Dear All, Mathematical concepts such as 1, singleton set, and objects satisfying universal mapping properties are placed in well-defined positions. One ready illustration: the way 1 is related to a singleton set (property-value of a structure) is determinately definite and different from the ways in which singletons are related to objects satisfying universal mapping properties (example, sorting). We can also, for example, read vividly going from 1 to singleton set to terminal object to objects satisfying universal mapping properties to map object to its size--a number--all in the space of a line segment: a figure is the locus of a varying element (Conceptual Mathematics, page 83). Mathematical concepts, from this perspective, appear to be clearly organized. Would you be kind enough to point me to our current understanding (say, a textbook) of the structure of the body of mathematical concepts. Happy Philosophy Day! Thank you, posina [For admin and other information see: http://www.mta.ca/~cat-dist/ ]