Full Idea
Any new discovery as to mathematical method and principles is likely to upset a great deal of otherwise plausible philosophising, as well as to suggest a new philosophy which will be solid in proportion as its foundations in mathematics are securely laid.
Gist of Idea
Discoveries in mathematics can challenge philosophy, and offer it a new foundation
Source
Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.283)
Book Reference
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.283
A Reaction
This is a manifesto for modern analytic philosophy. I'm not convinced, especially if a fictionalist view of maths is plausible. What Russell wants is rigour, but there are other ways of getting that. Currently I favour artificial intelligence.