Body, Category of Sets, Category Theory, Concept, Conceptual Mathematics, Element, Example, Figure, Function, Locus, Map Object, Mathematical Concept, Mathematics, Object, One, Organization, Philosophy, Property, Set, Singleton Set, Size, Sorting, Structure, Terminal Object, Textbook, Understanding, Universal Mapping Property, Value, Varying Element
Body of mathematical concepts
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
From → Note to self
Posina Venkata Rayudu
From: ralphw@bakermountain.org, Nov 20, 2012, To: Venkata Rayudu Posina
You might have a look at “Mathematics Form and Function” by Mac Lane and at “Sets for Mathematics” by Lawvere and Rosebrugh.
Ralph Wojtowicz
Baker Mountain Research Corporation
P.O. Box 68
Yellow Spring, WV 26865
web : http://www.bakermountain.org