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Topic: Ordinals describable by a finite string of symbols
Replies: 27   Last Post: Jul 8, 2013 9:56 PM

 Messages: [ Previous | Next ]
 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
>
>
> >>> On 7/7/2013 8:06 AM, Julio Di Egidio wrote:
>
> >>>> "Julio Di Egidio" <jul..@diegidio.name> wrote in message
>
> >>>> news:krbohl\$av6\$1@dont-email.me...
>
> >>>>
>
> >>>>> We know it when you know it, it self-represents
>
> >>>>
>
> >>>> 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
>
>
> >
>
> > 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.
>
>
>
>
> 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 co-workers, 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.

Date Subject Author
7/5/13 fom
7/5/13 fom
7/6/13 Shmuel (Seymour J.) Metz
7/7/13 Peter Percival
7/7/13 fom
7/8/13 Shmuel (Seymour J.) Metz
7/8/13 fom
7/5/13 fom
7/5/13 fom
7/6/13 LudovicoVan
7/6/13 fom
7/6/13 LudovicoVan
7/6/13 fom
7/6/13 LudovicoVan
7/7/13 LudovicoVan
7/7/13 LudovicoVan
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom
7/8/13 apoorv
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom