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Full Idea
Two obvious propositions of which one can be deduced from the other both become more certain than either in isolation; thus in a complicated deductive system, many parts of which are obvious, the total probability may become all but absolute certainty.
Gist of Idea
If one proposition is deduced from another, they are more certain together than alone
Source
Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279)
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.279
A Reaction
Thagard picked this remark out, in support of his work on coherence.
| 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] |