Communicative Rationality, Logic, and Mathematics

In this article the following thesis is explained and substantiated: Sense and meaning of mathematics finally lie in the fact that mathematics is able to support the rational communication of humans. The essence of the argumentation is that the effective support becomes possible by the close connection between mathematics and logic (in the sense of Peirce's late philosophy) by which, in his turn, the communicative rationality (in the sense of Habermas' theory of communicative action) can be activated. How such a support may be concretely performed shall be illustrated by the development of a retrieval system for the library of the Center of Interdisciplinary Technology Research at Darmstadt University of Technology.

[1]  J. Habermas.  Theorie des kommunikativen Handelns , 1981 .

[2]  Gerd Stumme,et al.  Begriffliche Wissensverarbeitung: Methoden und Anwendungen , 2000 .

[3]  Harry S. Delugach,et al.  Conceptual Structures at Work , 2004, Lecture Notes in Computer Science.

[4]  Peter Øhrstrøm,et al.  Working with Conceptual Structures - Contributions to ICCS 2000 , 2000 .

[5]  John F. Sowa,et al.  Conceptual Structures: Information Processing in Mind and Machine , 1983 .

[6]  Galia Angelova,et al.  Conceptual Structures: Integration and Interfaces , 2002, Lecture Notes in Computer Science.

[7]  Susanne Prediger,et al.  Kontextuelle Urteilslogik mit Begriffsgraphen: ein Beitrag zur Restrukturierung der mathematischen Logik , 1998 .

[8]  Frithjof Dau,et al.  The Logic System of Concept Graphs with Negation , 2003, Lecture Notes in Computer Science.

[9]  Philip Kitcher,et al.  The nature of mathematical knowledge , 1985 .

[10]  Rudolf Wille.  Contextual logic summary , 2000 .

[11]  John F. Sowa,et al.  Conceptual Structures: Fulfilling Peirce's Dream , 1997, Lecture Notes in Computer Science.

[12]  Rudolf Wille,et al.  Existential Concept Graphs of Power Context Families , 2002, ICCS.

[13]  Julia Klinger.  The Logic System of Protoconcept Graphs , 2005 .

[14]  R. Wille,et al.  Ein TOSCANA-Erkundungssystem zur Literatursuche , 2000 .

[15]  Hartmut von Hentig.  Magier oder Magister? : über die Einheit der Wissenschaft im Verständigungsprozeß , 1972 .

[16]  Rudolf Wille,et al.  Formal Concept Analysis as Applied Lattice Theory , 2006, CLA.

[17]  Rudolf Wille.  Begriffsdenken: Von der griechischen Philosophie bis zur Künstlichen Intelligenz heute , 1995 .

[18]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[19]  Frithjof Dau,et al.  From Formal Concept Analysis to Contextual Logic , 2005, Formal Concept Analysis.

[20]  Rudolf Wille.  Mensch und Mathematik: logisches und mathematisches Denken , 2001 .

[21]  Rudolf Wille.  Implicational Concept Graphs , 2004, ICCS.

[22]  L. Guttman.  What is Not What in Statistics , 1977 .

[23]  Charles S. Peirce,et al.  The essential Peirce , 1992 .

[24]  Susanne Prediger.  Mathematische Logik in der Wissensverarbeitung , 2000 .

[25]  Rudolf Wille,et al.  Conceptual Graphs and Formal Concept Analysis , 1997, ICCS.

[26]  Siegfried Blasche,et al.  Enzyklopädie Philosophie und Wissenschaftstheorie , 1995 .

[27]  Peter Becker,et al.  The ToscanaJ Suite for Implementing Conceptual Information Systems , 2005, Formal Concept Analysis.

[28]  Rudolf Wille.  Kommunikative Rationalität und Mathematik , 2002 .

[29]  Hilary Putnam,et al.  Reasoning and the logic of things , 1992 .

[30]  K. Apel,et al.  Schriften zum Pragmatismus und Pragmatizismus , 1976 .

[31]  Rudolf Wille.  Formal Concept Analysis and Contextual Logic , 2009 .

[32]  Jean Piaget,et al.  Einführung in die genetische Erkenntnistheorie , 1973 .

[33]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[34]  Rudolf Wille.  Transdisziplinarität und allgemeine Wissenschaft , 2002 .

[35]  Jan C. Schmidt,et al.  Perspektiven interdisziplinärer Technikforschung : Konzepte, Analysen, Erfahrungen , 2002 .