Metamathematical problems

1973 ◽  
Vol 38 (3) ◽  
pp. 500-516 ◽  
Author(s):  
Abraham Robinson

When a logician approaches the world of mathematics, he may have in mind one or more of several purposes. He may try to find in mathematics a framework for formalizing commonly accepted laws of thought or perhaps laws of thought that are not commonly accepted. He may want to assist the mathematician by providing him with firm foundations for his theories. But it may also be the case that the logician wishes to use his own characteristic tools—formalized languages, explicit relations between symbols and objects, rigidly expressed and controlled rules of deduction—in order to gain a better understanding of the various and variegated kinds of structures, methods, theories and theorems that are to be found in mathematics. We may then expect him to adopt the attitude of the physicist or psychologist who (whatever his professed philosophy) feels that he deals with phenomena of the external world, whose rules cannot be imposed by him arbitrarily. He, or those that come after him, may indeed use the understanding thus gained in order to modify these phenomena, but as a scientist he would not regard this possibility as his only justification.For many years now, I have concentrated on the third of the lines of approach sketched above, and it seemed natural that I should discuss it again on the present occasion. However, today I do not wish to emphasize past developments but, using some of them as a background, I propose to enumerate a number of open problems. These problems seemed to me of some interest not only for their own sake but also because their solution might well require weapons whose introduction would close definite gaps in our armory.

2020 ◽  
Vol 70 (S) ◽  
pp. 71-83
Author(s):  
Grzegorz W. Kolodko

AbstractIn the era of irreversible globalisation, the worldwide economic and political rules of play must take into account of the growing importance of China. Rather than fight the country, one should pragmatically cooperate on solving the mounting global problems. Contemporarily, both China should adapt to the external world and the world itself should adapt to China. There is no possibility of imposing on it a model developed elsewhere, especially that these days liberal democracy is experiencing a systemic crisis in many countries. Neither is there a chance to impose the Chinese model on others, though it seems tempting to a country; it is not an exportable ‘commodity,’ but its elements may prove useful elsewhere. China is not aiming for global domination; instead, it is consistently integrating with the world to maintain its own development. The only reasonable way forward is thorough observation, mutual learning and pragmatic collaboration based on the non-orthodox economic thought.


2006 ◽  
pp. 75-92 ◽  
Author(s):  
S. Moiseev

The number of classical banks in the world has reduced. In the majority of countries the number of banks does not exceed 200. The uniqueness of the Russian banking sector is that in this respect it takes the third place in the world after the USA and Germany. The paper reviews the conclusions of the economic theory about the optimum structure of the banking market. The empirical analysis shows that the number of banks in a country is influenced by the size of its territory, population number and GDP per capita. Our econometric estimate is that the equilibrium number of banks in Russia should be in a range of 180-220 units.


2006 ◽  
pp. 126-134
Author(s):  
L. Evstigneeva ◽  
R. Evstigneev

“The Third Way” concept is still widespread all over the world. Growing socio-economic uncertainty makes the authors revise the concept. In the course of discussion with other authors they introduce a synergetic vision of the problem. That means in the first place changing a linear approach to the economic research for a non-linear one.


2020 ◽  
pp. 49-81
Author(s):  
Bruno Van der Maat

The current pandemic has seen some adverse reactions from the most diverse religious groups all over the world to government regulations. After having described some of their manifestations, this contribution analyzes what the Bible and some post biblical (patristic and Talmudic) traditions say about illness and pandemics. As it is ascertained that these sources contain very limited material on these subjects, the third part of this article proposes some ethical reflections regarding the official response to the pandemic as well as some pastoral implications. Key Words: Pandemic, Religion, Bible, Talmud, Pastoral Care.


Author(s):  
Larisa V. Kalashnikova

The article enlightens the probem of nonsense and its role in the development of creative thinking and fantasy, and the way how the interpretation of nonsense affects children imagination. The function of imagination inherent to a person, and especially to a child, has a powerful potential – to create artificially new metaphorical models, absurd and most incredible situations based on self-amazement. Children are able to measure the properties of unfamiliar objects with the properties of known things. It is not difficult for small researchers to replace incomprehensible meanings with familiar ones; to think over situations, to make analogies, to transfer signs and properties of one object to another. The problem of nonsense research is interesting and relevant. The element of the game is an integral component of nonsense. In the process of playing, children cognize the world, learn to interact with the world, imitating the adults behavior. Imagination and fantasy help the child to invent his own rules of the game, to choose language elements that best suit his ideas. The child uses the learned productive models of the language system to create their own models and their own language, attracting language signs: words, morphs, sentences. Children’s dictionary stimulates word formation and language nomination processes. Nonsense-words are the result of children’s dictionary, speech errors and occazional formations, presented in the form of contamination, phonetic transformations, lexical substitution, implemented on certain models. The first two models are phonetic imitation and hybrid speech, based on the natural language model. The third model of designing nonsense is represented by words that have no meaning at all and can be attributed to words-portmonaie. Due to the flexibility of interframe relationships and the lack of algorithmic thinking, children can not only capture the implicit similarity of objects and phenomena, but also create it through their imagination. Interpretation of nonsense is an effective method of developing imagination in children, because metaphors, nonsense as a means of creating new meanings, modeling new content from fragments of one’s own experience, are a powerful incentive for creative thinking.


Author(s):  
Pavel Gotovetsky

The article is devoted to the biography of General Pavlo Shandruk, an Ukrainian officer who served as a Polish contract officer in the interwar period and at the beginning of the World War II, and in 1945 became the organizer and commander of the Ukrainian National Army fighting alongside the Third Reich in the last months of the war. The author focuses on the symbolic event of 1961, which was the decoration of General Shandruk with the highest Polish (émigré) military decoration – the Virtuti Militari order, for his heroic military service in 1939. By describing the controversy and emotions among Poles and Ukrainians, which accompanied the award of the former Hitler's soldier, the author tries to answer the question of how the General Shandruk’s activities should be assessed in the perspective of the uneasy Twentieth-Century Polish-Ukrainian relations. Keywords: Pavlo Shandruk, Władysław Anders, Virtuti Militari, Ukrainian National Army, Ukrainian National Committee, contract officer.


Author(s):  
Isao Okayasu ◽  
Chi-Ok Oh ◽  
Duarte B Morais

Running is one of the most popular activities in the world. Runners’ attitudes and behaviors vary depending on their running style. This study aims to construct different measures of running specialization based on the theory of specialization. This study also tests a runner’s stage of specialization segmentation based on recreation specialization and examines the predictive relationship between a runner’s specialization and event attachment. Three groups of sampling data assess the performance of diverse specialization measures for running in three marathon events. First, two surveys were conducted with marathon participants to assess the performance of diverse specialization measures for runners. Second, the third dataset was used to examine the relationship between a runner’s recreation specialization and event attachment.The study results showed that the 15 measures of specialization showed a good fit to the data. Our research showed how runners’ recreation specialization is connected to their event attachment. In addition, this study suggested event management for subdivisions of runners. Its practical implication is that recreation specialization for running can help us understand event attachment.


2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Siluvai Raja

Education has been considered as an indispensable asset of every individual, community and nation today. Indias higher education system is the third largest in the world, after China and the United States (World Bank). Tamil Nadu occupies the first place in terms of possession of higher educational institutions in the private sector in the country with over 46 percent(27) universities, 94 percent(464) professional colleges and 65 percent(383) arts and science colleges(2011). Studies to understand the profile of the entrepreneurs providing higher education either in India or Tamil Nadu were hardly available. This paper attempts to map the demographic profile of the entrepreneurs providing higher education in Arts and Science colleges in Tamil Nadu through an empirical analysis, carried out among 25 entrepreneurs spread across the state. This paper presents a summary of major inferences of the analysis.


2019 ◽  
Vol 29 (5) ◽  
pp. 135-150

The springboard for this essay is the author’s encounter with the feeling of horror and her attempts to understand what place horror has in philosophy. The inquiry relies upon Leonid Lipavsky’s “Investigation of Horror” and on various textual plunges into the fanged and clawed (and possibly noumenal) abyss of Nick Land’s work. Various experiences of horror are examined in order to build something of a typology, while also distilling the elements characteristic of the experience of horror in general. The essay’s overall hypothesis is that horror arises from a disruption of the usual ways of determining the boundaries between external things and the self, and this leads to a distinction between three subtypes of horror. In the first subtype, horror begins with the indeterminacy at the boundaries of things, a confrontation with something that defeats attempts to define it and thereby calls into question the definition of the self. In the second subtype, horror springs from the inability to determine one’s own boundaries, a process opposed by the crushing determinacy of the world. In the third subtype, horror unfolds by means of a substitution of one determinacy by another which is unexpected and ungrounded. In all three subtypes of horror, the disturbance of determinacy deprives the subject, the thinking entity, of its customary foundation for thought, and even of an explanation of how that foundation was lost; at times this can lead to impairment of the perception of time and space. Understood this way, horror comes within a hair’s breadth of madness - and may well cross over into it.


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