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Full Idea
In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
Gist of Idea
To study formal systems, look at the whole thing, and not just how it is constructed in steps
Source
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.204
A Reaction
This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.
| 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] |