Re: My investigations into Godels Incompleteness Theorem


Daryl McCullough wrote:
John Jones says...

Daryl McCullough wrote:

Godel says that a sentence has a string (which is arguable).

No, Godel doesn't talk about strings. I'm the one saying that,
and no, it's really not arguable.

Really, he should not then go on to use the sense (theorem)
of that sentence as if it was the sentence itself.

He doesn't do that. You are deeply confused about this.

Let's try something much simpler. Consider the sentence
of arithmetic

0+0=0

Under the usual interpretation of the symbols "0", "+",
and "=", that is a true sentence, and in fact, it
is a theorem of Peano Arithmetic. Do you agree?

Now, the above sentence corresponds to a string
that is 5 characters in length, and whose first
character is "0", whose second character is "+",
whose third character is "0", whose fourth character
is "=" and whose fifth character is "0". Do you
agree?

Okay, then here is an example of a property of strings:

is a string that is 5 characters in length, and
whose first character is "0", whose second character
is "+", whose third character is "0", whose fourth
character is "=" and whose fifth character is "0"

Let's call that property "P".

Here is a fact about property P:

For any sentence S in the language of arithmetic,
if the string corresponding to S has property P,
then S is a theorem.

Do you agree? If not, why not?

--
Daryl McCullough
Ithaca, NY

Before you switch the computer off, I say that the properties of a
string are not conferred on the sentence that is constructed out of it.
Any more than the properties of a letter are conferred on the meaning
of a word.
When you make a string you lose the sense of the of the sentence and
merely address individual signs. What you are claiming is that the
meaning of a sentence is exhibited in its string, which is simply not
true.

.

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