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Full Idea
There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives).
Gist of Idea
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite
Source
JC Beall / G Restall (Logical Consequence [2005], 3)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.6
| 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] |