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Full Idea
The premises [of a science] ...are pretty certain to lead to a number of new results which could not otherwise have been known.
Gist of Idea
Finding the axioms may be the only route to some new results
Source
Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.282)
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.282
A Reaction
I identify this as the 'fruitfulness' that results when the essence of something is discovered.
| 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] |
| 17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
| 17631 | Induction is inferring premises from consequences [Russell] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [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] |
| 17638 | If one proposition is deduced from another, they are more certain together than alone [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] |