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.
There is also inductive logic, which is best represented by statistical decision theory, and there are modal logics. I have seen description of "quantum logics", but I do not see them as more than partial representations.
-- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University email@example.com Phone: (765)494-6054 FAX: (765)494-0558