Definition
In an axiomatic system like Euclidean geometry, Undefined Terms are the basic, primitive words that are used to define all other terms. Because every definition must use other words, there must be a starting point of terms that are accepted without formal definition, though they are described by their properties.
Why It Matters
Undefined terms are the ‘brute facts’ that prevent an infinite regress of definitions; they remind us that every system of thought must eventually rest on a few simple, intuitive primitives that we accept without proof in order to build anything at all.
Core Concepts
- Point: A location in space that has no size (zero dimensions). It is represented by a dot and named with a capital letter.
- Line: An infinite set of points that extends in two opposite directions without end. It has “straightness” and one dimension (length).
- Plane: A flat surface that extends infinitely in all directions. It has two dimensions (length and width) but no thickness.
- Set/Element: Geometry treats figures as sets of points.