Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
LudovicoVan

Posts: 3,206
From: London
Registered: 2/8/08
Re: Ordinals describable by a finite string of symbols
Posted: Jul 7, 2013 6:02 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"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@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
>> 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 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
Read Re: Ordinals describable by a finite string of symbols
fom
7/5/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/6/13
Read Re: Ordinals describable by a finite string of symbols
Shmuel (Seymour J.) Metz
7/7/13
Read Re: Ordinals describable by a finite string of symbols
Peter Percival
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/8/13
Read Re: Ordinals describable by a finite string of symbols
Shmuel (Seymour J.) Metz
7/8/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/5/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/5/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/6/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/6/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/6/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/6/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/6/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/8/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.