NDLI: Main Problems of Diagrammatic Reasoning. Part I: The generalization problem

Content Provider	Springer Nature Link
Author	Kulpa, Zen
Copyright Year	2008
Abstract	The paper attempts to analyze in some detail the main problems encountered in reasoning using diagrams, which may cause errors in reasoning, produce doubts concerning the reliability of diagrams, and impressions that diagrammatic reasoning lacks the rigour necessary for mathematical reasoning. The paper first argues that such impressions come from long neglect which led to a lack of well-developed, properly tested and reliable reasoning methods, as contrasted with the amount of work generations of mathematicians expended on refining the methods of reasoning with formulae and predicate calculus. Next, two main groups of problems occurring in diagrammatic reasoning are introduced. The second group, called diagram imprecision, is then briefly summarized, its detailed analysis being postponed to another paper. The first group, called collectively the generalization problem, is analyzed in detail in the rest of the paper. The nature and causes of the problems from this group are explained, methods of detecting the potentially harmful occurrences of these problems are discussed, and remedies for possible errors they may cause are proposed. Some of the methods are adapted from similar methods used in reasoning with formulae, several other problems constitute new, specifically diagrammatic ways of reliable reasoning.
Starting Page	75
Ending Page	96
Page Count	22
File Format	PDF
ISSN	12331821
Journal	Foundations of Science
Volume Number	14
Issue Number	1-2
e-ISSN	15728471
Language	English
Publisher	Springer Netherlands
Publisher Date	2008-10-30
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Diagrammatics Diagrammatic reasoning Rigorous reasoning Reasoning errors Generalization Diagram particularity Divergence Mathematical Logic and Foundations Methodology of the Social Sciences Philosophy of Science
Content Type	Text
Resource Type	Article
Subject	History and Philosophy of Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

The Role of Diagrams in Mathematical Arguments

Diagrammatic Models in the Engineering Sciences

How to Get It. Diagrammatic Reasoning as a Tool of Knowledge Development and its Pragmatic Dimension

The Precautionary Principle: Scientific Uncertainty and Type I and Type II Errors

The forgotten individual: diagrammatic reasoning in mathematics

Analogical Reasoning and Modeling in the Sciences

Preface to Part Two

Remodeling the Past

Abductive Reasoning as a Way of Worldmaking

Main Problems of Diagrammatic Reasoning. Part I: The generalization problem

Similar Documents

The Role of Diagrams in Mathematical Arguments

Diagrammatic Models in the Engineering Sciences

How to Get It. Diagrammatic Reasoning as a Tool of Knowledge Development and its Pragmatic Dimension

The Precautionary Principle: Scientific Uncertainty and Type I and Type II Errors

The forgotten individual: diagrammatic reasoning in mathematics

Analogical Reasoning and Modeling in the Sciences

Preface to Part Two

Remodeling the Past

Abductive Reasoning as a Way of Worldmaking

Main Problems of Diagrammatic Reasoning. Part I: The generalization problem