Re: G�del's sentence is not self-referential

On Nov 24, 9:59 am, LauLuna <laureanol...@xxxxxxxx> wrote:
Contrary to what some posters have stated in a recent thread on
impredicative sentences in G�del's proof, there is no self-referential
proposition involved in it.

Let's consider the well known G�del's sentence G.

1. G is just a closed formula, that is, a string of symbols, a purely
syntactic object. As such, G is about nothing because it says nothing.
A sentence must always be distinguished from a proposition; the latter
is a semantic object, which may be defined as the information content
an interpreted sentence conveys. So, 'snow is white' and 'la nieve es
blanca' are two different sentences expressing one and the same
proposition. On the other hand, ambiguous sentences may express more
than one proposition.

Sentences cannot as such be self-refrential, for they perform no
reference at all.

2. G�del's proof exploits the possibility of interpreting G as two
distinct but logically equivalent proposititions; I will call them
'AritG' and 'MetaG'. These are propositions, not sentences.

AritG is what G says when interpreted as a standard arithmetical
statement. AritG speaks about natural numbers, it asserts the non
existence of a number possessing a certain property. So, AritG is not
self-referential.

MetaG is the proposition which G expresses under its meta-theoretical
interpretation. The proposition MetaG is about the sentence G as a
mere symbol string, not about itself.

3. A proposition can safely refer to the sentence that expresses it,
without any peril of circularity or paradox; consider

'this sentence has five words'

I believe that no proposition can be about itself, but this is not
essential now, since nothing of the kind is present in G�del's proof.

4. To conclude: the simple distinction between sentences and
propositions shows that G�del's proof relies on no self-referential
proposition.

Regards

Please check where you got your material from and give due credit for
ownership.

Even though you conflate string with sentence and present them both
against a proposition, your proposition and sentence/string are
getting worryingly close to what I have been saying. Are you thinking
of writing/publishing this material?

I wrote in post 154 of "My investigations into Godel's incompleteness
theorem", this:.

"Godel is claiming, and everyone else,
that a sentence has a unique string and that the string represents or
corresponds to the sentence. But in that case, either

1) the string is simply a sign (and not a string) representing the
sentence. This cannot correlate sentence and string as 2) and 3) can,

2) or the sentence is identified by occupying a position on the page
laid out in ink in the same place as the string (in which case it is
also not a string but a position),

3) or string and sentence collaborate in implicit self-reference
("this
sentence is a string"), invoking obscure identity relationship,

4) or the string is unique to the sentence, in which case there is
one
sentence for a particular length and character depicting string. In
this case the string is the sentence - otherwise it is not a string
but
a referencing device, and these are arbitrary and not unique (see1)).
"

.