On May 26, 4:49 pm, Nam Nguyen <namducngu...@shaw.ca> wrote: > On 26/05/2013 3:52 AM, Zuhair wrote: > > > > > > > > > > > On May 26, 11:03 am, Nam Nguyen <namducngu...@shaw.ca> wrote: > >> On 26/05/2013 12:52 AM, Zuhair wrote: > > >>> Frege wanted to reduce mathematics to Logic by extending predicates by > >>> objects in a general manner (i.e. every predicate has an object > >>> extending it). > > >> [...] > > >>> Now the above process will recursively form typed formulas, and typed > >>> predicates. > > >> Note your "process" and "recursively". > > >>> As if we are playing MUSIC with formulas. > > >>> Now we stipulate the extensional formation rule: > > >>> If Pi is a typed predicate symbol then ePi is a term. > > >>> The idea behind extensions is to code formulas into objects and thus > >>> reduce the predicate hierarchy into an almost dichotomous one, that of > >>> objects and predicates holding of objects, thus enabling Rule 6. > > >>> What makes matters enjoying is that the above is a purely logically > >>> motivated theory, I don't see any clear mathematical concepts involved > >>> here, we are simply forming formulas in a stepwise manner and even the > >>> extensional motivation is to ease handling of those formulas. > >>> A purely logical talk. > > >> Not so. "Recursive process" is a non-logical concept. > > >> Certainly far from being "a purely logical talk". > > > Recursion is applied in first order logic formation of formulas, > > Such application isn't purely logical. Finiteness might be a purely > logical concept but recursion isn't: it requires a _non-logical_ > concept (that of the natural numbers). > > > and all agrees that first order logic is about logic, > > That doesn't mean much and is an obscured way to differentiate between > what is of "purely logical" to what isn't. > Recursion utilized in first order logic is to me a part of logic, so is that utilized here.