On 6/2/2013 7:49 AM, Herman Rubin wrote: > On 2013-06-01, Julio Di Egidio <firstname.lastname@example.org> wrote: >> "fom" <fomJUNK@nyms.net> wrote in message >> news:9bWdnVL04P_k_DTMnZ2dnUVZ_t6dnZ2d@giganews.com... >>> On 5/31/2013 10:36 AM, Julio Di Egidio wrote: > >>>> Isn't indeed self-referentiality >>>> (circularity) the essential character of the (any) purely logical >>>> system? > >>> My answer to that is yes. > >>> I have done a great deal of work to understand how modern mathematical >>> logic has reached the point where its foundations are almost >>> exclusively focused on non-circularity. So, while you see this >>> condition as a matter of fact, such a claim in the mathematics >>> community may get you some metaphorical version of tar and feathers. > >> My point was that mathematical logic is not logic, it's mathematics: it's an >> abuse of language. Then I don't see why the mathematician should flame the >> logician for a claim on logic, all the more so when the logician in question >> is saying that mathematics cannot be reduced to logic in any meaningful >> sense (and vice versa). In simpler terms, what I can see in the logistic >> approach is, firstly reduce all endeavours to mechanics, then call >> mathematics logic, finally assert that all derives from logic. > > Mathematical logic is not all of logic, but it is logic, not > mathematics. There is more to the logic which is used by > mathematicians, such as in metamathematics, than is in the > first order predicate calculus, which is what is used in > mathematical proofs. There are metamathematical proofs of > mathematical theorems which do not have mathematical proofs. >
Out of curiosity, could you give an example of such a theorem?