apoorv
Posts:
53
Registered:
4/11/13


Re: Ordinals describable by a finite string of symbols
Posted:
Jul 8, 2013 3:02 PM


On Monday, July 8, 2013 3:32:17 AM UTC+5:30, Julio Di Egidio wrote: > "fom" <fomJUNK@nyms.net> wrote in message > > news:_9idnQkXucdXIETMnZ2dnUVZ_gqdnZ2d@giganews.com... > > > On 7/7/2013 1:10 PM, Julio Di Egidio wrote: > > >> "fom" <fom?.@nyms.net> wrote in message > > >> news:6LSdnVj9KObNO0TMnZ2dnUVZ_sadnZ2d@giganews.com... > > >>> On 7/7/2013 8:06 AM, Julio Di Egidio wrote: > > >>>> "Julio Di Egidio" <jul..@diegidio.name> wrote in message > > >>>> news:krbohl$av6$1@dontemail.me... > > >>>> > > >>>>> We know it when you know it, it selfrepresents > > >>>> > > >>>> Oops, I just meant: We know it when we know it... > > >>> > > >>> It is common among the men with whom I > > >>> work to hear, "It is what it is". > > >>> > > >>> I take it to be an article of faith > > >> > > >> Is that all you could gather? Then I'll give you another pearl to think > > >> about: dogmatism and scepticism are the two sides of the same coin. But > > >> take your time... > > > > > > Well, I had been thinking in terms of the > > > fact that experience has an unavoidable > > > subjective sense. It invariably admits the > > > reduction of linguistic expressions to mere > > > syntax. But, it is also the subjective > > > experience that affords meaningful interpretation. > > > > I do not see how linguistic expression (language) can be reduced to syntax: > > a sign is not a symbol, the magic is all in the interpreter. > > > > > It is in the transition from subjective to > > > objective where all of the difficulties seem to > > > arise. > > > > We have already spoken about these seeming difficulties: what "objectivity" > > I would ask? I.e. same cart before the horses. There just is no such thing > > as a purely syntactical proof. > > > > Julio When we say, in sentential logic, From A & B , infer A iour reasoning appears to be purely syntactical. Even semantic inference of the type The sun is shining> it is bright Perhaps has a syntactic basis to it . We are perhaps, based on experience, Informally and subconsciously setting, The sun is shining <> it is bright & There is no artificial light. FOPL brings in , as a logical axiom, AxPx > Pa for every a . So long as the domain is finite, AxPx is but a finite conjunction of the type Pa&Pb etc and semantic Inference is nothing but purely syntactic inference. It is infinite domains where the two differ. Apoorv
> > > The sense in which mathematicians had to face > > > this is nicely summarized in DeMorgan, > > > > > > "As soon as the idea of acquiring > > > symbols and laws of combination, > > > without given meaning, has become > > > familiar, the student has the notion > > > of what I will call a symbolic > > > calculus; which, with certain symbols > > > and certain laws of combination, is > > > symbolic algebra: an art, not a > > > science; and an apparently useless > > > art, except as it may afterwards > > > furnish the grammar of a science. > > > The proficient in a symbolic calculus > > > would naturally demand a supply > > > of meaning. Suppose him left without > > > the power of obtaining it from > > > without: his teacher is dead, and he > > > must invent meanings for himself. > > > His problem is: Given symbols and > > > laws of combination, required meanings > > > for the symbols of which the right > > > to make those combinations shall be > > > a logical consequence. He tries, > > > and succeeds; he invents a set of > > > meanings which satisfy the conditions. > > > Has he then supplied what his teacher > > > would have given, if he had lived? > > > In one particular, certainly: he has > > > turned his symbolic calculus into a > > > significant one. But it does not > > > follow that he has done it in a way > > > which his teacher would have taught > > > if he had lived. It is possible > > > that many different sets of meanings > > > may, when attached to the symbols, > > > make the rules necessary consequences." > > > Augustus De Morgan > > > > > > My coworkers, however, would tend to make > > > the remark along the lines of their respective > > > faiths. And, to be honest, when suspended > > > in a rowboat on two wires 300 feet above > > > grade, I do too.

