Re: Analytic Truth-makers

On 7/22/24 10:12 PM, olcott wrote:

On 7/22/2024 8:42 PM, Richard Damon wrote:

On 7/22/24 8:44 PM, olcott wrote:

On 7/22/2024 7:17 PM, Richard Damon wrote:

On 7/22/24 8:11 PM, olcott wrote:

On 7/22/2024 7:01 PM, Richard Damon wrote:

On 7/22/24 12:42 PM, olcott wrote:

I have focused on analytic truth-makers where an expression
of language x is shown to be true in language L by a sequence
of truth preserving operations from the semantic meaning of x
in L to x in L.
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In rare cases such as the Goldbach conjecture this may
require an infinite sequence of truth preserving operations
thus making analytic knowledge a subset of analytic truth. https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
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There are cases where there is no finite or infinite sequence
of truth preserving operations to x or ~x in L because x is
self- contradictory in L. In this case x is not a
truth-bearer in L.
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So, now you ADMIT that Formal Logical systems can be
"incomplete" because there exist analytic truths in them that
can not be proven with an actual formal proof (which, by
definition, must be finite).
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*No stupid I have never been saying anything like that* If g and
~g is not provable in PA then g is not a truth-bearer in PA.
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What makes it different fron Goldbach's conjecture?
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You are just caught in your own lies.
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YOU ADMITTED that statements, like Goldbach's conjecture, might be
 true based on being only established by an infinite series of
truth preserving operations.
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You seem to be too stupid about this too. You are too stupid to grasp
the idea of true and unknowable.
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In any case you are not too stupid to know that every expression that
requires an infinite sequence of truth preserving operations would
not be true in any formal system.

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So, is Goldbach'c conjecture possibly true in the formal system of
Mathematics, even if it can't be proven?
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 No. If it requires an infinite sequence of truth preserving
operations it is not true in any system requiring a finite
sequence.

So you LIED when you said Goldbach's conjuecture could bve actually TRUE even if it could only be established to be true by an infinite sequence of truth preserving operations.
Remember, you said:

In rare cases such as the Goldbach conjecture this may require an infinite sequence of truth preserving operations thus making analytic knowledge a subset of analytic truth.

Or are statements that are analytic truth not always true statements?

 

If so, why can't Godel's G be?
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 Gödel's G is true in MM.

And in PA, as proven,
YOu are just showing your ignorance.

 

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In PA, G (not g, that is the variable) is shown to be TRUE, but
only estblished by an infinite series of truth preserving
operations, that we can show exist by a proof in MM.
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No stupid that is not it. A finite sequence of truth preserving
operations in MM proves that G is true in MM. Some people use lower
case g.

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But the rules of construction of MM prove that statements matching
certain conditions that are proven in MM are also true in PA.
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 That is merely a false assumption.

So, how can the fact that it is shown that no number CAN satisfy the relationship not make it true that no number does satisfy the relationship?
You seem to have an error in your logic?

 

And G meets that requirements. (note g is the number, not the statement)
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We can show in MM, that no natural number g CAN satisfy that
relationship, because we know of some additional properties of that
relationship from our knowledge in MM that still apply in PA.
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Thus, Godel PROVED that G is true in PA as well as in MM.
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 That is merely a false assumption. Truth-makers cannot cross system
boundaries.

It didn't need to. The truth-makers are the fact that no number will satisfy that relationship. That is just an established fact.
We just got a short cut to allow us to do it faster in MM
or, do you thing that two system that share the same rules of arithmetic could have x+y = 5 in one systen but = 6 in the other?

 

He also PROVED that there can't be a proof in PA for it.
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Here is the convoluted mess that Gödel uses https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf

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And your inability to understand it doesn't make it wrong.
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 It is only his false conclusion that makes him wrong.
His false conclusion is anchored in an incorrect
foundation of expressions that are true on the basis
of their meaning.
 

And what is the error?
Claiming the answer is wrong, but not being able to show an error just says that YOUR logic is wrong.
Sorry, but that is how logic works, at least that is how working logic works.

It makes YOU wrong.
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The truth of G transfers, because it uses nothing of MM, the Proof
 does not, as it depends on factors in MM, so can't be expressed in
PA.

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No stupid that is not how it actually works. Haskell Curry is the
only one that I know that is not too stupid to understand this. https://www.liarparadox.org/Haskell_Curry_45.pdf
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Really, then show what number g could possibly sattisfy the relationship.
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 Incorrect foundation of truth-makers.

Nope, stupidity of Olcott.

 

I don't think you even undertstand what Curry is talking about, in fact, from some of your past comments, I am sure of that. (Note, not all "true" statements in L are "elementary statements" for the theory L as I believe you have stated in the past.

 Mere stupidly empty rhetoric entirely bereft of any supporting
reasoning probably used to try to hide your own ignorance.

Good discription of your argument.

 A theory is thus a way of picking out from the statements of F
a certain subclass of true statements.
  Curry, Harkell B. 1977. Foundations of Mathematical Logic. Page:45
   The statements of F are called elementary statements to distinguish them from other statements which we may form from them … A theory (over F is defined as a conceptual class of these elementary statements. Let T be such a theory. Then the elementary statements which belong to T we shall call the elementary theorems of T; we also say that these elementary statements are true for T. Thus, given T, an elementary theorem is an elementary statement which is true. A theory is thus a way of picking out from the statements of F a certain subclass of true statements.
https://www.liarparadox.org/Haskell_Curry_45.pdf
 

Yep, you just don't understand what he is saying.
I guess you are just too dumb to reason with, and you have proven that your logic of "correct reasoning" is justs a method you use to come up with wrong answers.