And so on...: reasoning with infinite diagrams

Synthese 186 (1):371 - 386 (2012)
  Copy   BIBTEX

Abstract

This paper presents examples of infinite diagrams (as well as infinite limits of finite diagrams) whose use is more or less essential for understanding and accepting various proofs in higher mathematics. The significance of these is discussed with respect to the thesis that every proof can be formalized, and a "pre" form of this thesis that every proof can be presented in everyday statements-only form

Categories

Keywords

Reprint years

DOI

10.1007/s11229-011-9985-6

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,100

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

The Finite and the Infinite in Frege's Grundgesetze der Arithmetik.Richard Heck - 1998 - In Matthias Schirn (ed.), The Philosophy of mathematics today. New York: Clarendon Press.
Diagrams and proofs in analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.
Peirce and the logical status of diagrams.Sun-joo Shin - 1994 - History and Philosophy of Logic 15 (1):45-68.
Diagrams as locality aids for explanation and model construction in cell biology.Nicholaos Jones & Olaf Wolkenhauer - 2012 - Biology and Philosophy 27 (5):705-721.
Perceiving the infinite and the infinitesimal world: Unveiling and optical diagrams in mathematics. [REVIEW]Lorenzo Magnani & Riccardo Dossena - 2005 - Foundations of Science 10 (1):7-23.
A new applied approach for executing computations with infinite and infinitesimal quantities.Yaroslav D. Sergeyev - 2008 - Informatica 19 (4):567-596.
On automating diagrammatic proofs of arithmetic arguments.Mateja Jamnik, Alan Bundy & Ian Green - 1999 - Journal of Logic, Language and Information 8 (3):297-321.
On Infinite Number and Distance.Jeremy Gwiazda - 2012 - Constructivist Foundations 7 (2):126-130.
Diagrams as sketches.Brice Halimi - 2012 - Synthese 186 (1):387-409.

Analytics

Added to PP
2010-02-07

Downloads
190 (#104,627)

6 months
17 (#149,054)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

What are mathematical diagrams?Silvia De Toffoli - 2022 - Synthese 200 (2):1-29.
Who's Afraid of Mathematical Diagrams?Silvia De Toffoli - 2023 - Philosophers' Imprint 23 (1).
Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
Plans and planning in mathematical proofs.Yacin Hamami & Rebecca Lea Morris - 2020 - Review of Symbolic Logic 14 (4):1030-1065.

View all 16 citations / Add more citations

References found in this work

Science and method.Henri Poincaré - 1914 - New York]: Dover Publications. Edited by Francis Maitland.
Science and method.Henri Poincaré - 1914 - Mineola, N.Y.: Dover Publications. Edited by Francis Maitland.
The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
Logical reasoning with diagrams.Gerard Allwein & Jon Barwise (eds.) - 1996 - New York: Oxford University Press.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.

View all 24 references / Add more references