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Full Idea
A theory is 'non-conservative' if it allows us to prove mathematical facts that go beyond what the background mathematical theory can prove on its own.
Gist of Idea
A theory is 'non-conservative' if it facilitates new mathematical proofs
Source
Leon Horsten (The Tarskian Turn [2011], 01.4)
Book Ref
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.7
A Reaction
This is an instance of the relationship with mathematics being used as the test case for explorations of logic. It is a standard research method, because it is so precise, but should not be mistaken for the last word about a theory.
| 16891 | Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge] |
| 16906 | The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion] |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| 17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| 14620 | Theories in logic are sentences closed under consequence, but in truth discussions theories have axioms [Fine,K] |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| 15328 | A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten] |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |