• Korean Journal of Logic
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• v.23 no.2
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• pp.117-159
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• 2020

In the early Wittgenstein's Tractatus, both philosophy of logic and that of mathematics belong to the most crucial subjects of it. What is the philosophical view of the early Wittgenstein in the Tractatus? Did he, for example, accept Frege and Russell's logicism or reject it? How did he stipulate the relation between logic and mathematics? How should we, for example, interpretate "Mathematics is a method of logic."(6.234) and "The Logic of the world which the proposition of logic show in the tautologies, mathematics shows in equations."(6.22)? Furthermore, How did he grasp the relation between mathematical equations and tautologies? In this paper, I will endeavor to answer these questions.

• Journal of the Korea Society of Computer and Information
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• v.4 no.4
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• pp.1-8
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• 1999

In the logic where we study the principle and method of human, the binary logic with the proposition which has one-valued property that it can be assigned the truth value 'truth'or 'false'. Although most of the traditional binary logic which was drawn by human includes fuzziness hard to deal with, the knowledge for expressing it is not precise and has less degree of credit. This study uses multi-valued logic in order to slove the problem above that .When compared with the data processing ability of the binary logic, Multi-valued logic has an at a high speed. Therefore the Inference can be possible by minimization multi-valued logic in stead of using the information stead of using the information system based on the symbolic binary logic.

• Korean Journal of Logic
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• v.20 no.2
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• pp.163-196
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• 2017

Wittgenstein declares in the Tractatus Logico-Philosophicus that he resolved Russell's Paradox. According to him, a function cannot be its own argument. If we assume that a function F(fx) can be its own argument, a proposition "F(F(fx))" will be given, where the outer function F has a meaning different from the inner function F. In consequence, "F(F(fx))" will not be able to have a definite sense. Why, however, does Wittgenstein call into question a function F(fx) and "F(F(fx))"? To answer this question, we must examine closely Russell's own resolution of Russell's Paradox. Only when we can understand Russell's resolution can we do Wittgenstein's resolution. In particular, I will endeavor to show that the idea in Wittgenstein's 1913 letter to Russell provides a decisive clue for this problem.

• Korean Journal of Logic
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• v.11 no.2
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• pp.93-125
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• 2008

The radical probabilitists deny that propositions represent experience. However, since the impact of experience should be propagated through our belief system and be communicated with other agents, they should find some alternative protocols which can represent the impact of experience. The useful protocol which the radical probabilistists suggest is the Bayes factors. It is because Bayes factors factor out the impact of the prior probabilities and satisfy the requirement of commutativity. My main challenge to the radical probabilitists is that there is another useful protocol, q(E|$N_p$) which also factors out the impact of the prior probabilities and satisfies the requirement of commutativity. Moreover I claim that q(E|$N_p$) has a pragmatic virtue which the Bayes factors have not.

• 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.17 no.1
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• pp.1-32
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• 2014

Both 5.52 and 5.521 of the Tractatus Logico-Philosophicus raise several questions. In this paper I will explicate Wittgenstein's concept of generality by answering such questions. These questions and problems are closely intertwined. I will try to show what follows. It is ${\xi}$-conditions that are most decisive on the concept of generality of the Tractatus. Except Ramsey, commentators such as Anscombe, Glock, Kenny etc. failed in accurately grasping the Wittgenstein's thoughts concerning ${\xi}$-condition and their claims are not fair at all. Futhermore, from a view point of history of logic, 5.52 has very important significances. That is to say, it anticipates for the first time a possibility of infinitary logic and the concept of universe of discourse in model theory.

• Korean Journal of Logic
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• v.17 no.1
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• pp.109-136
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• 2014

Every (semantic) antirealist accepts one or another form of verification principle. The principle has strong and weak forms, the strong form being highly counterintuitive but the weak one being more plausible. Understandably, antirealists have preferred the weak form of verification principle. Unfortunately, the socalled knowability paradox shows that those two forms are indeed equivalent. To solve this problem, Edgington suggests a yet new form of verification principle. Unfortunately, her new principle has its own difficulty. To overcome this difficulty, Edgington provides a new model of knowledge, according to which every true proposition is somehow associated with a known counterfactual conditional. In this paper, I shall argue that even this new model of knowledge confronts with an insurmountable problem. It is a well-known fact that, in the microscopic levels, some facts manage to occur despite very low physical chances. I will argue that the counterfactuals linked with those facts cannot be known due to the existence of epistemic defeaters. Hence, Edgington's knowledge model does not work in all cases.

• Korean Journal of Logic
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• v.16 no.3
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• pp.407-436
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• 2013

I examine the notion of truth in the intuitionistic type theory and provide a better explanation of the objective intuitionistic conception of mathematical truth than that of Dag Prawitz. After a brief explanation of the distinction among proposition, type and judgement in comparison with Frege's theory of judgement, I examine the judgements of the form 'A true' in the intuitionistic type theory and explain how the determinacy of the existence of proofs can be understood intuitionistically. I also examine how the existential judgements of the form 'Pf(A) exists' should be understood. In particular, I diagnose the reason why such existential judgements do not have propositional contents. I criticize an understanding of the existential judgements as elliptical judgements. I argue that, at least in two respects, the notion of truth explained in this paper is a more advanced version of the objective intuitionistic conception of mathematical truth than that provided by Prawitz. I briefly consider a subjectivist's objection to the conception of truth explained in this paper and provide an answer to it.

• Korean Journal of Logic
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• v.16 no.3
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• pp.309-346
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• 2013

This paper deals with the problem, which logic of language and which metaphysics Wittgenstein suggests in the Tractatus logico-philosophicus. I will ultimately show how he bases the metaphysics on the logic of language. The logic of language by which Wittgenstein sets the limit to the language 'in the language' is the logical syntax of the language. And Wittgenstein extends the idea of the logical syntax to the understanding the nature of the world, i.e. to the metaphysics. The logical form the language(proposition) must have is the form of the world(or the nature of the world), and it can be determined only together with the logical syntax of the language. But what is the logical form(form of the world) 'cannot be said', since the proposition saying it is devoid of 'sense' and 'says nothing'. Therefore Wittgenstein expresses that the logical form(form of the world) 'can only be shown' in the proposition that has sense. The Metaphysics Wittgenstein wants to base on the logic of language(the logical syntax) must be mystical.

• Korean Journal of Logic
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• v.13 no.2
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• pp.27-59
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• 2010

After the unexpected death of the late professor Young-Jung Kim on July 28th last year, 4 pieces of paper unpublished were discovered. Those papers reveal that he had a grand program. In particular, we found that he had his own ideas and theory which he called "Presupposition Logic" and "Field Logic". In this paper, I will call his program "Presupposition Logic Program". He explored a new logic system, Presupposition Logic, in order to realize necessity and possibility of the closer relationship between logic and critical thinking. In this paper, I will expound what his "presupposition" and "Presupposition Logic" are and why he thought Presupposition Logic is necessary from a perspective of logic. And I will critically elucidate what was the problem that troubled him.