I do not want to presuppose anything as known. I see in my…
“I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek.”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
He argues that redefining basic geometric concepts with group axioms leads to vague, unproductive results.
In simple terms: Redefining points, lines, planes with group theory creates confusion.
Key Takeaway
Avoid overcomplicating fundamental definitions.
Themes
mathematics
philosophy
definition
Mood
analytical
critical
Type
philosophical
academic
When to use this quote
- teaching geometry
- research methodology
- philosophical debate
Key Concepts
axiomatic systems
conceptual clarity
Questions to Reflect On
- Is simplicity more valuable than completeness?
- When should new frameworks be introduced?
A Different Perspective
Complex redefinitions can obscure understanding.