Mathematical Knowledge and the Origin of Phenomenology

2021 ◽  
Vol 21 ◽  
pp. 273-294
Author(s):  
Gabriele Baratelli ◽  

The paper is divided into two parts. In the first one, I set forth a hypothesis to explain the failure of Husserl’s project presented in the Philosophie der Arithmetik based on the principle that the entire mathematical science is grounded in the concept of cardinal number. It is argued that Husserl’s analysis of the nature of the symbols used in the decadal system forces the rejection of this principle. In the second part, I take into account Husserl’s explanation of why, albeit independent of natural numbers, the system is nonetheless correct. It is shown that its justification involves, on the one hand, a new conception of symbols and symbolic thinking, and on the other, the recognition of the question of “the formal” and formalization as pivotal to understand “the mathematical” overall.

PARADIGMA ◽  
2019 ◽  
Vol 40 (2) ◽  
pp. 196-217
Author(s):  
Luis Andrés Castillo ◽  
Juan Luis Prieto G. ◽  
Ivonne C. Sánchez ◽  
Rafael Enrique Gutiérrez

En los últimos años, los profesores han tratado cada vez más de utilizar los recursos didácticos para apoyar sus clases, un hecho que se ha agregado con la llegada de las tecnologías digitales. En este contexto surgió la tendencia de que los profesores se convirtieran en creadores de este tipo de recursos, pero dejando de lado la sistematización y el deber de compartir con sus compañeros la experiencia de desarrollar este tipo de recursos. Por esta razón, el presente trabajo describe una experiencia concreta de elaborar un simulador con el software GeoGebra para estudiar una situación de tiro libre en el fútbol, utilizando nociones de movimiento parabólico. La elaboración del simulador incluye la resolución de siete "tareas de simulación", que destacan los objetos y los procesos matemáticos que justifican las técnicas de construcción utilizadas por los autores. Finalmente, se presentan algunas reflexiones derivadas de la experiencia de desarrollo del simulador, que consideran, por un lado, el conocimiento matemático movilizado en la producción del simulador y, por otro lado, las acciones y capacidades requeridas para tal elaboración.AbstractIn recent years, teachers have increasingly sought the use of didactic resources to support their classes, a fact that has been added with the arrival of digital technologies. In this context, the tendency has emerged that teachers have become creators of this type of resources, but leaving aside the systematization and the duty to share with their peers the experience of developing this type of resources. For this reason, the present work describes a concrete experience of developing a simulator with GeoGebra software for the study of a situation of free kick in football, using notions of parabolic movement. The elaboration of the simulator includes the resolution of seven "simulation tasks", which highlight the objects and mathematical processes that should justify the construction techniques used by the authors. Finally, some reflections derived from the simulator development experience are presented, which consider, on the one hand, the mathematical knowledge mobilized in the production of the simulator and, on the other hand, the actions and capabilities required for such an elaboration.ResumoNos últimos anos, professores têm procurado cada vez mais o uso de recursos didáticos para apoiar suas aulas, fato que foi acrescentado com a chegada das tecnologias digitais. Nesse contexto surgiu a tendência que os professores se tornaram criadores desse tipo de recursos, mas deixando de lado a sistematização e o dever de dividir com seus pares a experiência de desenvolver este tipo de recursos. Por este motivo, o presente trabalho descreve uma experiência concreta de elaboração de um simulador com o software GeoGebra para o estudo de uma situação do tiro livre no futebol, utilizando noções do movimento parabólico. A elaboração do simulador inclui a resolução de sete “tarefas de simulação”, que destacam os objetos e processos matemáticos que devem justificar as técnicas de construção utilizadas pelos autores. Finalmente, apresentam-se algumas reflexões derivadas da experiência de desenvolvimento do simulador, que consideram, por um lado, o conhecimento matemático mobilizado na produção do simulador e, por outro lado, as ações e capacidades necessárias para tal elaboração. 


1982 ◽  
Vol 25 (4) ◽  
pp. 487-490
Author(s):  
Gerd Rodé

AbstractThis paper gives a new characterization of the dimension of a normal Hausdorff space, which joins together the Eilenberg-Otto characterization and the characterization by finite coverings. The link is furnished by the notion of a system of faces of a certain type (N1,..., NK), where N1,..., NK, K are natural numbers. It is shown that a space X contains a system of faces of type (N1,..., NK) if and only if dim(X) ≥ N1 + … + NK. The two limit cases of the theorem, namely Nk = 1 for 1 ≤ k ≤ K on the one hand, and K = 1 on the other hand, give the two known results mentioned above.


Author(s):  
PAWEŁ PARYS

AbstractIt is well known that simply typed λ-terms can be used to represent numbers, as well as some other data types. We show that λ-terms of each fixed (but possibly very complicated) type can be described by a finite piece of information (a set of appropriately defined intersection types) and by a vector of natural numbers. On the one hand, the description is compositional: having only the finite piece of information for two closed λ-terms M and N, we can determine its counterpart for MN, and a linear transformation that applied to the vectors of numbers for M and N gives us the vector for MN. On the other hand, when a λ-term represents a natural number, then this number is approximated by a number in the vector corresponding to this λ-term. As a consequence, we prove that in a λ-term of a fixed type, we can store only a fixed number of natural numbers, in such a way that they can be extracted using λ-terms. More precisely, while representing k numbers in a closed λ-term of some type, we only require that there are k closed λ-terms M1,. . .,Mk such that Mi takes as argument the λ-term representing the k-tuple, and returns the i-th number in the tuple (we do not require that, using λ-calculus, one can construct the representation of the k-tuple out of the k numbers in the tuple). Moreover, the same result holds when we allow that the numbers can be extracted approximately, up to some error (even when we only want to know whether a set is bounded or not). All the results remain true when we allow the Y combinator (recursion) in our λ-terms, as well as uninterpreted constants.


1993 ◽  
Vol 6 (1) ◽  
pp. 311-341 ◽  
Author(s):  
Jürgen Renn

The ArgumentIn this paper I present and argue for a model of conceptual development in science and apply it to the transition from classical to modern physics associated with Einstein. The model claims a continuous and rational transition between incompatible subsequent conceptual systems in mathematical science and explains its mechanism. The model was developed in a study of the transition from preclassical to classical mechanics. I argue for a strong structural analogy between the transition from preclassical to classical mechanics on the one hand and from classical to modern physics on the other. The first transition is briefly sketched here by reference to Galileo and his disciples; in the second transition Planck and Lorentz on the one hand and Einstein on the other play the respective roles.A detailed and documented reconstruction of the transition from preclassical to classical mechanics on the basis of this model has already been published and is only briefly referred to in the paper. The transition from classical to modern physics is portrayed here much more extensively—though of course merely in broad brush strokes. Einstein–s role in this transition is reconstructed in the light of a conceptualization of his scientific knowledge as an active structure of thought, shaped by his intellectual experience. In this way, the development of his individual thinking is shown to be part of the overall process of conceptual transformation from classical to modern physics. The reconstruction sketched in this paper is to be considered as a proposal to be substantiated, reformed, and improved by future detailed studies.


1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.


Author(s):  
Stefan Krause ◽  
Markus Appel

Abstract. Two experiments examined the influence of stories on recipients’ self-perceptions. Extending prior theory and research, our focus was on assimilation effects (i.e., changes in self-perception in line with a protagonist’s traits) as well as on contrast effects (i.e., changes in self-perception in contrast to a protagonist’s traits). In Experiment 1 ( N = 113), implicit and explicit conscientiousness were assessed after participants read a story about either a diligent or a negligent student. Moderation analyses showed that highly transported participants and participants with lower counterarguing scores assimilate the depicted traits of a story protagonist, as indicated by explicit, self-reported conscientiousness ratings. Participants, who were more critical toward a story (i.e., higher counterarguing) and with a lower degree of transportation, showed contrast effects. In Experiment 2 ( N = 103), we manipulated transportation and counterarguing, but we could not identify an effect on participants’ self-ascribed level of conscientiousness. A mini meta-analysis across both experiments revealed significant positive overall associations between transportation and counterarguing on the one hand and story-consistent self-reported conscientiousness on the other hand.


2005 ◽  
Vol 44 (03) ◽  
pp. 107-117
Author(s):  
R. G. Meyer ◽  
W. Herr ◽  
A. Helisch ◽  
P. Bartenstein ◽  
I. Buchmann

SummaryThe prognosis of patients with acute myeloid leukaemia (AML) has improved considerably by introduction of aggressive consolidation chemotherapy and haematopoietic stem cell transplantation (SCT). Nevertheless, only 20-30% of patients with AML achieve long-term diseasefree survival after SCT. The most common cause of treatment failure is relapse. Additionally, mortality rates are significantly increased by therapy-related causes such as toxicity of chemotherapy and complications of SCT. Including radioimmunotherapies in the treatment of AML and myelodyplastic syndrome (MDS) allows for the achievement of a pronounced antileukaemic effect for the reduction of relapse rates on the one hand. On the other hand, no increase of acute toxicity and later complications should be induced. These effects are important for the primary reduction of tumour cells as well as for the myeloablative conditioning before SCT.This paper provides a systematic and critical review of the currently used radionuclides and immunoconjugates for the treatment of AML and MDS and summarizes the literature on primary tumour cell reductive radioimmunotherapies on the one hand and conditioning radioimmunotherapies before SCT on the other hand.


2017 ◽  
Vol 47 (188) ◽  
pp. 487-494
Author(s):  
Daniel Mullis

In recent years, political and social conditions have changed dramatically. Many analyses help to capture these dynamics. However, they produce political pessimism: on the one hand there is the image of regression and on the other, a direct link is made between socio-economic decline and the rise of the far-right. To counter these aspects, this article argues that current political events are to be understood less as ‘regression’ but rather as a moment of movement and the return of deep political struggles. Referring to Jacques Ranciere’s political thought, the current conditions can be captured as the ‘end of post-democracy’. This approach changes the perspective on current social dynamics in a productive way. It allows for an emphasis on movement and the recognition of the windows of opportunity for emancipatory struggles.


1996 ◽  
pp. 13-23
Author(s):  
Mykhailo Babiy

Political ideological pluralism, religious diversity are characteristic features of modern Ukrainian society. On the one hand, multiculturalism, socio-political, religious differentiation of the latter appear as important characteristics of its democracy, as a practical expression of freedom, on the other - as a factor that led to the deconsocialization of society, gave rise to "nodal points" of tension, confrontational processes, in particular, in political and religious spheres.


2003 ◽  
pp. 15-26
Author(s):  
P. Wynarczyk
Keyword(s):  
The Core ◽  

Two aspects of Schumpeter' legacy are analyzed in the article. On the one hand, he can be viewed as the custodian of the neoclassical harvest supplementing to its stock of inherited knowledge. On the other hand, the innovative character of his works is emphasized that allows to consider him a proponent of hetherodoxy. It is stressed that Schumpeter's revolutionary challenge can lead to radical changes in modern economics.


Sign in / Sign up

Export Citation Format

Share Document