WEYL REEXAMINED: “DAS KONTINUUM” 100 YEARS LATER

2020 ◽  
Vol 26 (1) ◽  
pp. 26-79
Author(s):  
ARNON AVRON
Keyword(s):  
20Th Century ◽  
Mathematical Analysis ◽  
Foundations Of Mathematics ◽  
Mathematical Ideas ◽  
Modern System ◽  
Famous Book ◽  
Hermann Weyl ◽  
Mathematics And Physics

AbstractHermann Weyl was one of the greatest mathematicians of the 20th century, with contributions to many branches of mathematics and physics. In 1918, he wrote a famous book, “Das Kontinuum”, on the foundations of mathematics. In that book, he described mathematical analysis as a ‘house built on sand’, and tried to ‘replace this shifting foundation with pillars of enduring strength’. In this paper, we reexamine and explain the philosophical and mathematical ideas that underly Weyl’s system in “Das Kontinuum”, and show that they are still useful and relevant. We propose a precise formalization of that system, which is the first to be completely faithful to what is written in the book. Finally, we suggest that a certain set-theoretical modern system reflects better Weyl’s ideas than previous attempts (most notably by Feferman) of achieving this goal.

Reforms of Administrative Law in the PRC and Vietnam: The Possible Role of the Legal Tradition

2003 ◽  
Vol 72 (2) ◽  
pp. 253-290
Author(s):  
Karin Buhmann
Keyword(s):  
Human Rights ◽  
20Th Century ◽  
Good Governance ◽  
Administrative Law ◽  
Modern China ◽  
Executive Power ◽  
Reform Process ◽  
Legal Tradition ◽  
Late 20Th Century ◽  
Modern System

AbstractThe article takes its point of departure in administrative law and good governance as possible avenues for increased implementation of rights, including human rights. The author discusses the role that pre-modern East Asian ideas on governance and pre-modern administrative law and institutions for monitoring the executive's use of power may play for the substance and focus of the reforms of administrative law that have been undertaken in the late 20th century in the People's Republic of China (PRC) and in Vietnam. The article discusses the possible influence of ideas and institutions inspired by Confucianism and the School of Legalism, including such features as a meritocratic civil service, institutions for monitoring the executive and for dealing with complaints, instrumental use of law, and use of rewards, punishments and instruction to achieve the aims of the law. The author compares the prevalence of the features of pre-modern China and Vietnam with elements in legislation and institutions implemented under the late 20th century reform processes in the PRC and Vietnam. The article concludes that the legacy of the pre-modern system of administrative law and governance and related institutions appears to play a role in the modern reform process that is more than accidental, and that this legacy results in a relatively strong emphasis on a principle of legality in the legislation implemented under the reforms and in a relatively weaker emphasis on the principle of equality. The article suggests that features of the premodern legacy, especially the emphasis on exercise of executive power in accordance with law, may be explored as providing potential for contributing to an increased quality of public administration and an increased implementation of rule of law and specific rights, including human rights and rights of relevance to trade and investment. It is also suggested that these features of the pre-modern system may be explored by the development community and international organizations as potential for creating ownership and sustainability of governance and law reforms that are of interest to external partners of the PRC and Vietnam.

scholarly journals Istota totalitaryzmu. Wokół teorii Zbigniewa Brzezińskiego i Carla Friedricha

2021 ◽  
Vol 43 (2) ◽  
pp. 171-199
Author(s):  
Adam Wielomski
Keyword(s):  
Cold War ◽  
20Th Century ◽  
West Germany ◽  
The Political ◽  
Individual Freedom ◽  
Liberal Democratic ◽  
Famous Book ◽  
The Usa ◽  
Definition Of ◽  
The Cold War

The aim of this text is a contemporary estimation of the thesis formed in a famous book by Zbigniew Brzeziński and Carl Friedrich, Totalitarian Dictatorship and Autocracy (1956). This is a classic text of Western political science about totalitarianism, simultaneously scientific and political. Scientific, because it presents the idea of three types of political regimes in the 20th century: totalitarian, authoritarian, and liberal-democratic. Political, because the term “totalitarianism” was very useful in the time of the Cold War. This term presents the old (Nazi Germany) and new (Stalinist Russia) totalitarian states as equal political enemies of the USA, equal in their hostility to political and individual freedom, i.e. America’s creed. By using this term, the Americans can create a horrible picture of Russian communism as totalitarian, the same as Hitler’s regime, while presenting old enemies (West Germany, Italy, and Japan) as good friends of both the USA and freedom, because in this moment these states are democratic and liberal. The new term ended the old line of the delimitation between fascist or pro fascist and antifascist states and legitimates the new alliance between the USA and Franco’s Spain. The author analyses the definition of totalitarianism by Brzeziński and Friedrich as well as the political and ideological accusations made against this book by leftist critics.

Three Classical Methods to find the Cube Roots: A Connective Perspective on Lilavati, Vedic and Pande's Procedures

2021 ◽  
Vol 4 (1) ◽  
pp. 23-32
Author(s):  
Krishna Kanta Parajuli
Keyword(s):  
Comparative Study ◽  
South Asian ◽  
History Of Mathematics ◽  
The Other ◽  
Cube Root ◽  
Mathematical Ideas ◽  
Famous Book ◽  
History Of ◽  
The Comparative Study ◽  
South Asian Region

South Asian region has made a glorious history of mathematics. This area is considered as fer- tile land for the birth of pioneer mathematicians who developed various mathematical ideas and creations. Among them, three innovative personalities are Bhaskaracarya, Gopal Pande and Bharati Krishna Tirthaji and their specific methods to find cube root are mainly focused on this study. The article is trying to explore the comparative study among the procedures they adopt. Gopal Pande disagrees with the Bhaskaracarya's verse. He used the unitary method against that method mentioned in Bhaskaracarya's famous book Lilavati to prove his procedures. However, the Vedic method by Tirthaji was not influenced by the other two except for minor cases. In the case of practicality and simplicity, the Vedic method is more practical and simpler to understand for all mathematical learners and teachers in comparison to the other two methods.

From cultural historian to cultural critic: Johan Huizinga and the spirit of the 1930s

2002 ◽  
Vol 10 (4) ◽  
pp. 485-499 ◽  
Author(s):  
H. L. WESSELING
Keyword(s):  
The Netherlands ◽  
20Th Century ◽  
Middle Ages ◽  
Cultural Criticism ◽  
The World ◽  
Famous Book ◽  
Johan Huizinga ◽  
Cultural Historian ◽  
The Masses ◽  
The Middle Ages

The Dutch historian Johan Huizinga, who lived from 1872 to 1945, is considered to be one of the greatest historians of the 20th century. His work has been translated into many languages. More than 80 years after its first appearance, his most famous book, The Waning of the Middle Ages, is still read the world over and regularly reprinted. Huizinga is now mainly read and admired by historians, although his book, Homo ludens, is also appreciated by anthropologists. In the 1930s, he was even more well-known but in a different capacity: not as a cultural historian but as a cultural critic. His book, In the Shadows of Tomorrow, which appeared in 1935, was soon translated into eight languages. It was as influential as Ortega y Gasset's, The Rebellion of the Masses, and made him ‘the most famous man of the Netherlands’. This paper will describe Johan Huizinga's transition from cultural historian to cultural critic and discuss how far his cultural criticism can be seen as an example of ‘the spirit of the 1930's’.

What is Neologicism?

2006 ◽  
Vol 12 (1) ◽  
pp. 60-99 ◽  
Author(s):  
Bernard Linsky ◽  
Edward N. Zalta
Keyword(s):  
20Th Century ◽  
Set Theory ◽  
The Other ◽  
Early 20Th Century ◽  
Foundations Of Mathematics ◽  
The One

Logicism is a thesis about the foundations of mathematics, roughly, that mathematics is derivable from logic alone. It is now widely accepted that the thesis is false and that the logicist program of the early 20th century was unsuccessful. Frege's [1893/1903] system was inconsistent and the Whitehead and Russell [1910–1913] system was not thought to be logic, given its axioms of infinity, reducibility, and choice. Moreover, both forms of logicism are in some sense non-starters, since each asserts the existence of objects (courses of values, propositional functions, etc.), something which many philosophers think logic is not supposed to do. Indeed, the tension in the idea underlying logicism, that the axioms and theorems of mathematics can be derived as theorems of logic, is obvious: on the one hand, there are numerous existence claims among the theorems of mathematics, while on the other, it is thought to be impossible to prove the existence of anything from logic alone. According to one well-received view, logicism was replaced by a very different account of the foundations of mathematics, in which mathematics was seen as the study of axioms and their consequences in models consisting of the sets described by Zermelo-Fraenkel set theory (ZF). Mathematics, on this view, is just applied set theory.

scholarly journals On a Curious Chance Resemblance: Rudolf von Laban’s Kinetography and the Geometric Abstractions of Sophie Taeuber-Arp

Arts ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 15
Author(s):  
Flora L. Brandl
Keyword(s):  
20Th Century ◽  
Constitutive Relationship ◽  
Avant Garde ◽  
Visual Aesthetics ◽  
Modern System ◽  
Geometric Abstraction ◽  
Visual Artist ◽  
Dance Notation ◽  
Rudolf Von Laban ◽  
Applied Arts

This paper investigates a case of historical co-emergence between a modern system of dance notation and the rise of geometric abstraction in the applied arts during the first decades of the 20th century. It does so by bringing together the artistic careers of the choreographer Rudolf von Laban and the visual artist Sophie Taeuber-Arp. Comparing their pedagogical agendas and visual aesthetics, this paper argues that the resemblances between Laban’s Kinetography and Taeuber-Arp’s early geometric compositions cannot be a matter of pure coincidence. The paper therefore presents and supports the hypothesis of a co-constitutive relationship between visual abstraction and the dancing body in the European avant-garde.

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