• Korean Journal of Logic
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• v.22 no.1
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• pp.151-182
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• 2019

According to the realization criterion that distinguishes deductive argument from inductive argument, the realized necessity relation between the premises and the conclusion defines deductive argument. In this case, 'invalid deductive argument' is an oxymoron. According to the intention criterion, the intended necessity relation between the premises and the conclusion defines deductive argument. In this case, 'invalid deductive argument' is not an oxymoron. In this paper, we will argue for the intention criterion. The realization criterion cannot classify an elliptical argument without referring to the intention represented in the argument. It cannot distinguish an argument from a set of propositions that is not an argument either. On the other hand, the problem that an intention may not be recognized in an argument can be resolved by referring to the principle of charity. Moreover, by distinguishing the expressions showing the conviction or the attitude to the argument from the intention of the argument, we conclude that the intention criterion successfully distinguishes deductive argument from inductive argument.

• 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.

• Korean Journal of Logic
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• v.23 no.1
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• pp.25-53
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• 2020

Hong and Yeo choose the intention criterion instead of the realization criterion for distinguishing deductive and inductive argument in their paper. This study aims to criticize their argument. I contend that their argument confuses argument reconstruction and argument classification[evaluation], and is making the mistake of utilizing the realization criterion when attempting to make up for the difficulties of the intention criterion. Also, most logicians, including Hong and Yeo, support the division of the argument into deductions, inductions, and bad arguments. Here I insist on a binary division of only deduction and induction. Finally, I argue that there is no need to teach the distinction between deduction and induction when teaching logic.

• Journal of Korean Philosophical Society
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• v.141
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• pp.187-202
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• 2017

The aim of this paper is to clarify the difference between the concept of deduction-induction and Aristotle's concept of syllogismos-epagoge. First, Aristotle does not use the expression 'invalid syllogismos'. But a valid deduction is distinguished from a invalid deduction in modern logic. Second, from Aristotle's point of view syllogismos is paralleled by epagoge. Because syllogismos is equivalent to epagoge in logical form. But a disturbing lack of parallelism exists between deduction and induction by which the standards for establishing inductive conclusions are more demanding than those for deductive ones. Third, instructors in introductory logic courses ordinarily stress the need to evaluate arguments first in terms of the strength of the conclusion relative to the premises. Accordingly, students may be told to assume that premises are true. But Aristotle does not assume that premises are true. A syllogismos start from the conceptually true premise and a epagoge start from the empirically true premise.

• The Mathematical Education
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• v.26 no.1
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• pp.11-19
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• 1987

The purpose of this research is to investigate the strategies for problem solving used by teachers and students and obtain some information which would be useful to enhance the ability of problem solving of the students. For this purpose we apply the thinking aloud method to study 6 graders and 6 teachers who were asked to solve 5 word problems. And we create a coding system to analyze those strategies. Using this coding system, we code the examinees and problems. we come up with the following facts from our study. (1) The number of strategies used by teachers is less than that used by students. (2) The characteristic of the strategies used by students is to set up an equation. (3) There is deep relationship between understanding the question and choosing the successful strategies for problem solving. (4) The students use the inductive argument more often than the teachers in the case of nonroutine mathematical problem. (5) The student of high success rate have fewer strategies than the others. From the above facts. it proposes the following conclusion for the enhancement of the ability of problem solving: So far the teachers usually use a few typical strategies for problem solving. But they need to create various strategies for pqoblem solving. It makes it possible for the students to choose proper strategies according to their ability. The students need to be given nicely constructed problem with enough time.

• Progress in Superconductivity
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• v.1 no.1
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• pp.20-25
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• 1999

We constructed a high-$T_c$ scanning SQUID microscope (SSM) operating in the liquid nitrogen. We used a washer-type YBCO SQUID with inner and outer dimensions of $12{\mu}m$ and $36{\mu}m$, respectively, which was grown on the $SrTiO^3$ bicrystal substrate. The sample, rather than SQUID, was scanned using two stepping motors. We also developed readout electronics, stepping motor controller, and the software for system control and data display. We took images of various samples using our SSM and found that the spatial resolution is about $40{\mu}m$ and noise level is lower than $10^{-7}T/{\surd}Hz$ at 100 Hz and higher at lower frequencies. The noise level was much higher than that of a typical SQUID due to the other coupling from the electric parts. We present a simple argument on the inductive coupling between the sample and the SQUID which should be under-stood for the proper interpretation of the obtained images. By comparing the measured data with the simulation results the gap between the SQUID and the sample is estimated to be $40{\mu}m$.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1163-1184
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• 2007

In this presentation dedicated to the tricentennial birth anniversary of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707-1783), we begin by remarking about the so-called Basler problem of evaluating the Zeta function ${\zeta}(s)$ [in the much later notation of Georg Friedrich Bernhard Riemann (1826-1866)] when s=2, which was then of vital importance to Euler and to many other contemporary mathematicians including especially the Bernoulli brothers [Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)], and for which a fascinatingly large number of seemingly independent solutions have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. We then investigate various recent developments on the evaluations and representations of ${\zeta}(s)$ when $s{\in}{\mathbb{N}}{\backslash}\;[1],\;{\mathbb{N}}$ being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ${\zeta}(2n+1)(n{\in}{\mathbb{N}})$ which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ${\zeta}(3)$ can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger $Ap\'{e}ry$ (1916-1994) in his proof of the irrationality of ${\zeta}(3)$. Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.

• Korean Journal of Logic
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• v.15 no.2
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• pp.223-250
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• 2012

The reference-class problem is known as a problem that frequentism on the nature of probability is supposed to encounter. Alan H$\acute{a}$jek argues that other theories on the nature of probability also meet this problem inevitably and claims that we can resolve the problem by regarding conditional probabilities as primitive. In this paper I shall present an adequate way of understanding the reference-class problem and its philosophical implications by scrutinizing his argument. H$\acute{a}$jek's claim is to be classified into the following two: (i) probability is relative to its reference class and (ii) what is known as the 'Ratio' analysis of conditional probability is wrong. H$\acute{a}$jek believes that these two are to be closely related but I believe these two should be separated. Moreover, I shall claim that we should accept the former but not the latter. Finally, regarding the identity condition of reference class I shall distinguish the extensional criterion from the non-extensional one. I shall claim that the non-extensional criterion is the right one for the identity condition of reference class by arguing that the reference-class problem should be regarded as an instance of the qua-problem.

• Journal of the Korean earth science society
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• v.30 no.6
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• pp.759-772
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• 2009

The purpose of this study was to understand characteristics of eighth graders' conclusions presented in their self-directed scientific inquiry reports. We developed a framework, Analysis of Conclusions of Self-Directed Scientific Inquiry, to analyze students' conclusions. We then compared the conclusions with the inquiry questions students generated to find out whether the questions affected students' conclusions. In addition, we analyzed students' responses from the survey about their perceptions of drawing conclusions. According to the results, the conclusions were characterized into two categories, i.e., scientific basic assumption and scientific explanation. Almost half of the students' conclusions fall under the scientific basic assumptions. Most of the scientific explanations were deductive explanations and inductive explanations. Then, the kinds of conclusions were affected by the inquiry questions because the scientific explanations were made more than the scientific basic assumptions in answering the inquiry questions. Some students couldn't recognize differences between conclusions and experiment results.