• School Mathematics
• /
• v.18 no.4
• /
• pp.839-856
• /
• 2016

In 2009 revision and 2015 revision mathematics national curriculum, 'proof' was moved to high school from middle school in consideration of the cognitive development level of students, and 'proof by contradiction' was stated in the "success criteria of learning contents" of the first year high school subject while it had been not officially introduced in $7^{th}$ and 2007 revision national curriculum. Proof by contradiction is known that it induces a cognitive conflict due to the unique nature of rather assuming the opposite of the statement for proving it. In this article, based on the logical, mathematical and historical analysis of Proof by contradiction, we looked about the introductions and the applications of the current textbooks which had been revised recently, and searched for improvement measures from the viewpoint of discovery, explanation, and consilience. We suggested introducing Proof by contradiction after describing the discovery process earlier, separately but organically describing parts necessary to assume the opposite and parts not necessary, disclosing the relationships with proof by contrapositive, and using the viewpoint of consilience.

• Journal of the Korea Safety Management & Science
• /
• v.17 no.2
• /
• pp.215-228
• /
• 2015

A creative innovation and an innovative problem-solving of industrial companies can be achieved by overcoming the challenges of technical and physical contradictions. The approaches to address conflicting and paradoxical problems, such as technical and physical contradictions have a crucial role in advancing the quality assessment for manufacturer and service provider. The term, technical contradiction, depicts the state that improvement of one ends of IFR (Ideal Final Result) leads to unfavorable condition of the other ends, and results in conflicting problem. Another type of contradictions that's discussed in this study is a physical contradiction which is due to two mutually opposing states of the means of ends, and gives paradoxical situation. By integrating the means-ends chain perspectives, the physical contradiction that is a specifically root-causes, "means", can be initially addressed to resolve the downstream problem of technical contradiction which represents a general and abstract goals, "ends". This research suggests IFR resolution processes to handle both physical contradiction of means and technical contradiction of ends by employing causal relationship with IFR, effects and causes. In summary, the study represents three major processes that resolve such contradictions are demonstrated as follows: 1) Derivation of causal and hierarchical relationship among IFR, ends and means by considering CAED (Cause-And-Effect Diagram) and LT (Logic Tree). 2) Identification of causal relationship between physical contradiction and technical contradiction by using TPCT (TRIZ Physical Contradiction Tree) and TCD (Technical Contradiction Diagram). 3) Application of integrated TRIZ principles by classifying 40 inventive principles into 4 general conditions of the separation principle of mutually opposite states in space, in time, based on conditions, and between the parts and the whole. In order to validate the proof of proposed IFR resolution processes, the analysis of the TRIZ case studies from National Quality Circle Contest in the years, 2011 to 2014 have been proposed. The suggested guidelines that are built based on TRIZ principles can uniquely enhance the process of quality innovation and assessment for quality practitioners.

• Membrane Journal
• /
• v.25 no.4
• /
• pp.367-372
• /
• 2015

In pressure-retarded osmosis (PRO) and forward osmosis (FO) processes, solvent (permeate) flux depends on which surface the draw solution faces. There are two operation modes. PRO mode indicates that the active layer faces the draw solution, and FO mode means that the porous substrate fronts the draw stream. It is often observed that the PRO mode produces higher flux than that of FO under the same operating conditions. The current work uses the method of proof by contradiction, and mathematically proves the intrinsic flux inequality between the two modes.

• Korean Journal of Logic
• /
• v.20 no.2
• /
• pp.241-271
• /
• 2017

Dialetheism is the view that there exists a true contradiction. This paper ventures to suggest that Priest's argument for Dialetheism from $G{\ddot{o}}del^{\prime}s$ theorem is unconvincing as the lesson of $G{\ddot{o}}del^{\prime}s$ proof (or Rosser's proof) is that any sufficiently strong theories of arithmetic cannot be both complete and consistent. In addition, a contradiction is derivable in Priest's inconsistent and complete arithmetic. An alternative argument for Dialetheism is given by applying $G{\ddot{o}}del$ sentence to the inconsistent and complete theory of arithmetic. We argue, however, that the alternative argument raises a circularity problem. In sum, $G{\ddot{o}}del^{\prime}s$ and its related theorem merely show the relation between a complete and a consistent theory. A contradiction derived by the application of $G{\ddot{o}}del$ sentence has the value of true sentences, i.e. the both-value, only under the inconsistent models for arithmetic. Without having the assumption of inconsistency or completeness, a true contradiction is not derivable from the application of $G{\ddot{o}}del$ sentence. Hence, $G{\ddot{o}}del^{\prime}s$ and its related theorem never can be a ground for Dialetheism.

• Journal of the Korea Safety Management & Science
• /
• v.15 no.1
• /
• pp.283-292
• /
• 2013

This paper aims to propose a new steps of hypothesis testing using analysis process and improvement process in the six sigma DMAIC. The six sigma implementation models proposed in this paper consist of six steps. The first step is to establish a research hypothesis by specification directionality and FBP(Falsibility By Popper). The second step is to translate the research hypothesis such as RHAT(Research Hypothesis Absent Type) and RHPT(Research Hypothesis Present Type) into statistical hypothesis such as $H_0$(Null Hypothesis) and $H_1$(Alternative Hypothesis). The third step is to implement statistical hypothesis testing by PBC(Proof By Contradiction) and proper sample size. The fourth step is to interpret the result of statistical hypothesis test. The fifth step is to establish the best conditions of product and process conditions by experimental optimization and interval estimation. The sixth step is to draw a conclusion by considering practical significance and statistical significance. Important for both quality practitioners and academicians, case analysis on six sigma projects with implementation guidelines are provided.

• The Korean Society of Law and Medicine
• /
• v.14 no.2
• /
• pp.143-172
• /
• 2013

In order to achieve the purpose of treatment for patients by a doctor, the instruction explanation obligation, which means that he should give patients the description in more details to prepare for postoperative sequelae or complications, is common with the advice explanation obligation as a doctor should ex-plain some information to patients. Since the advice explanation obligation is the benefit and protection of the law for self determination right, but the instruction explanation obligation is one for the integrity of body and life, one can be distinct from the other. Judgments giving the instruction on the concept of instruction explanation obligation, specific methods of implementation and a range of compensation for damage are recently being made by courts at all levels including the Supreme Court. It is the time to systematize them. The contents which have been mainly discussed so far include the essence of above mentioned instruction explanation obligation. However, when the tendency of practice is considered, the efforts are required to admit the organic relevance between instruction explanation obligation and advice explanation obligation and to explain the relationship without any contradiction. For whereabouts of li-ability of proof, patients theoretically demonstrate the failure to implement it. However, when the theoretical consistency is maintained, it is likely to fail the intent to recognize the instruction explanation obligation and it may ask patients to prove something impossible to be proven. Thus, these things should be considered. Moreover, as the instruction explanation obligation is associated with medicine instruction obligation of a pharmacist and the coverage is being extended, it is the time to require the systematic study on the theoretical limit.