Type-theoretical checking and philosophy of Mathematics

1998 ◽  
Author(s):  
Nicolaas Govert de Bruijn
Keyword(s):  
Set Theory ◽  
Subject Matter ◽  
Mutual Influence ◽  
Mathematical Reasoning ◽  
Philosophy Of Mathematics ◽  
General Information ◽  
Point Of View ◽  
De Bruijn ◽  
Level Of Understanding ◽  
The Way

After millennia of mathematics we have reached a level of understanding that can be represented physically. Humankind has managed to disentangle the intricate mixture of language, metalanguage and interpretation, isolating a body of formal, abstract mathematics that can be completely verified by machines. Systems for computer-aided verification have philosophical aspects. The design and usage of such systems are influenced by the way we think about mathematics, but it also works the other way. A number of aspects of this mutual influence will be discussed in this paper. In particular, attention will be given to philosophical aspects of type-theoretical systems. These definitely call for new attitudes: throughout the twentieth century most mathematicians had been trained to think in terms of untyped sets. The word “philosophy” will be used lightheartedly. It does not refer to serious professional philosophy, but just to meditation about the way one does one’s job. What used to be called philosophy of mathematics in the past was for a large part subject oriented. Most people characterized mathematics by its subject matter, classifying it as the science of space and number. From the verification system’s point of view, however, subject matter is irrelevant. Verification is involved with the rules of mathematical reasoning, not with the subject. The picture may be a bit confused, however, by the fact that so many people consider set theory, in particular untyped set theory, as part of the language and foundation of mathematics, rather than as a particular subject treated by mathematics. The views expressed in this paper are quite personal, and can mainly be carried back to the author’s design of the Automath system in the late 1960s, where the way to look upon the meaning (philosophy) of mathematics is inspired by the usage of the unification system and vice versa. See de Bruijn 1994b for various philosophical items concerning Automath, and Nederpelt et al. 1994, de Bruin 1980, de Bruijn 1991a for general information about the Automath project. Some of the points of view given in this paper are matters of taste, but most of them were imposed by the task of letting a machine follow what we say, a machine without any knowledge of our mathematical culture and without any knowledge of physical laws.

Subjective Point of View of a Student on Ways of Subject Matter Structure Creation by the Teacher

2015 ◽  
Vol 5 (2) ◽  
pp. 148-171
Author(s):  
Denisa Gunišová ◽  
Jana Duchovičová
Keyword(s):  
Subject Matter ◽  
Point Of View ◽  
Subjective Perception ◽  
Cognitive Frames ◽  
Teacher Work ◽  
Approach To Teaching ◽  
The Subject ◽  
Definition Of ◽  
Level Of Understanding ◽  
Education Process

Authors in this contribution focus on issue of subject matter structure creation by the teacher as an important psycho-didactic domain of education process and how does a student perceive this structure. The aim of the teacher is not only to impart the knowledge to students but also to show them and teach them possible ways of how to understand the subject matter better and how to get to the fundamentals of it. Based on the structure of subject matter created by the teacher a student creates cognitive frames which become basis for his further learning. We pay attention to definition of epistemology of subject matter structure, questions of psycho-didactic approach to teaching, creating structure of subject matter and how does the teacher work with the text. Empirical part of the contribution investigates teachers' preferences of subject matter structure and statistically describes subjective perception of level of understanding of the subject matter by a student influenced by the particular subject matter structure realized by the teacher.

Interactioneel Leraarsgedrag In Relatie Tot Het Schoolvak

1984 ◽  
Vol 18 ◽  
pp. 52-69
Author(s):  
Th. Wubbels ◽  
H.A. Créton ◽  
H.P. Hooymayers
Keyword(s):  
System Theory ◽  
Subject Matter ◽  
Point Of View ◽  
Language Teachers ◽  
Teacher Behaviour ◽  
Modern Language ◽  
Vital Importance ◽  
The Subject ◽  
Teacher Trainers ◽  
The Way

In this paper we describe findings concerning a limited part of teacher behaviour namely relational skills. These skills are of vital importance if a teacher is to create a good classroom atmosphere. On the basis of theories of Leary (1957) and Watzlawick et al. (1968) we have constructed a model that describes relational aspects of teacher behaviour. This model focusses on teacher behaviour as revealed in teacher pupil interactions. These interactions are analysed by means of the system theory of communication. We have investigated teacher behaviour as observed by teachers and pupils, with the help of an instrument called 'The Questionnaire for Interactional Teacher Behaviour'. It is found that from the pupils' point of view good teachers are distinguished from bad teachers by the amount of kindness and understanding they show, their helpfulness and the way they manage a class. We also investigated the behaviour that teachers themselves wish to display. They agree about the need to be kind, helpful and understanding but differ in the amount of strict behaviour they want to display and in the amount of freedom and independence they want to give to pupils. We also investigated with this questionnaire the teacher behaviour of teachers who teach different subjects. It is found that pupils consider modern language teachers in particular to behave differently from other teachers; they are stricter, less kind and give less independence to pupils. This different behaviour of modern language teachers may be due to the structure of the subject matter, or to the way in which languages are taught at universities to future teachers. We think teacher trainers should be concerned with our findings because when teachers, and particularly language teachers, become older they seem to have increasing difficulty in creating and maintaining an adequate relationship with their pupils.

Reasons to Criminalize

2018 ◽  
pp. 143-181
Author(s):  
Vincent Chiao
Keyword(s):  
Criminal Law ◽  
Subject Matter ◽  
Public Law ◽  
Point Of View ◽  
Harm Principle ◽  
The Political ◽  
Legal Moralism ◽  
The Public ◽  
Political Ideal ◽  
The Way

This chapter extends the public law conception to the theory of criminalization. The first half of the chapter is devoted to considering whether the criminal law has a privileged subject matter or “core,” focusing especially on Feinberg’s influential account of the criminal law as a system of direct prohibitions. The chapter argues that a subject-matter-based approach has difficulty coming to grips with actual criminal law systems in modern administrative states, in which so-called mala prohibita offenses predominate. The second half of the chapter turns to sketching how we might approach the question of criminalization from a public law point of view, both in general and with reference to the political ideal of anti-deference (sketched in Chapter 3) in particular. Along the way, the chapter argues that the (very popular) wrongfulness principle turns out to be either empty or implausible, and hence that we should reject any version of the harm principle, or of legal moralism, that presupposes it.

Philosophy of Mathematics

Philosophy ◽  
2010 ◽  
Author(s):  
Otávio Bueno
Keyword(s):  
Philosophy Of Science ◽  
Set Theory ◽  
Category Theory ◽  
Mathematical Reasoning ◽  
Philosophy Of Mathematics ◽  
Mathematical Practice ◽  
Mathematical Explanation ◽  
Excellent Work ◽  
Novel Approaches

Philosophy of mathematics is arguably one of the oldest branches of philosophy, and one that bears significant connections with core philosophical areas, particularly metaphysics, epistemology, and (more recently) the philosophy of science. This entry focuses on contemporary developments, which have yielded novel approaches (such as new forms of Platonism and nominalism, structuralism, neo-Fregeanism, empiricism, and naturalism) as well as several new issues (such as the significance of the application of mathematics, the role of visualization in mathematical reasoning, particular attention to mathematical practice and to the nature of mathematical explanation). Excellent work has also been done on particular philosophical issues that arise in the context of specific branches of mathematics, such as algebra, analysis, and geometry, as well as particular mathematical theories, such as set theory and category theory. Due to limitations of space, this work goes beyond the scope of the present entry.

Quine, Structure, and Ontology

2020 ◽  
Keyword(s):  
Set Theory ◽  
Philosophy Of Language ◽  
Philosophy Of Mathematics ◽  
Point Of View ◽  
Philosophy Of Time ◽  
Language History ◽  
History Of ◽  
Contemporary Work ◽  
And Mathematics ◽  
Nathan Salmon

Contemporary work on ontology, logic, philosophy of mathematics, philosophy of science, and philosophy of language still owes much to W.V. Quine. Nevertheless his views are now often dismissed because of mistaken or overly simplified conceptions of his philosophy. The development of his views over time are often overlooked, and in particular the growing importance of a kind of structuralism to his system as it evolved. This volume provides a fuller, richer picture of Quine’s views and their development. It is the first to investigate Quine’s views on structure and how it permeates and shapes his attitude to a range of philosophical questions. It includes contributions by world-famous philosophers and experts in a range of subfields including philosophical logic, philosophy of language, history of philosophy, mathematics, philosophy of time, and set theory. Chapters by Michael Resnik, Frederique Janssen-Lauret and Fraser MacBride, John Collins, Jaroslav Peregrin, and Paul Gregory explore whether Quine’s structuralism is epistemological, language-based, or ontological. Greg Frost-Arnold, Robert Sinclair, and Gary Kemp and Andrew Lugg explore Quine’s views on structure from a historical point of view. Nathan Salmón, Gila Sher, Marianna Antonutti Marfori, and Natalja Deng consider Quine’s views on the structure of logic, language, and theories in relation to contemporary philosophy, specifically ontology, the philosophy of logic and mathematics, philosophy of set theory, and philosophy of time.

The philosophy of logic

2012 ◽  
Vol 18 (4) ◽  
pp. 481-504 ◽  
Author(s):  
Penelope Maddy
Keyword(s):  
Subject Matter ◽  
Philosophy Of Mathematics ◽  
Philosophy Of Logic ◽  
Starting Point ◽  
The Subject ◽  
The Way

AbstractThis talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic—what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics—Logicism, Intuitionism, Formalism, Realism—and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam are among the philosophers considered along the way.

La enseñanza de la ética profesional a estudiantes de derecho: análisis de caso

2018 ◽  
pp. 145
Author(s):  
Juan Pablo Beca
Keyword(s):  
Professional Ethics ◽  
Ethics Education ◽  
Teaching Experience ◽  
Point Of View ◽  
Theory And Practice ◽  
Ethics Course ◽  
Approach Theory ◽  
Competency Based ◽  
Catholic Tradition ◽  
The Way

ResumenEl trabajo analiza el curso Ética Profesional en la carrera de Derecho en la Universidad Católica de Temuco. Examina la forma como se abordaba la ética profesional antes de la creación del curso, y lo que ha ocurrido con él a través de sucesivos cambios curriculares y la introducción del modelo por competencias. El curso aporta al sello identitario, mediante un enfoque multidisciplinario. El curso ha vinculado teoría y práctica, desde que comenzó a implementarse, hasta llegar actualmente a comprenderlo en la lógica de competencias. Esta mirada implica formar a los estudiantes para resolver dilemas éticos, lo que se hace mediante la metodología del ver–juzgar–actuar. Esta metodología de discernimiento es propia de la tradicióncatólica, pero se usa en este contexto sin un cariz religioso. El método en cuestión permite ir educando la autonomía a fn de tomar decisiones. Se analiza la importancia de contextualizar la enseñanza ética y la forma como esto se ha hecho en el curso. Finalmente se aborda la relevancia de formar la conciencia ética de los estudiantes.Palabras clave: Experiencia de enseñanza – Ética profesional –Método de discernimient.ResumoO artigo analisa o curso de Ética Profssional na Escola de Direito na Universidade Católica de Temuco. Examina a forma de como abordar a ética profssional antes da criação do curso, e o que tem acontecido com ele através de sucessivas mudanças curriculares e a introdução do modelo de competências. O curso aporta ao selo de identidade, através de uma abordagem multidisciplinar. O curso tem ligado teoria e prática, desde que começou a se programar até chegar atualmente a compreendê-lo na lógica de competência. Este olhar implica formar aos estudantes para resolver dilemas éticos, o que é feito pela metodologia do ver-julgar-agir. Este método de discernimento é próprio da tradição Católica, mas é usado neste contexto, sem um aspecto religioso. O método em questão permite ir educando na autonomia com a fnalidade de tomar decisões. Analisa-se a importância de contextualizar o ensino da ética e a forma como isso tem sido feito no curso. Finalmente se aborda a relevância de formar consciência ética dos estudantes.Palavras-chave: Experiência de ensino - Ética Profssional - Método de discernimento.AbstractThis paper analyses the Professional Ethics course at the School of Law of Universidad Católica de Temuco. It reviews the way in which ethics was addressed before the course was created, and what has happened with it through the subsequent curricular changes and the implementation of a competency based model. The course contributes to the seal of identity through a multidisciplinary approach. Theory and practice have been progressively bound together since the course was introduced, to reach a point, nowadays, in which the course is understood within the logic of competencies. This point of view implies educating students for solving ethical dilemmas, which is done through the see–judge–act methodology. This discernment methodology belongs to the Roman Catholic tradition, but is used in this context without its religious complexion. This method allows educating autonomy in order to make decisions. It also analyses the importance of contextualizing ethics education and the way in which this has been done in the course. Finally, it addresses the relevance ofcreating an ethical consciousness of the students.Keywords: Teaching experience – Professional Ethics – Discernment method

INTERIOR DESIGN AND ARCHITECTURE THROUGH THE PRISM OF TIME: FROM CONFLICT TO COOPERATION

2020 ◽  
Vol 1 (1) ◽  
pp. 32-37
Author(s):  
I. Naydenova
Keyword(s):  
Interior Design ◽  
Mutual Influence ◽  
Time Frame ◽  
Research Area ◽  
Point Of View ◽  
Living Space ◽  
Self Sufficiency ◽  
Functional Zoning ◽  
Architecture And Design ◽  
Xix Century

As a research area, interior design took shape in the 20s of the last century, despite the fact that the practice of decorating living spaces dates back many hundreds of years. However, the "self-sufficiency" of design and its connection with architecture to this day is the subject of scientific discussions of urban specialists, historians, art historians, and anthropologists. The article discusses the leading artistic styles and trends that prevailed in architecture and design from the point of view of their mutual influence on each other. Time frame of the research: from the middle of XIX century to the first half of XX century. As a result of the research of foreign experience in the formation of interior design, the main stages of the movement development and its relationship with architecture in two formations were identified: activities directly dependent on architectural decisions, activities that determine the entire design process to a large extent: from the functional zoning of the premises to the features of the placement of utilities in the building. Entering the information era in art as a whole is characterized by the rejection of slogans that clearly delineate stylistic boundaries and determine the role of a designer in creating the living space. The determining factor influencing the integrity of the building’s appearance in a modern view is the harmony of the facade and the internal content, which was made possible thanks to the equal interaction of the architect and designer, starting from the first half of the 20th century.

THE METADIALOGUE CONCEPT IN ITS LINGUISTIC ASPECT

2019 ◽  
Vol 29 (5) ◽  
pp. 721-726
Author(s):  
Yu.V. Kupriyanova ◽  
I.M. Vasilyanova
Keyword(s):  
Subject Matter ◽  
Dynamic Structure ◽  
Point Of View ◽  
Semantic Relations ◽  
Human Cognition ◽  
Main Research ◽  
Key Points ◽  
Research Findings ◽  
The Subject ◽  
Linguistic Aspect

The article summarizes the key points in the development of the metadialogue phenomenon from a linguistic point of view. Some stages of the development of this concept and the difficulties associated with its structuring are covered. The main research findings of modern foreign and domestic experts on its study are considered. Some characteristics of the subject of the research from the standpoint of various pragmatic installations are given. On the basis of the dynamic structure of the metadialogue development, certain principles of semantic relations connected with the dialectical nature of human cognition are presented. Excursion into the history and evolution of the concept is presented. Several types of formulation of the subject matter are given. In accordance with the goal of speech exposure, internal problems of the development of metadialogue are highlighted and the critical points related to solving these problems are described. The rules of metadialogue flow are explained at the level of steps, the success/failure of which directly affects the final result of communication. The prospects of development of the concept research in accordance with various types of discourse are indicated.

Chemical analysis: Information contribution of results

1991 ◽  
Vol 56 (3) ◽  
pp. 505-559 ◽  
Author(s):  
Karel Eckschlager
Keyword(s):  
Analytical Chemistry ◽  
Information Theory ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Information Gain ◽  
Analytical Signal ◽  
Point Of View ◽  
System A ◽  
Review Analysis ◽  
Theory Point

In this review, analysis is treated as a process of gaining information on chemical composition, taking place in a stochastic system. A model of this system is outlined, and a survey of measures and methods of information theory is presented to an extent as useful for qualitative or identification, quantitative and trace analysis and multicomponent analysis. It is differentiated between information content of an analytical signal and information gain, or amount of information, obtained by the analysis, and their interrelation is demonstrated. Some notions of analytical chemistry are quantified from the information theory and system theory point of view; it is also demonstrated that the use of fuzzy set theory can be suitable. The review sums up the principal results of the series of 25 papers which have been published in this journal since 1971.

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