Axioms Quote by Hans Reichenbach
“...the mathematician uses an indirect definition of congruence, making use of the fact that the axiom of parallels together with an additional condition can replace the definition of congruence.”
About This Quote
Source Essay: The Theory of Space and Time, 1928
Defining congruence indirectly uses parallel axioms plus extra conditions, showing definitions can be derived from related principles.
In simple terms: Definitions can be built from other axioms.
Use related principles to simplify complex definitions.
Themes
Mood
Type
When to use this quote
- mathematical proofs
- educational curricula
- philosophical debates
- technical documentation
Key Concepts
Questions to Reflect On
- When might a direct definition be preferable?
- How does this approach affect teaching geometry?
Reliance on indirect definitions may obscure intuitive understanding.