method was mentioned, and historic arguments on the compatibility of deductive statistical inference was summarized and analyzed. Philosophical arguments on the deductive confirmation for engineering experiments was introduced. Premise, procedure, and control of the experiments are studied. As an example of the deductive probability inference three groups of experimental data were used in order to find successful inferences respectively.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10a
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• pp.193-195
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• 2004

기존의 규칙 귀납법(Rule Induction)은 양성적 추론(positive reasoning)과 음성적 추론(negative reasoning)을 잘 반영하지 못하고 있지만 의학 분야의 추론은 양성적 추론과 음성적 추론을 모두 포함하고 있다. 이것이 의학 전문가들이 귀납된 규칙을 해석하는데 어려움을 가지게 되며, 진단 과정을 위해서 규칙을 해석하는 것을 쉽게 진행할 수 없는 이유이기도 하다. 본 연구에서는 양성적 규칙들과 음성적 규칙들의 귀납법을 위한 두 가지 알고리즘을 적용한 진단 시스템인 DS-ARI(Diagnosis System using Algorithms for Rule Induction)물 제안한다. 제안하는 시스템과 기존 시스템을 비교해 보았을 때 제안하는 시스템에서 전문가의 지식을 보다 정확하게 표현하여 정확성을 높이게 되었다.

• Korean Journal of Logic
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• v.17 no.1
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• pp.197-217
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• 2014

In my previous papers, I have argued that the so-called 'Uncontested Principle' does not hold for indicative conditionals based on inductive reasoning. This is mainly because if we accept that a material conditional '$A{\supset}C$' can be inferred from an indicative conditional based on inductive reasoning '$A{\rightarrow}_iC$', we get an absurd consequence such that we cannot distinguish between claiming 'C' to be probably true and claiming 'C' to be absolutely true on the assumption 'A'. However, in his recent paper "Uncontested Principle and Inductive Argument", Eunsuk Yang objects that my argument is unsuccessful in disputing the Uncontested Principle. In this paper, I show that his objections are irrelevant to my argument against the Uncontested Principle.

• Communications of Mathematical Education
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• v.8
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• pp.45-63
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• 1999

학교 수학의 궁극적인 목표는 “수학적 능력과 태도를 육성하는데 있다.” 이러한 목표를 달성하기 위해서는 수학의 기본적인 지식과 기능을 습득하는 일과 수학적으로 사고하는 능력을 기르는 일이 뒷받침되어야 할 것이다. 수학적 사고는 학교수학에서 지도되는 내용 그 자체에 관련된 것이 아니라 이들 수학을 수학내용을 이해하고 지식으로 획득하는 과정에서 행하여지는 수학적인 활동과 관련이 있다고 하겠다. 본고에서는 수학적인 활동의 방법적인 측면에서 귀납 추론, 연역 추론, 유비 추론에 대해서 개괄적으로 알아보고, 귀납 추론의 필요성 및 특성과 구체적인 적용 사례에 대해서 알아보고자 한다.

• Korean Journal of Logic
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• v.7 no.2
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• pp.121-146
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• 2004

본 논문은 베이즈주의가 확률론을 이용해서 제거적 귀납을 정교하게 발전시키고 있다고 주장한다. 이를 위해 본 논문은 두 가지 작업을 진행한다. 하나는 제거적 귀납이 무엇인가 하는것이고 다른 하나는 제거적 귀납이 베이즈주의에 기여하는 바가 무엇인가 하는 것이다. 먼저 본 논문은 제거적 귀납이 참인 가설을 포함하는 가능한 가설들의 총체로부터 경쟁가설들을 연역적 또는 귀납적으로 제거하고 남는 가설을 선택하는 추론형식임을 밝히고, 이 때 베이즈주의는 제거적 귀납을 정교하게 발전시킨 모습이기 때문에 제거적 귀납으로부터 기술적으로 도움 받을 측면은 없다고 주장한다. 그 대신 본 논문은 베이즈주의가 과학방법론으로 발전되는 데에서 직면하는 여러 가지 문제점을 해결하는 방법에 대해 제거적 귀납으로부터 조언을 얻을 수 있다고 주장한다. 이와 같은 논의를 통해 본 논문은 베이즈주의와 제거적 귀납주의의 결합은 유용한 과학방법론을 만들 수 있을 것으로 전망한다.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.461-472
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• 2015

Korean students are taught area formulas of parallelogram and triangle by inductive reasoning in current curriculum. Inductive thinking is a crucial goal in mathematics education. There are, however, many problems to understand area formula inductively. In this study, those problems are illuminated theoretically and investigated in the class of 5th graders. One way to teach area formulas is suggested by means of process of problem solving with transforming figures.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.95-113
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• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• Korean Journal of Cognitive Science
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• v.25 no.3
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• pp.233-257
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• 2014

Category-based induction is one of major inferential reasoning methods used by humans. This research tested the effect of perceived within-category variability on the inductive generalization. Experiment 1 manipulated variability by directly presenting category exemplars. After displaying low variable (low variability condition) or highly variable exemplars (high variability condition) depending on condition, participants performed inductive generalization task about a category in question. The results showed that participants have greater confidence in generalization when category variability was low than when it was high. Rather than directly presenting category exemplars in Experiment 2, participants performed induction task after they formed category variability impression by categorization task of identifying category exemplars. Experiment 2 also found the tendency that participants have greater inductive confidence when category variability was low. The variability effect discovered in this research is distinct from the diversity effect in previous research and the category-based induction model proposed by Osherson et al. (1990) cannot fully account for the variability effect in this research. Test of variability effect in category-based induction is discussed in the general discussion section.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.641-654
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• 2011

In order to grow students' rational and creative problem-solving ability which is one of the primary goals in mathematics education. students' proper understanding of mathematical concepts, principles, and rules must be backed up as its foundational basis. For the relevant teaching strategies. National Mathematics Curriculum advises that students should be allowed to discover and justify the concepts, principles, and rules by themselves not only through the concrete hands-on activities but also through inquiry-based activities based on the learning topics experienced from the diverse phenomena in their surroundings. Hereby, this paper, firstly, looks into both the meaning and the inductive reasoning process of mathematical principles and rules, secondly, suggest "learning through discovery teaching method" for the proper teaching of the mathematical principles and rules recommended by the National Curriculum, and, thirdly, examines the possible discovery-led teaching strategies using inductive methods with the related matters to be attended to.