• Korean Journal of Logic
• /
• v.14 no.3
• /
• pp.101-137
• /
• 2011

Based on his analysis of judgement forms in intuitionistic type theory, Martin-L$\ddot{o}$f claims that the usual logical laws and interesting mathematical judgements are synthetic, not analytic. He further claims that the logic of analytic judgements is decidable and complete, while the logic of synthetic judgements is undecidable and incomplete. The aim of this article is to clarify and examine his claims. In section 1, I explain and give some comments on the monomorphic version of intuitionistic type theory. In section 2, after clarifying Martin-L$\ddot{o}$f's distinction between analytic and synthetic judgements, I examine some possible objections to it and evaluate the thesis that the usual logical laws and interesting mathematical judgements are synthetic. In section 3, I clarify and examine the thesis that the logic of analytic judgements is decidable and complete, while the logic of synthetic judgements is undecidable and incomplete.

• Journal of Educational Research in Mathematics
• /
• v.26 no.3
• /
• pp.565-581
• /
• 2016

Intuition in the mathematical problem solving has been stressed the importance with the logic because intuition is the cognition that give significant clue or idea to problem solving. Fischbein classified intuition by the origin; primary intuition and secondary intuition And he said the role of the personal experience and school education. Through these precedent research, we can understand the social influence. This study attempt to investigate social intuition model of Haidt, moral psychologist that has surfaced social property of intuition in terms of the mathematical problem solving. The major suggestions in problem solving and the education of intuition are followed. First, I can find the social property of intuition in the mathematical problem solving. Second, It is possible to make the mathematical problem solving model by transforming the social intuitionist model. Third, the role of teacher is important to give the meaningful experience for intuition to their students. Fourth, for reducing the errors caused by the coerciveness and globality of intuition, we need the education of checking their own intuition. In other words, we need intuition education emphasized on metacognition.

• Korean Journal of Logic
• /
• v.14 no.1
• /
• pp.1-23
• /
• 2011

I take the position of the thirders on the sleeping beauty problem like Elga and criticize Lewisian halfers. In particular, I attack Franceschi's recent arguments for the halfers. In addition, I claim that Bostrom's and Kim's hybrid view is not satisfactory, because it is to pre-empt or to take the burden of proof that the problem is the genuine paradox. Consequently, the purpose of this paper is to show that the thirders' argument is more intuitive than others and what the fallacies of the halfer's arguments are.

• Korean Journal of Logic
• /
• v.22 no.2
• /
• pp.233-251
• /
• 2019

In this paper, I raise objections to Sungsu Kim's argument that Sartorio's hard-line reply to the manipulation argument fails. In attacking Sartorio's argument, Sungsu Kim claims that there are two problems with Sartorio's. I argue that Sungsu Kim's argument fails by responding to these two problems. With respect to the first problem, I provide a new example of dilution of responsibility. With respect to the second problem, I argue that, contrary to what Sungsu Kim assumes, for Sartorio's argument to succeed, our intuition that Ernie is responsible in the Lightning Strike Scenario does not have to be as strong as our intuition that Ernie is not responsible in the Diana scenario.

• Korean Journal of Logic
• /
• v.22 no.3
• /
• pp.351-395
• /
• 2019

Hempel's original intuitions about the raven's paradox are summed up in three ways. The first is known as the paradoxical conclusion: If one observes that an object a - about which nothing is antecedently known - is a non-black non-raven, then this observation confirms that all ravens are black. The second is an intuitive verdict of the misled conclusion of the paradox: If one observes that an object a - which is known to be a non-raven - is non-black (hence, is a non-black non-raven), then this observation does not confirmationally affect that all ravens are black. The third is a comparative claim between the two intuitions: the degree of confirmation appearing in the first intuition is greater than the degree of confirmation in the second intuition. The Standard Bayesian Solution of the paradox is evaluated to fleshed Hempel's intuitions out by establishing the first intuition. However, such an evaluation of this solution should be further analyzed because Hempel's intuition is not the only one. The solution of paradox does not establish the second intuition in a strict sense. However, I think the Bayesian solution will establish the second intuition based on its typical strategy of quantitative vindication. If only quantitative vindication is accepted, this evaluation of the solution remains valid. Nevertheless, the solution fails to establish the third intuition. In this article, I propose a new way to apply the Bayesian method to establish Hempel's intuitions, including the third intuition. If my analysis is correct, the Standard Bayesian Solution of the raven's paradox could indeed flesh Hempel's intuitions out by denying one of the assumptions considered essential.

• Korean Journal of Logic
• /
• v.22 no.1
• /
• pp.87-124
• /
• 2019

A dialetheic approach to the sorites paradox is to understand a borderline case as a true contradiction. In order to accommodate this approach, the possibility of an alternative that does not involve a contradiction should be considered first. Beall presents an alternative that has all virtues of dialetheic solution without contradiction. I do not think his alternative has no contradiction. Using the inclosure schema I will show it. Furthermore, I will show that all alternatives which do not accept the existence of cut-off point imply a contradiction. This means that we have to accept a true contradiction as long as we accept the intuition of vagueness, especially, what is called 'tolerance'.

• Korean Journal of Logic
• /
• v.17 no.1
• /
• pp.33-70
• /
• 2014

We still do not know against what histocial/philosophical background and motivation was Tarski's definition of logical consequence introduced, even if it has had such a strong influence. In view of the centrality of the notion of logical consequence in logic and philosophy of logic, it is rather shocking. There must be various intertwined reasons to blame for this uncomfortable situation. There has been remarkable progress achieved recently on the history of analytic philosophy and modern logic. In view of the recent developments of the controversies involved, however, we will have to wait years to resolve all this uneasiness. In this gloomy situation, Douglas Patterson's recent study of Tarski's philosophy of language and logic seems to have the potential to turn out to be a ground breaking achievement. [Patterson (2012)] This article aims at reporting the state-of-the-art in this problem area, and fathoming the future directions of research by examining critically some unclear components of Patterson's study.

• Journal for History of Mathematics
• /
• v.25 no.3
• /
• pp.29-39
• /
• 2012

As a product of modern proof theory, linear logic is a new form of logic developed for the purpose of enhancing programming language by Professor Jean-Yves Girard of Marseille University (France) in 1987 by supplementing intuitionist logic in a sophisticated manner. Thus, linear logic' s connectives can be explained using information processing terms such as sequentiality and parallel computation. For instance, A${\otimes}$B shows two processes, A and B, carried out one after another. A&B is linked to an internal indeterminate, allowing an observer to select either A or B. A${\oplus}$B is an external indeterminate, and as such, an observer knows that either A or B holds true, but does not know which process will be true. A ${\wp}$ B signifies parallel computation of process A and process B; linear negative exhibits synchronization, that is, in order for the process A to be carried out, both A and $A^{\bot}$ have to be accomplished simultaneously. Since the field of linear logic is not very active in Korea at present, this paper deals only with syntax aspect of linear logic in order to arouse interest in the subject, leaving semantics and proof nets for future studies.

• Korean journal of communication and information
• /
• v.54
• /
• pp.76-97
• /
• 2011

What are the meanings of abduction as a methodology of Cultural Studies? By contextualizing Charles Sanders Peirce's logic of abduction in the discipline of Cultural Studies, I explore the epistemological discussion on the modern scientific research methodology of social sciences. Abduction is a kind of logical inference, which is often associated with guessing or intuition. Peirce's method of abduction and Cultural Studies' contextual formation in effect address an alternative methodology to positivism. Criticizing the modern Eurocentric structure of knowledge construction, I suggest that the virtue of abduction, as a logic of discovery, should be re-discovered in the context of Cultural Studies. Abduction holds important lessons for Cultural Studies as well as social sciences in general because of its focus on intuition, empathy, and intellectual collaboration. Through its elaboration of the logic of abduction, Cultural Studies is able to maintain not only its epistemological ground but also its methodological communicability.

• Journal for History of Mathematics
• /
• v.12 no.1
• /
• pp.32-44
• /
• 1999

This paper is a sequel to [8]. Development of modern logic was initiated by Boole and Morgan. Boolean logic is one of their completed works. Cantor created the set theory along with cardinal and ordinal numbers. His theory on infinite sets brought about a remarkable development on modern mathematical theory, but generated many paradoxes (e.g. Russell Paradox) that in turn motivated mathematicians to solve them. Further, mathematicians attempted to construct sound foundations for Mathematics. As a result three important schools of thought were formed in relation to fundamentals of mathematics for the resolution of paradoxes of set theory, namely logicism developed by Russell and Whitehead, intuitionism lead by Brouwer and formalism contended by Hilbert and Bernays. In this paper, we examine the logic for intuitionism which is originated by Brouwer in 1908 and study Heyting algebra.