* Body of mathematical concepts
@ 2012-11-16 6:49 Venkata Rayudu Posina
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From: Venkata Rayudu Posina @ 2012-11-16 6:49 UTC (permalink / raw)
To: categories
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
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