Re: My investigations into Godels Incompleteness Theorem
- From: stevendaryl3016@xxxxxxxxx (Daryl McCullough)
- Date: 2 Oct 2006 10:42:40 -0700
John Jones says...
Daryl McCullough wrote:
That's because you asked an ambiguous question, which has an ambiguous
answer. If instead, you asked a question such as
What sentence has a string representation 5 characters long, whose
first character is "0", whose second character is "+", whose third
character is "0", whose fourth character is "=", whose fifth character
is "0"?
Then the answer would clearly be the *sentence* 0+0=0.
No, the problem persists. Sentences 'having' a string. Which sentences?
Every sentence has a corresponding string. There is a unique
mapping from sentences to strings, which everyone who is able
to type understands.
You are particular over which sentence. It is always the sentence that
appears in the same place as the string, which isn't doing maths.
You don't know anything about mathematics, so don't bring that up.
Or you use the fact that every sentence has a unique representation
as a string of characters. Once again, you *know* that every sentence
has a unique representation as a string of characters, otherwise you
wouldn't be able to use a keyboard. Your general claims are proved
ridiculous by the specific facts.
If every sentence had a truly unique representation as a string, a
string would be a sentence.
Every sentence corresponds to a string, but not every string
corresponds to a sentence.
You should ponder how communication via keyboards can possibly work,
if you claim there is no basis for relating sentences to character
strings.
There's no connection between keyboard and sentence.
That, like many statements you make, is completely false.
A sentences sense emerges. It does not emerge from any properties a
string has.
That's completely false. You are *typing* into a keyboard. You
are relying on a correspondence between sequences of keystrokes
and sentences.
There is no coherent sense in saying they correspond.
Perhaps not to a infant, and not to a dog. Perhaps not to
John Jones. But to an intelligent human being, yes there
is a coherent sense in which sentences correspond to character
sequences.
That's right isn't it?
No, it's nonsensical.
What sense do we get from saying sentence and
string correspond?
It's what makes typewriters and word processors and reading
possible. The correspondence between sentences and strings
of characters was one of the great inventions of human intelligence.
It is literally what makes math, science and civilization
itself possible.
What sense do you get from denying the correspondence?
--
Daryl McCullough
Ithaca, NY
.
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