On 6/1/2013 9:52 AM, Julio Di Egidio 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. >
This helps me to understand your position better.
I cannot disagree with you. In trying to understand foundational claims, I find myself in awe of the fact that one might think that the presumed explanatory power of mathematics derives from linguistic forms. On the other hand, the philosophical considerations of something like Russell's knowledge by acquaintance have significant merit. Thus, the approach to logic without regard to what mathematicians do is extremely interesting. They are very different subjects.
Did you feel that I had flamed Zuhair when I pointed out that we had different senses of demarcation? I certainly did not mean anything that way. And, if that is his interpretation then I shall offer an apology.
Although I do not study logic in the sense that others do, my questions have led me to respect logic as its own discipline. I recently posted this response to the question "What is a proof" on math.stackexchange.com