• Journal for History of Mathematics
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• v.22 no.3
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• pp.1-30
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• 2009

Frege's logicism has been frequently regarded as a development in number theory which succeeded to the so called arithmetization of analysis in the late 19th century. But it is not easy for us to accept this opinion if we carefully examine his actual works on real analysis. So it has been often argued that his logicism was just a philosophical program which had not contact with any contemporary mathematical practices. In this paper I will show that these two opinions are all ill-founded ones which are due to the misunderstanding of the theoretical place of Frege's logicism in the context of contemporary mathematical practices. Firstly, I will carefully examine Cantorian definition of real numbers and Frege's critiques of it. On the basis of this, I will show that Frege's aim was to produce the purely logical definition of ratios of quantities. Secondly, I will consider the mathematical background of Frege's logicism. On the basis of this, I will show that his standpoint in real analysis was much subtler than what we used to expect. On the one hand, unlike Weierstrass and Cantor, Frege wanted to get such real analysis that could be universally applicable. On the other hand, unlike most mathematicians who insisted on the traditional conceptions, he would not depend upon any geometrical considerations in establishing real analysis. Thirdly, I will argue that Frege regarded these two aspects - the independence from geometry and the universal applicability - as those which characterized logic itself and, by logicism, arithmetic itself. And I will show that his conception of real numbers as ratios of quantities stemmed from his methodological maxim according to which the nature of numbers should be explained by the common roles they played in various contexts to which they applied, and that he thought that the universal applicability of numbers could not be adequately explicated without such an explanation.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.45-60
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• 2009

Mathematical thinking can be symbolized by the external signs, and these signs determine in reverse the form of mathematical thinking. Each symbol - a symbol in algebra, a symbol in analysis, and a diagram which verifies syllogism - reflects the diverse characteristic of cogitation in mathematics and perfirms a heuristic function.

• Journal of the Korean Institute of Landscape Architecture
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• v.37 no.1
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• pp.87-99
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• 2009

This research is an introductory study that hopes to interpret the cultural scenic landscape by analyzing Korea's mountains, streams, topography, color, light, human behavior, and more based on real landscape paintings. It places its purpose on understanding our intrinsic cultural scenic landscape by investigating the changed topography and the differing life patterns caused bythe active national land development after the modern era. With Seoul, which is now difficult to find images of its past, and the surrounding areas of the Han riverbed, the interpretation related to its original topography, landscape, climate, weather, and human behaviors was observed while the main focus was placed on the climate of the perception held by people regarding Mt. Geumgang and other ranges which are not fully opened to the public yet. In order to comprehensively analyze the figures of features and appearing landscapes including color, light, and more, it was described through the concept called climate. Hereupon, the real landscape paintings by Gyunjae(Jeong-Seon), mainly bearing features of existing Korean mountains, wereutilized as visual historical material. However, not having all his works, other pieces with representative characteristics were utilized such as "Gyeong-Gyo-Myeong-Seung-Chup(a painting with picturesque sceneries around old Seoul)" and "Hae-Ak-Jeon-Shin-Chup(a landscape painting including even the spirits of the seas and mountains)" which contain the regions' distinct scenery. As a result, the old cultural scenic landscapes of Korea are regarded as containing diverse mountains and where the conceptions of the treatment of mountains were reflected.

• Journal of the Korean Institute of Traditional Landscape Architecture
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• v.32 no.3
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• pp.168-182
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• 2014

Several Sungsi Gardens were built up in Old West Village during the period of the Joseon Dynasty. Most of them were painted as True-View landscape painting. This study aims at examining original locations of representative gardens of the Old West Village by empirical investigation of related True-View landscape paintings. It seeks to demonstrate the garden landscape in True-View landscape painting by utilizing ArcGIS, 3D topographic modeling to observe geographical locations and landscape more realistically. After forming 3D topographic modeling of estimated locations of the gardens, location of objects at composition of 3D modeling similar to True-View landscape painting was found by shifting viewpoints. And by overlapping the cadastral map on the modeling, we could verify the current lot number of the garden sites. The interpretation of processes and results are as follows. In the early stage, Chungpunggye garden was built at the very end of Mt. InWang valley. The site is hidden from the outside, and appeared as 'Enclosed Landscape'. In the middle stage, Chunghuigak garden was built between Okryu-dong valley and the surrounding ridge. It appeared as 'Semi-Opened Landscape'. In the late stage, Seowon garden was built at the highest level of the ridge among the research areas. It appeared as 'Prospective Landscape'. In the last period, Songsukwon garden, was built at a point of contact of the ridge end and surrounding residential area. So it appeared as 'Opened Landscape' to the town. In other words, the location, landscape and social function of the gardens in Old West Village had been gradually opened in Joseon Dynasty.

• Journal of the Korean Institute of Traditional Landscape Architecture
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• v.29 no.2
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• pp.1-18
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• 2011

This study has been examined characteristics of Yeoju Lee family, rich group at Miryang in the middle of the Joseon Dynasty, around Geumsidang(今是堂) Lee Gwang-jin remains as a cultural landscape appeared in pictures, poetry, and a strange story. Geumsidang Lee Gwang-jin returned to his old home abandoned the middle government post after the death of Moonjeong queen in socially confused stage and tried to manage an annex to a Geumsidang located in Baekgok of Eungchun riverside, and Geumsidang he managed was affected by his teacher and uncle Wolyoun Lee Tae of a view of nature, filial behavior, and nature management etc. Also, 'Painting of 12 landscapes to Geumsidang' is landscape painting with the actual view not like the '8 landscapes of So-Sang' or '8 landscapes of Sa-Si' which is abstract landscape and Lee Gyeong-hong drew 12 landscapes of Geumsidang that includes Angbong(鶯峰: nightingale peak), Yongdu mountain(龍頭山), Mubong Buddhist temple(舞鳳寺), Maam mountain(馬巖山), Wolyeon-dae(月淵臺), Saindang village(舍人堂村), Youngnam-ru(嶺南樓), Miryang eubseong(密陽邑城), Eyeonso(梨淵沼: pear tree deep water), Yullim(栗林: chestnut tree forest), Miryang river(密陽江), Sammundong fields(沙門野), land and government office owned by Yeoju Lee family as landscape objects. 'Poems of 12 landscapes to Geumsidang' by Lee Yong-gu 11th sons of Lee Gwang-jin was written based on 'Painting of 12 landscapes to Geumsidang', and sang for time, season, and changes of the weather. All 12 poems are all a quatrain with seven Chinese characters in each line consisted of all 28 words, but does not match completely with shown elements in pictures because it is not a simple description of pictures but it is recreated by writer's personality. Therefore these painting shows not only th meaning of filial behavior but also village owned by Yeoju Lee family rich group in Miryang, and these poem recreated the pictures by changing as certain scenic spot with the object of enforcing territory of Yeoju Lee family.

• Journal of the Korean Institute of Landscape Architecture
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• v.29 no.4
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• pp.12-23
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• 2001

The research focused on the landscape of mountains and hills drawn in a landscape picture. The purpose of the research is to classify patterns of landscape drawning in landscape pictures and to clarify the characteristics of the pattern by a quantitative index. We selected 21 landscape pictures to understand the Landscape Setting Here(LSH) and Landscape Setting These(LST). We investigated size quantitative indices using 1 landscape picture. The index is a follow: altitude, Visual Distance, Angles, Angle of Appearance Size, Inclination, and Angle of Incidence. The following results were obtained by using this data. 1) It has been understood that we offer an important city view because the LSH of this research can establish understanding of the city structure. 2) We dividing 3 patterns by the LST space drawn in the landscape picture. 3 patterns are Ferry point, Beauty point, an Signal-fire point. 3) We clarified the landscape characteristics of each pattern and the characteristics between patterns by using the index according to this pattern. 4) We understood the problem concerning the Seoul city landscape examining the pattern of this research with the ordinance of Seoul city. It is necessary to standardized a system of pattern classification utilized in landscape pictures to establish a universally interpreted detailed quantitative index, which can be applied to research.

• Journal of the Korean Institute of Landscape Architecture
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• v.49 no.4
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• pp.1-14
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• 2021

This study examined the techniques of creating gardens overseas using native plants from the Korean peninsula, focusing on the case of 'Das Dritte Land', an art garden created in Berlin, Germany. While Korean garden artists are recognized worldwide and are planning to globalize Korean gardens, the purpose of this study is to share information so that Korean gardeners can expand their activities and rediscover the utilization and value of plants native to the Korean peninsula. The work began as part of a project to mark the 30th anniversary of the collapse of the Berlin Wall. To realize the landscape of Korea with the motif of Inwang Jesaekdo, the geographical shape of the Baekdu-Daegan trail was reproduced with black stone, and the naturalization of Korean peninsula species was utilized in the creation of a garden Berlin. It is a surreal bio-top utopia that blooms with the bio-groups of the Korean peninsula. This study examined the process of plant survey analysis, transportation and stabilization, planting planning, composition and monitoring, and targeting the self-growth of the Korean peninsula, which is a symbol of harmony between the South and the North. The planting of Korea's native plants in overseas gardens symbolizes the uniting of the ecosystems on the Korean peninsula. The process of the Korean peninsula's young plants taking root, flowering, and spreading along Germany's previously divided border metaphorically conveys the desire for the unification of the Korean peninsula. In addition, various art programs in the garden space suggest a foundation for cultural dialogue and communication between the two Koreas. Moreover, creating gardens overseas implies that the cooperation of plant research institutes plays an important role in the transfer of plants and the maintenance of life, while the advancement of Korean gardens overseas plays an essential role in the spread of garden culture in our country.

• Korean Journal of Heritage: History & Science
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• v.56 no.2
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• pp.172-203
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• 2023

<Cheongdamdo>(true-view landscape painting) was identified in this study to be a folding screen painting painted by Jeong Seon(a.k.a. Gyeomjae, 1676~1759) in the 32nd year of King Yeongjo(1756) while exploring the Cheongdam area located in Mt. Bukhansan near Seoul. Cheongdam Byeol-eop(Korean villa), consisting of Waunru Pavilion and Nongwolru Pavilion, was a cultural and artistic base at that time, where Nakron(Confucian political party) education took place and the Baegak Poetry Society met. <Cheongdamdo> is a painting that recalls a period of autumn rainfall in 1756 when Jeong Seon arrived in the Cheongdam valley with his disciple Kim Hee-sung(a.k.a. Bulyeomjae, 1723~1769) and met Hong Sang-han(1701~1769). It focuses on the valley flowing from Insubong peak to the village entrance. The title has a dual meaning, emphasizing "Cheongdam", a landscape feature that originated from the name of the area, while also referring to the whole scenery of the Cheongdam area. The technique of drastically brushing down(刷擦) wet pimajoon(hanging linen), the expression of soft horizontal points(米點), and the use of fine brush strokes reveal Jeong Seon's mature age. In particular, considering the contrast between the rock peak and the earthy mountain and symmetry of the numbers, the attempt to harmonize yin and yang sees it regarded as a unique Jingyeong painting(眞境術) that Jeong Seon, who was proficient in 『The Book of Changes』, presented at the final stage of his excursion. 「Cheongdamdongbugi」(Personal Anthology) of Eo Yu-bong(1673~1744) was referenced when Jeong Seon sought to understand and express the true scenery of Cheongdam and the physical properties of the main landscape features in the villa garden. The characteristics of this garden, which Jeong Seon clearly differentiated from the field, suppressed the view of water with transformed and exaggerated rocks(水口막이), elaborately creating a rain forest to cover the villa(裨補林), and adding new elements to help other landscape objects function. In addition, two trees were tilted to effectively close the garden like a gate, and an artificial mountain belt(造山帶), the boundary between the outer garden and the inner garden, was built solidly like a long fence connecting an interior azure dragon(內靑龍) and interior white tiger(內白虎). This is the Bibo-Yeomseung painting(裨補厭勝術) that Jeong Seon used to turn the poor location of the Cheongdam Byeol-eop into an auspicious site(明堂). It is interpreted as being devised to be a pungsu(feng shui) trick, and considered an iconographic embodiment of ideal traditional landscape architecture that was difficult to achieve in reality but which was possible through painting.

• Journal of the Korean Institute of Landscape Architecture
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• v.41 no.6
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• pp.72-83
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• 2013

This study suggests the necessity of landscaping alternatives for the succession of Takjok(濯足) culture by considering the background and meaning of Takjok's cultural phenomenon shown in old literatures and paintings and its result is as follows. An old idiom, 'Takyoung Takjok(濯纓濯足)' implying a disinterested living attitude from the mundane world and an attitude complying with nature, has been sublimated to 'Takjokjiyu(濯足之遊)' which means living in comfortable retirement through life in seclusion(隱逸). Classical scholars immerse their feet in soft-flowing(柔軟) water for 'Mulailche(物我一體; synchronized with nature)' which is a unified condition with 'Do(道; truth)' and connected to the stage of 'Yu(遊)', a free mental state, and its nature. The cultural phenomenon of Takjok appeared in the inherited landscape paintings in the Joseon dynasty period after the late stage of Koryo. Takjok shown in 'Pal Kyung Shi'(八景詩; poetry singing for the eight scenary) was described as not a transcendent scene, but as a scenery of daily life. Dense forest and water, such as a stream with clean water, rocks, and pine trees shown in Takjok paintings have been symbolized as a seclusion space for classical scholars with higher thinking and their mental states have been more emerged. Mental pleasures called as seclusion and Takjokjiyu have been relatively emphasized in the Takjok paintings of the Joseon Dynasty period contrary to the Chinese Takjok paintings emphasizing Chung Gye(淸溪; clean stream) and Chang Rang(滄浪; high and clean wave) and strongly representing the image of 'Chung Ryu'(淸流; clean flowing water) and the veneration for antiquity. The view of nature described in the Takjok paintings represents the provision of nature as a situation and attitudes of classical scholars and implies a Taoism perspective which describes the 'do' of nature. This view of nature itself remained intact(無爲自然) with the love of mountains and water, showing a side of the zeitgeist and aesthetic consciousness of China and Joseon. The 'Takjokjiyu' of both countries has be interpreted as a symbol of personality development, behavior, life in seclusion, or transcending the mundane world and has also been accepted as a method of summer vacation in the real world. It should be considered that Takjok includes ordinary people's wisdom to resist the hot weather, as well as the classical scholar's ideal and the veneration of antiquity. From this perspective, water space, Takjok rocks, and the use of water based on the environmental supportability should be newly focused as a recreational space and it reminds us that the spirit of Takjok is a classical mental healing method.

• Journal of the Korean Institute of Traditional Landscape Architecture
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• v.35 no.1
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• pp.10-24
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• 2017

The research takes note of the formation process and settling period of Gwandong-Palkyung(關東八景, Eight Sites of Eastern Korea), the representative palgyeong(prominent eight sites) and jipgyeong(集景, landscape collection of scenic beauty), and investigates the time of formation regarding the palkyung and jipgeyong of Gwandong's scenic beauty through the analysis and interpretation of bibliographic data, and reference data. The result of the study is as follows. As the first document that records the terminology of "Gwandong-Palkyung" is "Daphongeunggil(答洪應吉)" of Yi, Hwang(李滉), Gwandong-Palkyung is inferred to be settled within the recognition of the people even before the 16th century. The geographic analysis result including "Sinjeung Donggukyeojiseungram(新增東國輿地勝覽)", Gwandong-Palkyung expanded as Gwandong-Sipkyung in early to middle of the 16th century. The first confirmed landscape collection regarding Gwandong-Palkyung in this study is confirmed in Shin Zup(申楫)'s "Yeonggwandong-Palkyung(詠關東八景)", thus, the terminology of Gwandong-Palkyung existed before 16th century at the latest. The settlement time of current "Palkyung" collection is estimated to be early 17th century at the latest. Poetries regarding Gwandong-Palkyung, and the frequency on the appearance of Gwandong scenic beauties are analyzed as making clear of the concentrated phenomenon on the sceneries of Gwandong-Palkyung. On the other hand, the collection of Gwandong-Palkyung in the domain of arts is confirmed initially in the ${\ll}$Gwandongpalkyungdobyeong(關東八景圖屛)${\gg}$ of Heo, Pil(許泌). Gwandong-Palkyung, expressed as the actual scene landscape painting shows similar tendencies of the conditions in the jipgyeong from the poetry, but the appearance rate of the painting subject was more prominent in visual solidarity and cohesion due to the reflection of the importance on icon(圖像) of the art works produced with particular meaning in the case of fixed ideal system. From late Joseon to modern times, ${\ll}$palpokbyeongpung(八幅屛風)${\gg}$ of various forms of folk painting is a corroborative evidence notifying that the cultural phenomenon of Gwandong-Palkyung has entered the universal period of embrace. Also, the 13 scenic beauties of Gangwon-Do appearing in the games of Namseungdo and Myeongseungyuramdo include Gwandong-Palkyung, which confirms the settlement of Gwandog-Palkyung even within the culture of games in late Joseon. Such results demonstrate the existence of awareness regarding Gwandong-Palkyung from the first half of the 15th century, which is presumed to have completely settled in the 17th century through the continuous development of formative process in the 16th century. Ultimately, Gwandong-Palkyung is the concrete formation of regional scenic beauties that individually gained its reputations as scenery from the Koryo Dynasty to late 17th century. Gwandong-Palkyung of the scenic beauty of Gwandong is a unique cultural scenery of the region that have germinated and formed through the process of cutting and polishing of long time to collect the best eight of scenic beauty from the many participation of sightseeing culture.