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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.” quote by Hans Reichenbach
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“...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.”

Hans Reichenbach

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.

Key Takeaway

Use related principles to simplify complex definitions.

Themes

logic geometry definition methodology philosophy of science

Mood

analytical critical academic

Type

philosophical educational

When to use this quote

  • mathematical proofs
  • educational curricula
  • philosophical debates
  • technical documentation

Key Concepts

axiomatic systems indirect definition foundations of geometry

Questions to Reflect On

  • When might a direct definition be preferable?
  • How does this approach affect teaching geometry?
A Different Perspective

Reliance on indirect definitions may obscure intuitive understanding.

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