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Full Idea
It is an apparent absurdity in proceeding ...through many rather recondite propositions of symbolic logic, to the 'proof' of such truisms as 2+2=4: for it is plain that the conclusion is more certain than the premises, and the supposed proof seems futile.
Gist of Idea
It seems absurd to prove 2+2=4, where the conclusion is more certain than premises
Source
Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272)
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.272
A Reaction
Famously, 'Principia Mathematica' proved this fact at enormous length. I wonder if this thought led Moore to his common sense view of his own hand - the conclusion being better than the sceptical arguments?
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| 10256 | For intuitionists, proof is inherently informal [Shapiro] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| 10885 | Computer proofs don't provide explanations [Horsten] |