Re: Analytic Expressions of language not linked to their semantic meaning are simply untrue

On 8/3/24 7:46 PM, olcott wrote:

On 8/3/2024 6:04 PM, Richard Damon wrote:

On 8/3/24 2:40 PM, olcott wrote:

On 8/3/2024 12:53 PM, Richard Damon wrote:

On 8/3/24 12:24 PM, olcott wrote:

On 8/3/2024 11:06 AM, Richard Damon wrote:

On 8/3/24 9:44 AM, olcott wrote:

On 8/3/2024 4:50 AM, Mikko wrote:

On 2024-08-02 12:19:31 +0000, olcott said:
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On 8/2/2024 1:43 AM, Mikko wrote:

On 2024-07-31 14:46:17 +0000, olcott said:
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On 7/31/2024 3:03 AM, Mikko wrote:

On 2024-07-30 13:40:55 +0000, olcott said:
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On 7/30/2024 2:33 AM, Mikko wrote:

On 2024-07-29 00:44:41 +0000, olcott said:
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The truth about every expression of language that can be known
to be true on the basis of its meaning expressed in language is
that a lack of connection simply means untrue.

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Does that really mean something? If the significance of the lack of
connection is restricted to sentences where the connection exists
then it seems that you are talking about nothing.
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https://plato.stanford.edu/Entries/analytic-synthetic/
I had to redefine the analytic side of the analytic/synthetic
distinction because Quine convinced most everyone that this
distinction does not exist.

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You cannot redefine side wihout redefining the other side and the
distinction itself. Is your redefinition equivalent to the one
at https://plato.stanford.edu/Entries/analytic-synthetic/ or did
you find out that that distincition is not the one that exists?

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Quine got totally confused by synonymity. He never understood
that the term {Bachelor} was defined in terms of
(~Married + Adult + Male).

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It is not a good idea to lie about other people.
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When reqding Quine, you should ask yourself why your presentation
is much less convincing than Quine's.

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Try and show the details of how I am incorrect.

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What you said (quoted above) about Quine is insulting and unjustified,
which alone is wrong.
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The bottom line here is that every objection that he could
have possibly made is addressed by this augmentation to
the definition of {analytic truth}
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*Original definition* of {Analytic truth}
Every expression of (formal or natural language) that is
true on the basis of its meaning...
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*Is augmented by this*
within a system of reasoning is only true when this
expression is linked by truth preserving operations to
its meaning within this system using this language.
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The superset of all of these systems that contains all
analytic truth is called {the accurate model of the actual world}.
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And so you agree that Godel's G is True in PA.
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It seems that you are the only one that believes that
there are any sequence of truth preserving operations
from G to the axioms of PA showing that G is true in PA.
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You are sorely mistaken in that beleif, but that error is caused by your ignorance of the topic.
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Anyone who understands Godel's proof would understand that fact.
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Note, you have the sentence backwards, the sequence is from the axioms to G, not G to the axioms.
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That just shows you don't understand how to do logical proofs.
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We know what we can demonstrate by a sequence from the axioms to the statement.
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We can form an actual proof for each individual number, but just cranking the Relationship (which will always have a finite number of steps) showing that this number does not satisfy the relationship.
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By just chaining the infinite set of these proofs for every number, we get that infinite chain of steps that establish G as true.

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Ah I see now.
There is not a proof with an infinite sequence of steps
that proves G in PA as you claimed. Instead an infinite
set of proofs fails to prove G in PA.

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There is no such thing as a proof with an infinite number of steps.
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That is like talking about a triangle with 5 sides.
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The infinite sequence of steps shows that G is true, as it shows that no number exists that statisfies the given PRR, which is exactly what G claims.
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 That is not a sequence of steps in PA
It is an infinite set of finite sequences of steps in PA.

which can be placed end to end to form a single sequence.

 

Your misuse of the word "prove" just shows your utter ignorance of what you are talking about.
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 That was my mistake.
 

The infinite set of proofs DOES estabilish that G is true, as G is a statment that claims that no number satisfied that relationship. Having a proof for every possible that it doesn't satisfiy that relationship, shows that G is in fact true, as no number can exist that falsifies G.
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 Yet PA is incapable of evaluating this.

Of course it is capable.

I don't think that PA can even represent more than
one proof at a time, so it is no sequence of steps in PA.

Why do you say that?
Do you have a source of that?
Note, PA could be the field of Peano Arithmatic.

 

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Yet that would be back to the simple version of G that
merely claims to be unprovable in PA. Not some other
different highly abstract relationship that you had
been claiming.

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There is no such G, except in your imagination.
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 *Gödel stated that this was his intention*
...We are therefore confronted with a proposition which asserts
its own unprovability. 15 ... (Gödel 1931:40-41)

Right, we reach that point as a result proven as an interpretation in MM. It is NOT the actual statement of G, only a result that can be derived from it in MM. That because of the nature of the relationship generated, G can only be true if it is unprovable, but a proof becomes the evidence that it is not true.
Such a statement, must be true and unprovable, as a provable statement that is false is a contradiction.
Note, a statement can not be derived that has that meaning solely from information in the system, or IT becomes the proof that forces the contradiction, but when that meaning requires information from a meta-system, it establishes the truth (and unprovability) of the statement.
The fact that you don't seem to understand how formal system and meta-systems work makes this all unintelligible.

 

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Do you understand that no one needs to have any
understanding of the proof to refute it when they
can show that its conclusion is incorrect?
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Doesn't work that way. Since your "proof" that it is wrong is based on your own assumptions, all you prove is that your assumptions are untrue.
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 I may not have done it correctly yet any proof can be
refuted by simply showing that its conclusion is wrong
with no need to even understand any of the steps.
 

Nope. At best you can show that one of three things are true:
1) YOUR proof is wrong.
2) The proof you are refuting is wrong, or
3) The system is inconsistant.
To get anyone to think anything past the first option, you need a SOLID proof.
You are just proving you don't understand how logic works, so you don't get by option 1.
If your argument needs ANY non-standard claims, the result will be the assumption of option 1.