Undefined Concepts in Elementary Geometry
It is said in a book on geometry, which I am reading now a days that:
Point, Line, and Plane are undefined terms. These terms underlie the definitions of all geometric terms. They can be given meanings by way of descriptions. However, the descriptions given to them should not be taken as definitions.
First of all, what is the difference between a definition and a description? Is a concept undefined when it cannot be explained in terms of other concepts which may or may not have a proper definition of themselves? Is a description of something reports of its properties, its features but does not exactly tell what it really is?
A line can be defined in terms of points. Because we say that the extremities of a line are points, that means a point is a part of a line. And, the same we can do to describe a surface. What exactly is an undefined term then?
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$\begingroup$Rather than use the term "undefined", I would use the term - "primitive" . A primitive notion is one that is not defined using previously defined concepts. It is assumed to be understood by intuition and/or experience.
You give the example of the line , which can be defined using the concept of points. I think then you say that a point can be defined using the concept of lines. Here, you used A to define B and then B to define A, which is circular reasoning. We must accept one of the other A or B, as primitive and then define the other using it.
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