The Euclidean Diagram

In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133 (2008)
  Copy   BIBTEX

Abstract

This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary for this to work. Case-branching occurs when a construction renders a diagram un-representative. The roles of diagrams in reductio arguments, and of objection in probing a demonstration, are discussed.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,261

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Euclidean Functions of Computable Euclidean Domains.Rodney G. Downey & Asher M. Kach - 2011 - Notre Dame Journal of Formal Logic 52 (2):163-172.
Prolegomena to a cognitive investigation of Euclidean diagrammatic reasoning.Yacin Hamami & John Mumma - 2013 - Journal of Logic, Language and Information 22 (4):421-448.
Diagram Contents and Representational Granularity.Kenneth Manders - 1996 - In Jerry Seligman & Dag Westerstahl (eds.), Logic, Language and Computation. Center for the Study of Language and Inf. pp. 1.
Diagram-Based Geometric Practice.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 65--79.
The Diagram Prize.Bruce Robertson - 2012 - Logos 23 (4):30-32.
Matrix iterations and Cichon’s diagram.Diego Alejandro Mejía - 2013 - Archive for Mathematical Logic 52 (3-4):261-278.

Analytics

Added to PP
2014-02-01

Downloads
13 (#1,041,239)

6 months
1 (#1,478,781)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Kenneth Manders
University of Pittsburgh

References found in this work

No references found.

Add more references