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Full Idea
Gödel undermined Frege's assumption that all but the basic truths are provable in a system, but insofar as one conceives of proof informally as an epistemic ordering among truths, one can see his vision as worth developing.
Gist of Idea
Despite Gödel, Frege's epistemic ordering of all the truths is still plausible
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Apriority (with ps) 1
Book Ref
Burge,Tyler: 'Truth, Thought, Reason (on Frege)' [OUP 2001], p.361
A Reaction
[compressed] This 'epistemic ordering' fits my thesis of seeing the world through our explanations of it.
| 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] |