I was thinking about a formal system that involves a set of primitives along with a property that, when applied to the model of planar one-dimensional objects, can distinguish between straight lines and curved lines. The system I came up with was:
Primitive terms:
a. 2-D Environment
b. Direction (also 2-D based)
c. Opposite direction
d. Equal direction
e. 1-D object
f. Point on 1-D object
g. Continuous
Definition of "Straight Line":
- A "straight line" is any continuous 1-D object in a 2-D environment for which the direction of the object at any (arbitrary) point on the object is either equal or opposite to the direction of the object at any other (arbitrary) point on it.
Now, my question is can this definition be considered to be a necessary and sufficient criterion for being a straight line, when all the primitive terms are assumed to have the meanings that we imply when we use the terms in real life? Also, can any term be considered redundant for the system?
All suggestions regarding changes for developing the system are welcome.
EDIT: As commented by @Gribouillis, there is a problem in the system, as line segments are also classified as straight lines according to the definition I came up with.