Re: My investigations into Godels Incompleteness Theorem


Daryl McCullough wrote:
John Jones says...

1) My first concern is the least of them: equivalence of string and
number. Can the natural numbers do something that our string cannot? Is
our string example a suitable example to use in place of natural
numbers?

Strings and natural numbers work equally well. You can code a string
as a natural, and vice-versa, so there is no significant difference
between them.

2) I have serious misgivings about the correspondence of a particular
string with a particular sentence. It seems that the only ground for a
correspondence between them is the fact that they occupy the same
space. Otherwise, a string of 50 letters would correspond to any
sentence containing fifty letters, and not just to one particular
sentence. And, we cannot quote particular shared properties between a
string and sentence as a ground for their correspondence because the
statement

I can't make any sense of your objection here. The
sentence "Snow is white" clearly corresponds to the
string whose first character is "S", whose second
character is "n", whose third character is "o", etc.

3) I have another quite serious misgiving. IF a sentence can somehow
be matched or correspond to a string without any problems of the sort
mentioned above, then I need to know either

a) how a sentence can transmutate into a string; AND how the theorem S
can logically address a transmutation if that transmutation is its
foundation, or

I can't make any sense of this objection, either.

--
Daryl McCullough
Ithaca, NY

I see. This might be important then.
I need to know the nature of "correspondence". It seems to be crucial
to the enterprise. We might say of an object that it is both red and
square, but if these are properties of an unnamed object then I must
say what that object is. If I do not say what that object is then I
cannot assign the properties red and square to the same object.
Similarly for strings and sentences,

so my question is: What object bears the properties 'string' and
'sentence'?

However, this formulation may not be acceptable. Instead, we might say
that a sentence and a string are not properties of an object, but
entertain a relationship of "correspondence".

But what is correspondence in this case? We may say that a
correspondence relationship is an identity relationship. In other
words, things that correspond are identical. Just like 'the morning
star is venus' and 'the evening star is venus', the two sentences have
the same reference but are not identical in sense. But even here we
need to posit a third material object (the planet venus) to account for
the identity.

It seems to me that what is happening is this: A property of a sentence
is being confused with the property of the presentation of a sentence.
The string is a property arising from the property of the presentation
of the sentence and not from a property of the sentence itself. In
other words presentation of sense is being confused with sense. This is
the basis of the "correspondence" relationship between string and
sentence. But presentation of sense is not identical to sense.

An easy way to understand it is this: I can apply a formula for a
string to the form of a sentence, and get a string. This does NOT mean
that the sentence has the property of a string, or that there is a
correspondence or identity relationship between sentence and string.
The form of a sentence is unrelated to its sense, and a sentence is its
sense. Godel seems to be applying a reductionism of sense to property
when he speaks of a correspondenbce between string and sentence.
Another example of an unacceptable reduvctionsism is the formulation
'mind is matter', which also leads us into many circularities.

.

Relevant Pages

  • Re: Help with Linking to new documents
    ... My own TYPO alert: ... Please keep all correspondence within the Group, ... I'd build a formula that would create a string that looked like your ... I have a production worksheet that links to multiple invoices saved as ...
    (microsoft.public.excel.misc)
  • Re: My investigations into Godels Incompleteness Theorem
    ... Daryl McCullough wrote: ... and only if the string corresponding to S has property P. ... I have serious misgivings about the correspondence of a particular ... can logically address a transmutation if that transmutation is its ...
    (sci.logic)
  • Re: My investigations into Godels Incompleteness Theorem
    ... Daryl McCullough wrote: ... and only if the string corresponding to S has property P. ... I have serious misgivings about the correspondence of a particular ... can logically address a transmutation if that transmutation is its ...
    (sci.logic)
  • Re: My investigations into Godels Incompleteness Theorem
    ... Daryl McCullough wrote: ... and only if the string corresponding to S has property P. ... I have serious misgivings about the correspondence of a particular ... can logically address a transmutation if that transmutation is its ...
    (sci.logic)
  • Re: My investigations into Godels Incompleteness Theorem
    ... If you believe that there is some problem with this correspondence, ... do everything in vague generalities without checking to see whether ... do you agree that this corresponds to a string that is 15 ... What corresponds to a string that is 15 characters ...
    (sci.logic)
Quantcast