Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Semiotica

Journal of the International Association for Semiotic Studies / Revue de l'Association Internationale de Sémiotique

Editor-in-Chief: Danesi, Marcel

6 Issues per year


CiteScore 2016: 0.32

SCImago Journal Rank (SJR) 2015: 0.275
Source Normalized Impact per Paper (SNIP) 2015: 0.661

Online
ISSN
1613-3692
See all formats and pricing
In This Section
Volume 2011, Issue 187 (Jan 2011)

Issues

Blending in mathematics

James C. Alexander
  • Professor Emeritus at Case Western Reserve University.
  • Email:
Published Online: 2011-09-29 | DOI: https://doi.org/10.1515/semi.2011.063

Abstract

Mathematics is one of the richest, if more abstruse, areas of higher human cognition. It is a formal system, founded on a minimum of primitive concepts, but involving cognitive mechanisms, such as blending and framing, in an iterative manner, which lead to the rich structure of “higher” mathematics. The use of such cognitive mechanisms is done in a very controlled way, so as to maintain the rigor of the discipline. It is suggested that blending and other such mechanisms are incorporated into the formal structure of the discipline. This thesis is examined via a number of examples. This has the effect that blends are easy to make in mathematics. On the other hand, before blends and other processes were incorporated into mathematics, some blends that are obvious, even necessary, in hindsight, have taken a long time — sometimes centuries — to be realized. We hypothesis there is a cognitive cost to actualizing blends, which must be overcome. This phenomenon is investigated via the historical record.

Keywords:: blending; framing; conceptual integration; mathematics; structure; arrested blend

About the article

Published Online: 2011-09-29

Published in Print: 2011-10-01



Citation Information: Semiotica, ISSN (Online) 1613-3692, ISSN (Print) 0037-1998, DOI: https://doi.org/10.1515/semi.2011.063. Export Citation

Comments (0)

Please log in or register to comment.
Log in