The Cartesian Doubt Experiment and Mathematics

1998 ◽  
pp. 35-40
Author(s):  
Halil Turan
Keyword(s):  
Common Sense ◽  
Mathematical Proposition ◽  
Logical Operations ◽  
Substantial Problem ◽  
And Mathematics ◽  
Mathematical Operations ◽  
Cartesian Doubt ◽  
Positive Results

The view that Descartes called mathematical propositions into doubt as he impugned all beliefs concerning common-sense ontology by assuming that all beliefs derive from perception seems to rest on the presupposition that the Cartesian problem of doubt concerning mathematics is an instance of the problem of doubt concerning existence of substances. I argue that the problem is not 'whether I am counting actual objects or empty images,' but 'whether I am counting what I count correctly.' Considering Descartes's early works, it is possible to see that for him, the proposition '2+3=5' and the argument 'I think, therefore I am,' were equally evident. But Descartes does not found his epistemology upon the evidence of mathematical propositions. The doubt experiment does not seem to give positive results for mathematical operations. Consciousness of carrying out a mathematical proposition, however, unlike putting forth a result of an operation, is immune to doubt. Statements of consciousness of mathematical or logical operations are instances of 'I think' and hence the argument 'I count, therefore I am' is equivalent to 'I think, therefore I am.' If impugning the veridicality of mathematical propositions could not pose a difficulty for Descartes's epistemology which he thought to establish on consciousness of thinking alone, then he cannot be seen to avoid the question. Discarding mathematical propositions themselves on the grounds that they are not immune to doubt evoked by a powerful agent does not generate a substantial problem for Descartes provided that he believes that he can justify them by appeal to God's benevolence.

Utopie und Lebenszeit in der Aufklärung

Daphnis ◽  
2021 ◽  
Vol 49 (4) ◽  
pp. 655-681
Author(s):  
Oliver Bach
Keyword(s):  
Common Sense ◽  
Common Good ◽  
Political Community ◽  
Common Interest ◽  
Main Task ◽  
General Will ◽  
Utopian Literature ◽  
Substantial Problem ◽  
The Common ◽  
Existential Dimension

Abstract The aim of this article is to outline how Hans Blumenberg’s conception of lifetime and world time (Lebenszeit und Weltzeit, 1986) can help to elucidate a substantial problem of utopian literature and its development from the 16th to the 18th century: utopias always try to illustrate the ways by which the single members of a political community harmonise with the community as a whole. The congruence of private good and common good, private interest and common interest, private will and general will is a main task of 17th and 18th century political philosophy. Blumenberg’s book, however, allows us to focus on the existential dimension of this harmonisation: under which circumstances may the single members become so wise and virtuous within their lifetimes that they always know about and comply with the common good? 18th century utopias seem to find answers to this question in theories of moral sense, common sense and aesthetic education.

Promising Research, Programs, and Projects: Learning to Think through Reading and Mathematics

1996 ◽  
Vol 2 (5) ◽  
pp. 306-307
Author(s):  
Elizabeth D. Miller
Keyword(s):  
Problem Solving ◽  
Primary Students ◽  
Research Programs ◽  
And Mathematics ◽  
Mathematical Operations ◽  
Reading And Mathematics

During my many years of teaching primary students. I have come to realize that children do not do enough problem solving. Although they can perform mathematical operations. many do not really understand what they are doing. Too often we “train” our students in specific strategies involving particular problems.

scholarly journals Interdisciplinary Educational Approach STEM and HASS Knowledge Fields Using ICTs Support. Case of an Application for a Pilot Experiment

2020 ◽  
pp. 33-42
Author(s):  
Socrates C. Savelides ◽  
Rigo Fasouraki ◽  
Efthymios Georgousis ◽  
Katerina Kolokotroni ◽  
Maria S. Savelidi
Keyword(s):  
Social Sciences ◽  
Design Procedure ◽  
Educational Approach ◽  
Educational Management ◽  
Pilot Experiment ◽  
Science Technology ◽  
Thematic Approach ◽  
Pilot Implementation ◽  
And Mathematics ◽  
Positive Results

This paper investigates the possibility of a holistic interdisciplinary and cross-thematic educational approach of STEM (Science, Technology, Engineering, and Mathematics) and HASS (Humanities, Arts and Social Sciences) knowledge fields. The interdisciplinary educational approach of STEΜ and HASS knowledge branches, set out to resolve complex issues in an innovative way, can assist the development of the students into active and knowledgeable citizens so they will be able to face actual problems whose nature is always interdisciplinary. There is reference in elements which advocate the necessity of this holistic cross-thematic approach and additionally theories and techniques are established which are able to support it. Main characteristic of this development is its support with ICTs. Characteristics of a relevant educational scenario are presented. The scenario is implemented as a pilot experiment and relevant results can be extracted. The scenario is recommended as prototype due to its special interdisciplinarity, the educational techniques that were utilized, and its design procedure based on principles of Educational Management & Engineering and due to the positive results from its pilot implementation. Relevant conclusions are projected.

Qualitative Spatial Reasoning

2011 ◽  
pp. 3175-3180
Author(s):  
Shyamanta M. Hazarika
Keyword(s):  
Common Sense ◽  
Spatial Reasoning ◽  
Qualitative Reasoning ◽  
Physical Situation ◽  
Qualitative Spatial Reasoning ◽  
Common Sense Reasoning ◽  
Naive Physics ◽  
Qualitative Physics ◽  
And Mathematics ◽  
Common Sense Knowledge

Artificial Intelligence (AI) has, as one of its central topics, the ability to represent and reason with common sense knowledge. Early forays into common sense reasoning about the physical world involved solving textbook problems on physics and mathematics. These were not adequate for reasoning about most commonplace physical scenarios. A system suggested by DeKleer, involving both quantitative knowledge and qualitative information concerning the physical situation marked the starting point for qualitative physics (Weld & DeKleer, 1990). Hayes’ Naive Physics Manifesto (Hayes, 1985) paved the way for establishing qualitative physics (meantime re-christened qualitative reasoning) as an important topic of research within AI. Qualitative Reasoning (QR) is an approach for dealing with common sense knowledge without recourse to complete quantitative knowledge. Representation of knowledge is through a limited repository of qualitative abstractions. Space and spatial change is an important part of common sense reasoning. Naive Physics Manifesto proposed to represent space-time with four-dimensional histories. Despite early forays such as the Naive Physics Manifesto, representation of space within QR has been ill addressed. Nevertheless, there has been an increasing interest over the last few years in qualitative spatial reasoning - reasoning about space using qualitative abstractions.

ABOUT ETHNIC FEATURES OF RUSSIAN THINKING

2020 ◽  
Vol 10 (3) ◽  
pp. 194-198
Author(s):  
ZHANNA ANDRIEVSKAYA ◽  
Keyword(s):  
Common Sense ◽  
The West ◽  
Cultural Space ◽  
Space Forms ◽  
Russian People ◽  
Soviet State ◽  
Logical Operations ◽  
Characteristic Features ◽  
Original Type

This article discusses a specifically Russian type of thinking with its specific ethnic Russian type of rationality; the purpose of the article is to detect their characteristic features. It is revealed, that Russian thinking is not reduced to performing banal logical operations at the level of rational activity of “common sense”; it is indicated that it is characterized by a slight neglect of rationality, pragmatism, “common sense”, it contains some super-rational elements, that can not reduced to either rational or cognitive in general, and are the basis of such phenomena as, for example, “breadth of the Russian soul” - signs that are nonspecific for carriers of Western rationality; this reveals the existence of the Russian type of rationality, which cannot be reduced to either Western or Eastern typesof rationality. Thus, the purpose of this article - to discuss the irreducibility of the fundamental specifics of Russian thinking - first of all, value - to the Eastern and Western specifics of thinking - is achieved through consideration of these value attitudes, and above all, to the installation of refusal to reduce rational activity to rational, - Russian people “Thinks with the heart”, and not with reason, and, thus, the Russian cultural space forms a special type of rationality, moreover, it is not hybrid in the “ West - East ” coordinates, which is not a kind of an interest in the attitudes of Western and Eastern types of rationality, but representing a certain independent, immanent, autonomous, original, type of rationality that passed through a thousand years of its historical crystallization, from ancient pagan cults to its modern - post-Soviet state.

scholarly journals Modelagem para recomendação de calagem e adubação para as principais regiões produtoras de grãos do Brasil na linguagem SQL

2019 ◽  
Vol 40 ◽  
pp. 131
Author(s):  
Henrique Alfonso Priebe ◽  
Robert Rafael Araujo Oliveira ◽  
Adriano Rodrigues Luz ◽  
Eduardo Silveira Dornelles ◽  
Gustavo Alves da Silva Bezerra ◽  
...  
Keyword(s):  
Soil Analysis ◽  
Conceptual Modeling ◽  
Grain Crops ◽  
Modeling Process ◽  
Logical Operations ◽  
Fertilizer Recommendations ◽  
Productive System ◽  
Case Technologies ◽  
Logical Modeling ◽  
Mathematical Operations

The agribusiness has a significant importance to the Brazilian economy. In this case, technologies are needed to increase the efficiency of the productive system, but there are few technological tools that perform interpretations of soil analysis and fertilizer recommendations efficiently and comprehensively. In this context, the AgroFert system proposes to make corrective and fertilizer recommendations based on soil analyzes for several regions and grain crops of Brazil, through two systems: web and mobile, which uses a knowledge base in liming and fertilization. Therefore, this work aims at presenting the conceptual and logical modeling process of a database that have rules of information management to interpret the results of soil analysis reports and to recommend soil correctives and fertilizers. Rules were created that use comparisons, filtering, mathematical operations and logical operations, modeled in the SQL language, and when executed, generate interpretations of soil analysis and recommendations for correctives and fertilizers. The AgroFert covers the states of Rio Grande do Sul, Santa Catarina, Paraná, Minas Gerais and São Paulo and the biome of Cerrado. In addition to the conceptual modeling, 22 operations were created, totaling approximately 400 lines of code, and it was possible to recommend fertilizers for 13 grain crops. The results of the tests showed that the computerization of the data present in the RS / SC and Paraná manuals facilitated the interpretation of the data present in soil analysis reports, besides increasing the precision and agility in the recommendations of corrective and fertilizer producers.

scholarly journals Similarities and Differences in the Learning Profiles of Adolescents with SLD and SLI in Mathematics—A Preliminary Analysis

2021 ◽  
Vol 11 (7) ◽  
pp. 850
Author(s):  
Eleni Bonti ◽  
Afroditi Kamari ◽  
Maria Sofologi ◽  
Sofia Giannoglou ◽  
Georgia-Nektaria Porfyri ◽  
...  
Keyword(s):  
Mathematical Reasoning ◽  
Significant Degree ◽  
Written Language ◽  
Chi Square ◽  
Iq Testing ◽  
Language And Mathematics ◽  
Chi Square Test ◽  
Similarities And Differences ◽  
And Mathematics ◽  
Mathematical Operations

SLI and SLD constitute two independent neurodevelopmental disorders, which frequently cause challenges in the diagnosis process, especially due to their nature. This has caused disagreement among clinicians regarding their recognition as separate or overlapping disorders. The objective of the study was to enlighten the path of valid diagnosis and intervention during adolescence when the two disorders change their manifestation and overlap. Two hundred Greek adolescents (140 boys and 60 girls), 124 already diagnosed with SLD and 76 diagnosed with SLI, 12–16 years old, participated in the study. All participants were assessed in reading, oral and written language and mathematics (mathematical operations and mathematical reasoning) along with IQ testing. In order to determine statistically significant differences, the chi-square test, independent samples t-test, odds ratios and their 95 per cent confidence intervals were implemented. The results revealed that the SLI group presented significantly greater difficulties than SLD in their overall cognitive-mental profile and in most language and mathematical measurements (number concept, executive-procedural part of solving operations and mathematical reasoning). The similarity of the two groups was mainly detected in their deficient metacognitive, metalinguistic and metamnemonic strategies. The research concludes that SLD adolescents managed to overcome their difficulties to a significant degree, while adolescents with SLI still struggle with many learning areas.

1. Introduction

2020 ◽  
pp. 1-5
Author(s):  
Timothy Williamson
Keyword(s):  
Common Sense ◽  
Natural Science ◽  
Natural World ◽  
History Of Philosophy ◽  
Mathematical Methods ◽  
Philosophical Methods ◽  
History Of ◽  
And Mathematics ◽  
Better Than

The Introduction focuses on the history of philosophy and intersections between philosophy, common sense, natural science, and mathematics, exploring what it means to do philosophy well in practice. How do we confirm that the methods philosophers use are appropriate for answering their questions? How is philosophy related to science? From the ancient Greeks onwards, philosophy included the study of the natural world. Galileo and Newton were scientists, Descartes a mathematician. When natural science and mathematics grew apart and developed their distinct methodologies, why was philosophy not rendered obsolete? What can philosophical methods still do better than scientific and mathematical methods?

Teaching Aids and Manipulative Teaching Means

2021 ◽  
pp. 353-376
Author(s):  
Alexandros G. Kapaniaris
Keyword(s):  
Multiplication Table ◽  
Educational Robotics ◽  
Mathematical Concepts ◽  
Teaching Aids ◽  
Geometric Concepts ◽  
The Subject ◽  
Teaching Of Mathematics ◽  
And Mathematics ◽  
Mathematical Operations ◽  
Cognitive Areas

The subject matter of this essay concerns the use of manipulatives and teaching aids in the teaching of mathematics for the 1st and 2nd grade of primary school, combined with educational robotics applications. In particular, the use of the programmable bee-bot floor robot combines procedures that involve the use of manipulative means (creating a track as a cardboard model, painting, assembling), teaching aid tools (demonstration of the programmable bee-bot floor robot), and finally, the comprehension of simple programming and mathematical concepts. Through the implementation of an educational scenario aiming to familiarize students with the basic geometric concepts, mathematical operations (multiplication table), basic algorithmic structures (simple problems and step solving), there will be involvement with the cognitive areas of informatics (basic programming concepts)) and mathematics (geometry, calculations).

scholarly journals Similarities and Differences in the Learning Profiles of Adolescents with SLD and SLI in Mathematics

2021 ◽  
Author(s):  
Eleni Bonti ◽  
Afroditi Kamari ◽  
Maria Sofologi ◽  
Sofia Giannoglou ◽  
Georgia-Nektaria Porfyri ◽  
...  
Keyword(s):  
Mathematical Reasoning ◽  
Significant Degree ◽  
Written Language ◽  
Chi Square ◽  
Iq Testing ◽  
Language And Mathematics ◽  
Chi Square Test ◽  
Similarities And Differences ◽  
And Mathematics ◽  
Mathematical Operations

SLI and SLD constitute two autonomous neurodevelopmental disorders, which frequently cause challenges in the diagnosis process, especially due to their nature, which has caused disagreement among clinicians regarding their recognition as separate or overlapping disorders. The objective of the study was to enlighten the path of valid diagnosis and intervention during adolescence when the two disorders change their manifestation and overlap. 200 Greek adolescents (140 boys and 60 girls), 124 already diagnosed with SLD and 76 diagnosed with SLI, 12-16 years old, participated in the study. All participants were assessed in reading, oral and written language and mathematics (mathematical operations and mathematical reasoning) along with IQ testing. In order to determine statistically significant differences, the chi-square test, independent samples t-test, odd ratios and their 95 per cent confidence intervals were implemented. The results revealed that the SLI group presented significantly greater difficulties than SLD in their overall cognitive-mental profile and in most language and mathematical measurements (number concept, executive-procedural part of solving operations and mathematical reasoning). The similarity of the two groups was mainly detected in their deficient metacognitive, metalinguistic and metamnemonic strategies. The research concludes that SLD adolescents managed to overcome their difficulties to a significant degree, while adolescents with SLI still struggle with many learning areas.

Sign in / Sign up

Export Citation Format

Share Document