User:Boris Tsirelson/Sandbox1
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Defined or undefined
Facts are formulated via notions.
In the non-axiomatic approach, notions are nodes of a network whose connections are definitions. If some notions are forgotten they probably can be restored from the others.
Searching Google for "define:line" we get "a length without breadth or thickness". Similarly we find definitions for breadth, thickness and so on, recursively. Doing so we would get a large subnetwork; here is its small fragment:
- Line: a length without breadth or thickness
- Length: linear extent in space
- Linear: along a line↑
- Extent: a range of locations
- Location: point or extent↑ in space
- Space: unlimited expanse in which everything is located↑
- Breadth: the extent↑ from side to side
- Side: a surface forming part of the outside of an object
- Surface: the extended↑ two-dimensional outer boundary of a three-dimensional object
- Side: a surface forming part of the outside of an object
- Thickness: the dimension through an object as opposed to its length↑ or width
- Width: the extent↑ from side↑ to side↑
- Length: linear extent in space
(Up arrows mean: see above.) We observe that