Synthese 186 (1):257-288 (2012)

Abstract
Diagrams have played an important role throughout the entire history of differential equations. Geometrical intuition, visual thinking, experimentation on diagrams, conceptions of algorithms and instruments to construct these diagrams, heuristic proofs based on diagrams, have interacted with the development of analytical abstract theories. We aim to analyze these interactions during the two centuries the classical theory of differential equations was developed. They are intimately connected to the difficulties faced in defining what the solution of a differential equation is and in describing the global behavior of such a solution.
Keywords Differential equation  Diagram  Geometric intuition  Visual thinking  Integral curve  Tractional motion  Qualitative integration  Graphical integration
Categories (categorize this paper)
DOI 10.1007/s11229-012-0069-z
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,043
Through your library

References found in this work BETA

The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
Visualization in Logic and Mathematics.Paolo Mancosu - 2005 - In Paolo Mancosu, Klaus Frovin Jørgensen & Stig Andur Pedersen (eds.), Visualization, Explanation and Reasoning Styles in Mathematics. Springer. pp. 13-26.
Epistemology of Visual Thinking in Elementary Real Analysis.Marcus Giaquinto - 1994 - British Journal for the Philosophy of Science 45 (3):789-813.

View all 8 references / Add more references

Citations of this work BETA

Drawing on the Imagination: The Limits of Illustrated Figures in Nineteenth-Century Geometry.Jemma Lorenat - 2020 - Studies in History and Philosophy of Science Part A 82:75-87.

Add more citations

Similar books and articles

Diagrams as Sketches.Brice Halimi - 2012 - Synthese 186 (1):387-409.
Law Along the Frontier: Differential Equations and Their Boundary Conditions.Mark Wilson - 1990 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:565 - 575.
Peirce and the Logical Status of Diagrams.Sun-Joo Shin - 1994 - History and Philosophy of Logic 15 (1):45-68.
Pictures and Pedagogy: The Role of Diagrams in Feynman's Early Lectures.Ari Gross - 2012 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (3):184-194.

Analytics

Added to PP index
2012-02-10

Total views
70 ( #162,400 of 2,498,734 )

Recent downloads (6 months)
1 ( #426,098 of 2,498,734 )

How can I increase my downloads?

Downloads

My notes