Skip Navigation


Philosophia Mathematica Advance Access originally published online on January 23, 2006
Philosophia Mathematica 2006 14(3):378-391; doi:10.1093/philmat/nkj020
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
14/3/378    most recent
nkj020v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Van Bendegem, J. P.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Philosophia Mathematica (III), Vol. 14 No. 3 © The Author [2006]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

PAOLO MANCOSU, KLAUS FROVIN JØRGENSEN AND STIG ANDUR PEDERSEN, eds. Visualization, Explanation and Reasoning Styles in Mathematics. Synthese Library, Vol. 327. Dordrecht: Springer, 2005. Pp. x + 300. ISBN 1-4020-3334-6 (cloth), 1-4020-3335-4 (e-book).

Jean Paul Van Bendegem*

* Vrije Universiteit Brussel, Department of Philosophy, Centre for Logic and Philosophy of Science, Pleinlaan 2 B-1050 Brussel, Belgium. jpvbende@vub.ac.be

The first 150 words of the full text of this article appear below.


   1. Introduction
 
What is philosophy of mathematics and what is it about? The most popular answer, I suppose, to this question would be that philosophers should provide a justification for our presently most cherished mathematical theories and for the most important tool to develop such theories, namely logico-mathematical proof. In fact, it does cover a large part of the activity of philosophers that think about mathematics. Discussions about the merits and faults of classical logic versus one or other ‘deviant’ logics as the logical basis for mathematical theories, ranging from intuitionist over modal logic to paraconsistent logic, typically belong to this area, as do debates about the natural-number concept, its ‘nature’, its properties, especially its uniqueness, and so on. No doubt sociologists of knowledge could explain why (the community of) philosophers of mathematics came to select these particular problems and deal with them the way they do. What it does imply, however, . . . [Full Text of this Article]


   2. Mathematical Reasoning and Visualization
 

   3. Mathematical Explanation and Proof Styles
 

   4. Conclusion
 

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?