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괴델의 불완전성 정리:증명된 신화(神話)?

  • Hong, Seong-Gi
    • Korean Journal of Logic
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    • v.5 no.2
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    • pp.39-66
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    • 2002
  • 일반적으로 엄밀한 방법을 통하여 증명되었다고 말해지는 괴델의 불완전성 정리는 일련의 전제와 배경지식이 요구된다고 하겠다. 이들 중에서 무엇보다도 중요한 것은 정리의 증명에 사용되는 메타언어상의 수학적 참에 대한 개념이다. 일단 확인할 수 있는 것은 "증명도, 반증도 되지 않지만 참인 산수문장의 존재"라는 불완전성 정리의 내용에서 괴델이 가정하고 있는 수학적 참의 개념이 구문론적인 증명개념으로부터 완전히 독립되어야 한다는 점이다. 문제는 그가 가정하고 있는 수학적 참의 개념이 도대체 무엇이어야만 하겠는가라는 점이다. 이 논문은 이 질문과 관련하여 내용적으로 3부분으로 나누어 질 수 있다. I. 괴델의 정리의 증명에 필요한 전제들 및 표의 도움을 얻어 자세히 제시되는 증명과정의 개략도를 통해 문제의 지형도를 조감하였다. II, III. 비트겐슈타인의 괴델비판을 중심으로, "일련의 글자꼴이 산수문장이다"라는 주장의 의미에 대한 상식적 비판 및 해석에 바탕을 둔 모형이론에 대한 대안제시를 통하여 괴델의 정리를 증명하기 위해 필요한 산수적 참에 관한 전제가 결코 "확보된 것이 아니다"라는 점을 밝혔다. IV. 괴델의 정리에 대한 앞의 비판이 초수학적 전제에 대한 것이라면, 3번째 부분에서는 공리체계에서 생성 가능한 표현의 증명여부와 관련된 쌍조건문이 그 도입에 필수적인 괴델화가 갖는 임의성으로 인해 양쪽의 문장의 참, 거짓 여부가 서로 독립적으로 판단 가능하여야만 한다는 점에(외재적 관계!) 착안하여 궁극적으로 자기 자신의 증명여부를 판단하게 되는 한계상황에 도달할 경우(대각화와 관련된 표 참조) 그 독립성이 상실됨으로 인해 사실상 기능이 정지되어야만 한다는 점, 그럼에도 불구하고 이 한계상황을 간파할 경우(내재적 관계로 바뀜!)항상 순환논법을 피할 수 없다는 점을 밝혔다. 비유적으로 거울이 모든 것을 비출 수 있어도 자기 스스로를 비출 수 없다는 점과 같으며, 공리체계 내 표현의 증명여부를 그 체계내의 표현으로 판별하는 괴델의 거울 역시 스스로를 비출 수는 없다는 점을 밝혔다. 따라서 괴델문장이 산수문장에 속한다는 믿음은, 그 문장의 증명, 반증 여부도 아니고 또 그 문장의 사용에서 오는 것도 아니고, 플라톤적 수의 세계에 대한 그 어떤 직관에서 나오는 것도 아니다. 사실상 구문론적 측면을 제외하고는 그 어떤 것으로부터도 괴델문장이 산수문장이라는 근거는 없다. 그럼에도 불구하고 괴델문장을 산수문장으로 볼 경우(괴델의 정리의 증명과정이라는 마술을 통해!), 그것은 확보된 구성요소로부터 조합된 문장이 아니라 전체가 서로 분리불가능한 하나의 그림이라고 보아야한다. 이것은 비트겐슈타인이 공리를 그림이라고 본 것과 완전히 일치하는 맥락이다. 바론 그런 점에서 괴델문장은 새로운 공리로 도입된 것과 사실은 다름이 없다.

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Analysis of Nonlinear CA Using CLT (CLT를 활용한 비선형 CA의 분석)

  • Kwon, Min-jeong;Cho, Sung-jin;Kim, Han-doo;Choi, Un-sook;Lee, Kue-jin;Kong, Gil-tak
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.19 no.12
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    • pp.2968-2974
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    • 2015
  • Method for finding the attractors is the important object to investigate in the linear/additive CA because it is a primary interest in applications like pattern recognition, pattern classification, design of associative memory and query processing etc. But the research has been so far mostly concentrated around linear/additive CA and it is not enough to modelize the complex real life problem. So nonlinear CA is demanded to devise effective models of the problem and solutions around CA model. In this paper we introduce CLT as an upgraded version of RMT and provide the process for finding the attractors and nonreachable states effectively through the CLT.

A Qualitative Study of the Young Children's Perception of Faith (유아가 인식하는 신앙에 관한 질적 연구)

  • Kim, Sungwon
    • Journal of Christian Education in Korea
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    • v.63
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    • pp.283-315
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    • 2020
  • This study attempts to suggest the direction of Christian education for young children by analyzing concepts related to how they understand the faith. For this purpose, this researcher conducted interviews of seventeen young children who had not yet entered elementary school. Answers to ten interview questions were analyzed and research participants' understandings of belief and church were identified. The results have shown that participants consider faith to be religious practices such as prayer, praise and worship, the practice of good conduct, the key to heaven and providing direction and mission for their lives. Participants also revealed the acquisition and internalization of biblical knowledge and theological terms and listed parents, ministers or friends as the important role models of faith. They recognized the church as a place where religious practices are performed, where spiritual joy is felt and where pleasure is experienced because they do things they like. It is expected that these results would be used as the basis for future research regarding young children's faith and as the principles of the practice of it.

Meaning of Reality on Television -Focused on <THE WORLD AS PHANTOM AND AS MATRIX>, of Guünter Anders- (텔레비전에서 실재가 가진 의미 귄터 안더스의 <팬텀과 매트릭스로서의 세계>를 중심으로)

  • Shin, Shang-Ki
    • The Journal of the Korea Contents Association
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    • v.14 no.2
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    • pp.60-71
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    • 2014
  • Images of TV that crossed the reality & the virtual reality have been discussed for a long time, Then, With what feature can TV make messages of the reality & the virtual reality maintain to achieve such a target, and in which situation will the feature be exposed? One who answered first about these questions is a German critic, G$\ddot{u}$nter Anders. Anders called the reality confused with the reality and the confused world of the virtual reality Phantom, and thought human beings would live in the reproduced world created by media machine in the long run as a world that the Phantom created would be gloomy and confusing. The media, themselves, become images, and an image creates another image. Through this process, human beings became unaware of which image the reality was indeed. As TV often created these situations, we have been already seduced into the deep Phantom world before discussing right or wrong of the situation. Of course, the media reality & the reality can't be strictly distinguished. Because the means that help to form judgement of viewers is the media. The subject of practical judgement is the media reality not human beings.

Relations among Body Shape Perception, Interpersonal Problems, and Spiritual Well-being in Late Adolescents (후기청소년의 체형 인식, 대인관계 문제 및 영적 안녕 간의 관계)

  • Lee, Haeyoung;Yoo, Hana
    • The Journal of the Korea Contents Association
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    • v.15 no.10
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    • pp.327-335
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    • 2015
  • Purpose: This study is a descriptive survey to identify the relations of body shape perception, interpersonal problems, and spiritual well-being in late adolescents. Methods: The participants are 116 late adolescents in S and K city. This study was performed using a structured questionnaire from October 12 to November 16, 2012. The collected data were analyzed by t-test, Kruskal-Wallis test, Bonferroni correction, Pearson's correlation coefficient. Results: According to general characteristics of the participants, there were significant differences in body shape perception for gender, religion, experience of weight control, current body mass index, and wanted body mass index. There were significant differences in spiritual well-being for experience of drinking and religion. There was significant negative correlation between interpersonal problems and spiritual well-being. Conclusions: Therefore, nursing interventions will be needed to improve interpersonal problems and abnormal body shape perception and to enhance spiritual well-being of adolescents.

Application of Social Network Analysis on Learner Interaction in a GBS Learning Environment (GBS 학습 환경 하에서 상호작용 연구를 위한 사회 연결망 분석 기법의 적용)

  • Jo, Il-Hyun
    • The Journal of Korean Association of Computer Education
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    • v.6 no.2
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    • pp.81-93
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    • 2003
  • The purpose of the study was to explore the potential of the Social Network Analysis as an analytical tool for scientific investigation of learner-learner, or learner-tutor interaction within an e-Learning environment. Theoretical and methodological implication of the Social Network Analysis had been discussed. Following theoretical analysis, an exploratory empirical study was conducted to test statistical correlation between traditional performance measures such as achievement and team contribution index, and the centrality measure, one of the many quantitative measures the Social Network Analysis provides. Results indicate the centrality measure was correlated with the higher order learning performance and peer-evaluated contribution indices. An interpretation of the results and their implication to instructional design theory and practices were provided along with some suggestions for future research.

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Psychosocial Experience in Post-mastectomy Women (유방완전절제술을 받은 여성의 심리사회적 경험 : 자조집단 참여자 중심으로)

  • Lee, Yoon-Soo
    • Korean Journal of Social Welfare
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    • v.59 no.3
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    • pp.99-124
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    • 2007
  • The purpose of this study is to research psychosocial experience in post-mastectomy women, who participated in self-help group, using in-depth interviews and participant observations. Until recently, studies on post-mastectomy women in psychological perspectives had been maily done by nurses, and there are only few literatures in social welfare studies. Therefore, based on phenomenological theory, the meaning and essence of "the breast" and the lived experience of post-mastectomy women, i.e. emotional distress, and as a result has been explored, it has confirmed six clusters and explained them in detail. As a result, from the subjects' experience, the essence of 'A crossroad of life and death', 'sexual-identity crisis', 'feeling mortified due to double binded messages of others', 'conflict between physical and psychological disabilities', 'feelings of gratitude or wishfulness', and 'their realistic suggestions and wishes' has been shown. It has been founded that the subjects experienced not only self-identity crisis as women but also unending internal turmoil because of their passion to live. It has been hoped that this study will help to shape government policy and social welfare services on post-mastectomy patients.

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The Effect of the Government's Entrepreneurial Support Policy on Entrepreneurship and Entrepreneurial Intention (정부의 창업지원정책이 창업가의 기업가정신 및 창업의지에 미치는 영향)

  • Park, Nam-Gue;Kim, Myung-Sook;Ko, Jong-Wook
    • Asia-Pacific Journal of Business Venturing and Entrepreneurship
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    • v.10 no.6
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    • pp.89-98
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    • 2015
  • The purpose of this study was to investigate the effect of the Government's entrepreneurial support policy(educational support, financial support and marketing support) on entrepreneurship and entrepreneurial intention. This study examined educational support, fund support and marketing support as the The Government's entrepreneurial support polity variables and innovativeness, progressiveness and risk-taking as entrepreneurship variables. The sample of this study was composed of 331 existing and potential entrepreneurs selected from the national panel of a online web survey research firm. Data were collected using self-administerd structured questionnaires and analyzed employing structural equation modelling techniques. This study found that three entrepreneurship variables(innovativeness, progressiveness and risk-taking) had positive direct effects on entrepreneurial intention and that three Government's entrepreneurial support policy variables (educational support, financial support and marketing support) had positive direct effects on entrepreneurship, whereas these three variables had positive indirect effects on entrepreneurial intention. The theoretical and practical implications of the findings were discussed and the directions for future research were suggested.

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Perception of Drinking Water and Water Environment among Housewives in Gumi City Area (구미 지역 주부들의 먹는 물과 물 환경에 대한 인식)

  • Cheong, Cheol;Park, Hye-Gyoung
    • Journal of Science Education
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    • v.32 no.1
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    • pp.73-84
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    • 2008
  • The purpose of this study was to elucidate the perception of drinking water and water environment held by housewives in Gumi city area. The subject of this study were 20 housewives and surveyed with a questionnaire on a self-reporting basis. Results are as follows: 1. Housewives were concerned about drinking water and water environment as natural resource affecting Gumi city area. The percentage og the housewives who had used the purified tap water and the boiled water as drinking water was 35% and 30%, respectively. Also, The percentage of the safety of tap water was 75%. However, their perceived level about the safety of drinking water was relatively low. 2. Housewives suggests that a drinking water conservation campaign and active participation may be more effective if it is linked to local community. Furthermore, continuous education about drinking water and water environment promoting perception of tap water as drinking water.

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Analysis of In-Service Status and Educational Needs of Engineering Faculties (공과대학 교수들의 공학교육 연수실태와 교육요구 분석)

  • Kim, Jin-Soo;Choi, Yu-Hyun;Kim, Su-Kyung
    • Journal of Engineering Education Research
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    • v.11 no.2
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    • pp.50-64
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    • 2008
  • The final goal of this study is to develop the in-service program of engineering education for professors of engineering college. In this study, survey research method using questionnaire was used to engineering professors of universities and junior colleges. The study contents were analysis of in-service status and educational needs for professors of engineering college. Statistical package SPSS for windows, korean edition version 10.0, was used for analysing data. To do it, 97 questionnaire were used finally. Educational needs was divided into engineering teaching method, engineering evaluation method, and engineering basic competancy. Equation suggested by Borich was induced to calculate the educational needs. Results were that educational needs of engineering teaching method and engineering basic competency were high, respectively, but, educational needs of engineering evaluation method was low. It was known that we need to consider the results during in-service program development.