Consciousness with Body and Soul: an Attempt at Cohen’s Never-Written Psychology

There are contemporary tendencies to regard the human consciousness as an algorithm, or to reduce the human subjective to organic-natural processes or to see it as a social construction depending on cultural conditions. Such approaches pose a challenge to ethical humanism, as it seems, as if it requires new justification and groundings. How can we grasp and defend the concept of embodied subjectivity of man and its freedom to act? How can we think of its unity including thought, will and feeling, preventing it from getting lost in specialized potentials, and maintaining the person as an alert, responsible and self-founded unit? Furthermore, how is it possible to preserve the meaning of the name of the soul, since the notion of this traditional limit concept of the human subjective has fallen into disuse and likely vanished from the horizon? The essay asks for answer with the help of Hermann Cohen, the great Jewish philosopher of Neo-Kantianism, following the traces of his repeatedly stated, however never written systematic psychology. This first part of investigation confines itself to understand Cohen's early interpretation of Plato as the "primordial cell" of his psychology in order to show how the first three parts of his system of philosophy (Logic, Ethics, Aesthetics) answer to some of the questions and problems the early work had raised, with special attention to Cohens philosophy of religion. Self-movement of soul and its deep connection with the human body could be viewed and grasped from the unity of human culture as well as of the allness of man.

Transcendental Conditions, Schematism, and Naturalizing Kant’s “I think”

Considering how Kant’s synthetic unity of apperception could be “naturalized,” this paper seeks to liberate the Kantian theory of experience from any foundationalist renderings that blur the lines between the empirical and transcendental, without compromising Kant’s attempt to investigate how the invariant structures of experience condition and supply rules for our knowledge of the world. This paper begins with an overview of the Transcendental Deduction’s apperceptive “I think.” We then consider Sellars’ Myth of Jones and Sellars’ notion of noumenal reality as a “limit concept” not in metaphysical but alongside pragmatist lines, where the “in-itself” is schematized as a regulatory ideal that normatively orients science as a self-correcting enterprise. Providing a successor-account to Sellars’ naturalization of Kant’s ‘I think,’ we seek to develop hard-transcendental and soft-transcendental pragmatic conditions to describe protocols for revision and integration, proffering an anti-dogmatic metaphysical stance that, true to Kant, expands our understanding of perception and linguistic licensing to include the kind of sensory and conceptual capacities associated with sapient experience.

Investigation into Grade XI Students’ Misconception about the Limit Concept: A Case Study at Samtse Higher Secondary School in Bhutan

In the study of calculus, the concept of limit of function occupies a central role as it is important instruments used in the study of the theory of rate of change, continuity, integral calculus, and differential calculus. Despite its significance, the secondary students hold the inadequate understanding of the limit concepts, more over their concept image of the limit function deviated from the concept definition resulting in the misconception. This study aims to identify the misconception in the limit of function and possible causes of misconceptions. This study was done in two phases, a concept test based on limit of function was administered to all 25 students of Samtse Higher Secondary School. Subsequently, based on the errors and misconception demonstrated by students from the concept test, five students were purposively selected and interviewed to corroborate the finding from concept test to confirm the existence of misconception and its causes. Data from the transcripts, capturing essential and relevant bits of student's responses to each question, was collected. The data were analyzed and result of the study can be described as follows; it was found that learners only think of the manipulative aspect when solving problems on limits and not of the limit concept, confusion over the concept of the limit and value of function, and ambiguity regarding the formal definition of the limit of function. The possible cause of the misconceptions can be attributed to instrumental learning and lack of the sound knowledge in algebra which is cornerstone to understand the limit concept.

Effect of using GeoGebra software on students’ achievement at university level

This study examined the effect of using GeoGebra software on students’ achievement in the case of limit concepts at university level. The instruments used in this study were GeoGebra software, traditional teaching method, and Mathematics Achievement Test (MAT) taken to get the required information. A quasi-experimental design was used and the GeoGebra software introduced in teaching of the limit concept of Complex Analysis among twenty-nine students of section B and traditional teaching method introduced among thirty-one students of section A of the second semester of Master’s in Mathematics Education. After the pre-test, the control group students had been taken the limit concept and related problem in a traditional method and the experimental group students toughed the same content with interactive worksheets by using GeoGebra software. After five hours of lecture in both groups, the standardized MAT (2) was applied for the post-test to the students of both groups. The gathered quantitative data were analyzed by using SPSS 26 version of the scores of sixty students on both groups. As a result, the findings of the research showed that the pre-test scores of students in both groups were insignificant differences. But the pre-test and post-test scores of students in the experimental group and post-test scores of students in both groups were significant differences. The result showed that students were found more interactive in teaching through GeoGebra software and have a positive effect on students’ achievement on the limit concept.

Master Plan for the Loughborough University of Technology: An Endless Campus?

The Master Plan for the Loughborough University of Technology is a 143-page document that gathers the work undertaken by the institution to become a university, thus benefiting from the educational policies derived from the 1963 Robbins report in Britain. Arup Associates authored in 1966 a proposal whose main characteristic is its ascription to an infinite grid strategy and a systematized project. The different diagrams and growth schemes represent the geometric synthesis of some compositional and constructive rules: three grids overlap to produce a germ drawing to which a growth pattern is added for its territorial extension. For the sake of flexibility and adaptability, the project tries to avoid architectural obsolescence through the achievement of a “universal space unit”. Hence, a “discipline” is established whose definition turns out to be a succession of limitations. Through the reconstruction of the design process for the Loughborough University, the multiple meanings of the limit concept are portrayed in parallel to its idea of ​​a continuous and endless campus. A strict internal order, an intentionally open reading of the territory and a constructive standardization produce a kind of visual exhaustion of the whole that could be understood as a limit of spatial nature.

Dialectical Infinity and the Third Mathematical Crisis —On the Fundamental Error of Actual Infinity

This paper discusses the problem of finity and infinity based on the philosophical perspectives of opposing idealism and receiving dialectical materialism. Based on Hegel’s dialectical infinity view, this paper makes a comprehensive criticism of the thought of actual infinity. After Hegel’s dialectical infinite thought scientifically explained the limit concept in calculus, the Second Mathematical Crisis caused by the contradiction of infinitesimal quantity was solved thoroughly. However, the mathematics world has not learned the experience and lessons in history, has always adhered to the idealist thought and methodology of actual infinity, this thought finally brought the third crisis to mathematics. At the end of this paper, based on the infinite view of dialectical materialism, the author analyzes the Principle of Comprehension and the Maximum Ordinal Paradox, and points out that the essence of the Principle of Comprehension is a kind of actual infinity thought. Only by limiting the Principle of Comprehension to a potential infinity can we solve the Third Mathematical Crisis completely.

OBSTÁCULOS EPISTEMOLÓGICOS SOBRE EL CONCEPTO DE LÍMITE DE FUNCIONES EN MANUALES DE HISTORIA DE MATEMÁTICAS

Los estudios históricos muestran que el desarrollo epistemológico del cálculo diferencial e integral siguió una trayectoria larga e irregular y, en el sentido más formal, se formó a partir del siglo XVII. Actualmente, el concepto de límite se considera un concepto fundamental en la enseñanza del cálculo, ya que la base conceptual de este conocimiento tratado en los manuales de cálculo aborda este tema, parece casi siempre definido en términos del límite. En este artículo, presentamos los resultados de un estudio sobre los supuestos obstáculos epistemológicos en el desarrollo del concepto de límite a partir de la historia de los manuales de matemáticas, con miras a superarlo en el proceso de formación de estas ideas. Como ya se mencionó, el corte tomado para el análisis estará en el estudio de los obstáculos epistemológicos del límite de función en algunos manuales de historia de las matemáticas, enfocándose en los conceptos establecidos por d'Alembert, Cauchy y Weierstrass, enfatizando los aspectos dinámicos que aparecieron como un obstáculo epistemológico para formalización de este concepto estático.Palabras clave: Historia de las matemáticas. Obstáculo epistemológico. Cálculo Límite de funciones. EPISTEMOLOGICAL OBSTACLES ON THE FUNCTION LIMIT CONCEPT IN MATHEMATICS HISTORY MANUALS AbstractHistorical studies show that the epistemological development of Differential and Integral Calculus followed a long, irregular trajectory and, in the most formal sense, was shaped from the 17th century. Currently, the concept of limit is considered a fundamental concept in the teaching of Calculus, since the conceptual basis of this knowledge dealt with in Calculus manuals addresses this subject, it seems almost always defined in terms of the limit. In this article, we present the results of a study on the supposed epistemological obstacles in the development of the concept of limit from the history of mathematics manuals, with a view to overcoming it in the process of forming these ideas. As already mentioned, the cut taken for analysis will be in the study of the epistemological obstacles of function limit in some history of mathematics manuals, focusing on the concepts established by d'Alembert, Cauchy and Weierstrass, emphasizing the dynamic aspects that appeared as an epistemological obstacle to formalization of this static concept.Keywords: History of Mathematics. Epistemological obstacle. Calculus. Function Limit. OBSTÁCULOS EPISTEMOLÓGICOS SOBRE O CONCEITO DE LIMITE DE FUNÇÃO EM MANUAIS DE HISTÓRIA DA MATEMÁTICA ResumoEstudos históricos mostram que o desenvolvimento epistemológico do Cálculo Diferencial e Integral seguiu uma trajetoria long, irregular e, no sentido mais formal, foi moldado a partir do século XVII. Atualmente, o conceito de limite é considerado conceito fundamental no ensino de Cálculo, visto que a base conceitual desse conhecimento tratado nos manuais de Cálculo abordam esse assunto, parece quase sempre definida em termos do limite. Neste artigo, apresentamos os resultados de um estudo sobre os supostos obstáculos epistemológicos no desenvolvimento do conceito de limite a partir dos manuais de história da matemática, com um olhar para a sua superação no processo de formação dessas ideias. Conforme já mencionado, o recorte tomado para análise será no estudo dos obstáculos epistemológicos de limite de função em alguns manuais de história da matemática, focando os conceitos estabelecidos por d’Alembert, Cauchy e Weierstrass, enfatizando os aspectos dinâmicos que figuraram como obstáculo epistemológico à formalização deste conceito estático.Palavras-chave: História da Matemática. Obstáculo epistemológico. Cálculo. Limite de função.