Vortrag: Verbal Argumentation as Talk about Diagrams

Stammdaten
Titel: Verbal Argumentation as Talk about Diagrams
Beschreibung: Peirce had stated that all knowledge is based on observation and had explicated this bold statement by his notions of diagram and diagrammatic thinking. He also asserts this not only but even foremost applies to mathematics. The formulas of algebra and of formal logic are diagrams in the sense of Peirce as well as geometric figures and most traditional diagrams. First this is explicated by some examples which show the role of sense perception in mathematical reasoning with diagrams. Another central notion in Peirce is abduction which leads to hypotheses in the form of diagrams. This can be traced in mathematics in many places and a prominent example is the algebraic construction of roots of polynomials by field extensions ( Kronecker theorem) of which the complex numbers are a special case. Finally the question is posed what could take the role of diagrams in those areas of mathematics where the reasoning occurs mainly in a verbal/propositional form, like e.g. in general topology. A thesis is that one has to consider the definitions, lemmas and proved theorems as such as diagrams what comes close to a Wittgensteinian view of mathematics having the character of a grammar.
Schlagworte:
Typ: Vortrag auf Einladung
Homepage: -
Veranstaltung: Explanation and Proof in Mathematics (Essen)
Datum: 02.11.2006
Vortragsstatus:

Beteiligte
Willibald Dörfler
Willi.Doerfler@aau.at
Forschungsaktivitäten
zur Visitenkarte
(intern)
  • Vortragende/r

Zuordnung
Organisation Adresse
Fakultät für Technische Wissenschaften
  Institut für Didaktik der Mathematik
Sterneckstraße 15
A-9020 Klagenfurt
Österreich
  +43 463 2700 992505
   gordana.gajic@aau.at
https://www.aau.at/didaktik-der-mathematik/
zur Organisation
Sterneckstraße 15
AT - A-9020  Klagenfurt

Kategorisierung
Sachgebiete
Forschungscluster
  • Bildungsforschung
Vortragsfokus
  • Science to Science (Qualitätsindikator: n.a.)
Klassifikationsraster der zugeordneten Organisationseinheiten:
TeilnehmerInnenkreis Kein TeilnehmerInnenkreis ausgewählt
Publiziert?
  • Ja
Keynote-Speaker
  • Nein
Arbeitsgruppen Keine Arbeitsgruppe ausgewählt

Kooperationen
Keine Partnerorganisation ausgewählt