more from this thinker | more from this text
Full Idea
A theory is a set of formulae closed under first-order logical consequence.
Gist of Idea
A theory is some formulae and all of their consequences
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 5.1)
Book Ref
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.29
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] |