scholarly journals Domestication of Mathematical Pathologies

2021 ◽  
Vol 66 (3) ◽  
pp. 709-720
Author(s):  
Jerzy Pogonowski
Keyword(s):  
Concept Formation ◽  
Research Practice ◽  
Mathematical Research ◽  
Mathematical Objects ◽  
Mathematical Ideas ◽  
Scope Of Application ◽  
Cognitive Accessibility ◽  
Creative Role

Abstract Certain mathematical objects bear the name “pathological” (or “paradoxical”). They either occur as unexpected and (temporarily) unwilling in mathematical research practice, or are constructed deliberately, for instance in order to delimit the scope of application of a theorem. I discuss examples of mathematical pathologies and the circumstances of their emergence. I focus my attention on the creative role of pathologies in the development of mathematics. Finally, I propose a few reflections concerning the degree of cognitive accessibility of mathematical objects. I believe that the problems discussed in the paper may attract the attention of philosophers interested in concept formation and the development of mathematical ideas.

EU Non-Refoulement: (The Irrelevance of) Territoriality and Pre-Border Controls

2017 ◽  
Author(s):  
Violeta Moreno-Lax
Keyword(s):  
International Human Rights Law ◽  
Eu Law ◽  
Human Rights Law ◽  
Refugee Law ◽  
Functional Understanding ◽  
Scope Of Application ◽  
International Refugee Law ◽  
Border Controls ◽  
The Eu

This chapter identifies the content and scope of application of the EU prohibition of refoulement. Following the ‘cumulative standards’ approach, the analysis incorporates developments in international human rights law (IHRL) and international refugee law (IRL). Taking account of the prominent role of the ECHR and the Refugee Convention (CSR51) as sources of Article 19 CFR, these are the two main instruments taken in consideration. The scope of application of Articles 33 CSR51 and 3 ECHR will be identified in turns. Autonomous requirements of EU law will be determined by reference to the asylum acquis as interpreted by the CJEU. The main focus will be on the establishment of the territorial reach of EU non-refoulement. The idea that it may be territorially confined will be rejected. Drawing on the ‘Fransson paradigm’, a ‘functional’ understanding of the ‘implementation of EU law’ standard under Article 51 CFR will be put forward, as the decisive factor to determine applicability of Charter provisions. The implications of non-refoulement for the different measures of extraterritorial control considered in Part I will be delineated at the end.

Sense-Perception, Reasoning and Forms in Plotinus

Phronesis ◽  
2021 ◽  
pp. 1-32
Author(s):  
Eyjólfur K. Emilsson
Keyword(s):  
Crucial Role ◽  
Concept Formation ◽  
Sense Perception ◽  
Human Beings

Abstract This paper discusses the role of innate concepts derived from Intellect in Plotinus’ account of cognition of the sensible realm. Several passages have been claimed as evidence for such innateness, but an analysis of them shows that they do not support this claim. It is tentatively suggested that, nevertheless, some very general concepts such as difference, sameness and being are integral to the faculty of sense and play a crucial role in concept formation. It is further argued that reasoning about the sensible realm takes place to a large extent without the involvement of the higher realms of Plotinus’ hierarchy of being. Clearly, however, for value concepts such as those of goodness, justice and beauty human beings are dependent upon an illumination from Intellect.

scholarly journals Visuality Without Form: Video-Mediated Communication and Research Practice Across Disciplinary Contexts

2018 ◽  
Vol 25 (4) ◽  
pp. 417-431 ◽  
Author(s):  
Rebekah Cupitt ◽  
Per-Anders Forstorp ◽  
Ann Lantz
Keyword(s):  
Sign Language ◽  
Interdisciplinary Research ◽  
Meaning Making ◽  
Research Practice ◽  
Mediated Communication ◽  
Scholarly Research ◽  
Video Meeting ◽  
Television Producers

Visuality is a concept that crosses boundaries of practice and meaning, making it an ideal subject for interdisciplinary research. In this article, we discuss visuality using a fragment from a video meeting of television producers at Swedish Television’s group for programming in Swedish Sign Language. This example argues for the importance of recognizing the diversity of analytical and practice-derived visualities and their effect on the ways in which we interpret cultures. These different visualities have consequences for the methods and means with which we present scholarly research. The role of methods, methodology, and analysis of visual practices in an organizational and bilingual setting are key. We explore the challenges of incorporating deaf visualities, hearing visualities, and different paradigms of interdisciplinary research as necessary when visibility, invisibility, and their materialities are of concern. We conclude that in certain contexts, breaking with disciplinary traditions makes visible that which is otherwise invisible.

A Role for Technology in Mathematics Education

1996 ◽  
Vol 178 (2) ◽  
pp. 15-32 ◽  
Author(s):  
Albert A. Cuoco ◽  
E. Paul Goldenberg
Keyword(s):  
Mathematics Education ◽  
Curriculum Change ◽  
Mathematics Curriculum ◽  
New Technology ◽  
Habits Of Mind ◽  
Mathematical Research ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Mathematics Educators

New technology poses challenges to mathematics educators. How should the mathematics curriculum change to best make use of this new technology? Often computers are used badly, as a sort of electronic flash card, which does not make good use of the capabilities of either the computer or the learner. However, computers can be used to help students develop mathematical habits of mind and construct mathematical ides. The mathematics curriculum must be restructured to include activities that allow students to experiment and build models to help explain mathematical ideas and concepts. Technology can be used most effectively to help students gather data, and test, modify, and reject or accept conjectures as they think about these mathematical concepts and experience mathematical research.

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