LudovicoVan
Posts:
4,025
From:
London
Registered:
2/8/08


Re: Ordinals describable by a finite string of symbols
Posted:
Jul 7, 2013 6:02 PM


"fom" <fomJUNK@nyms.net> wrote in message news:_9idnQkXucdXIETMnZ2dnUVZ_gqdnZ2d@giganews.com... > On 7/7/2013 1:10 PM, Julio Di Egidio wrote: >> "fom" <fomJUNK@nyms.net> wrote in message >> news:6LSdnVj9KObNO0TMnZ2dnUVZ_sadnZ2d@giganews.com... >>> On 7/7/2013 8:06 AM, Julio Di Egidio wrote: >>>> "Julio Di Egidio" <julio@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
> 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.

