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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 Ref
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.
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| 17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
| 17629 | Which premises are ultimate varies with context [Russell] |
| 17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
| 17631 | Induction is inferring premises from consequences [Russell] |
| 17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
| 17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
| 17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| 17640 | Finding the axioms may be the only route to some new results [Russell] |
| 17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |