I would like to recommend the article by Lakoff and Nunez (bibliographical data below). It seems to me that some of the points they makes are points Bill Lawvere and Walter Noll have been making for years, and it is a pity that they didn't mention the work in categorial foundations, synthetic differential geometry, etc that makes some of the ideas rigorous. The article: George Lakoff and Rafael E. Nunez, The Metaphorical Structure of Mathematics: Sketching Out Cognitive Foundations for a Mind-Based Mathematics, in Mathematical Reasoning: Analogies, Metaphors and Images, edited by Lyn D. English, Lawrence Erlbaum Associates, 1997, pages 21-92. Too bad it is buried in the math ed ghetto. Charles Wells, Department of Mathematics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106-7058, USA. EMAIL: charles@freude.com. OFFICE PHONE: 216 368 2893. FAX: 216 368 5163. HOME PHONE: 440 774 1926. HOME PAGE: URL http://www.cwru.edu/artsci/math/wells/home.html "Some have said that I can't sing. But no one will say that I _didn't_ sing." --Florence Foster Jenkins