We come finally, however, to the relation of the ideal…
“We come finally, however, to the relation of the ideal theory to real world, or "real" probability. If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: "If this is what you want, try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician". In practice he is apt to say: "try this; if it works that will justify it".”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
Ideal mathematical systems are presented as abstract, with practical use left to philosophers or practitioners who test them empirically.
In simple terms: Math can be abstract; real use needs testing.
Key Takeaway
Test abstract ideas in real contexts.
Themes
philosophy
mathematics
application
probability
idealism
Mood
analytical
skeptical
inquisitive
Type
theoretical
practical
When to use this quote
- academic research
- engineering design
- policy modeling
- statistical analysis
Key Concepts
epistemology
pragmatism
methodology
Questions to Reflect On
- How do you decide when an abstract model is ready for real use?
- What role should philosophy play in applying mathematics?
A Different Perspective
Abstract theory may not translate directly without empirical validation.