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

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 LudovicoVan Posts: 4,034 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

>>> 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

>
> 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

> 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

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