Re: Mathematical incompleteness has always been a misconception [CORRECTION]

On 2/1/2025 12:23 PM, Richard Damon wrote:

On 2/1/25 1:10 PM, olcott wrote:

On 2/1/2025 7:56 AM, Richard Damon wrote:

On 1/31/25 10:43 PM, olcott wrote:

On 1/31/2025 7:52 PM, Richard Damon wrote:

On 1/31/25 12:42 PM, olcott wrote:

On 1/31/2025 10:08 AM, Richard Damon wrote:

On 1/31/25 10:20 AM, olcott wrote:

On 1/31/2025 8:49 AM, Richard Damon wrote:

On 1/30/25 8:24 PM, olcott wrote:

On 1/30/2025 7:06 PM, Richard Damon wrote:

On 1/30/25 6:10 PM, olcott wrote:

Within the entire body of analytical truth any expression of language that has no sequence of formalized semantic deductive inference steps from the formalized semantic foundational truths of this system are simply untrue in this system. (Isomorphic to provable from axioms).
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In other words when any expression of language of any system (formal or informal) has no semantic connection to its semantic meaning in this system then this expression is simply nonsense in this system. "This sentence is untrue" is Boolean nonsense.
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Copyright PL Olcott 2016 through 2025.
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Except that isn't what incompleteness says.
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Incompleteness is about the existance of statements which are TRUE, because there is a sequence of formal semantic deduction that reaches the statement, abet an infinite one, but there is no finite sequnce of formal semantic deduction to form a proof.
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That might be correct. If it is correct then all then
all that it is really saying is that math is incomplete
because some key pieces were intentionally left out.

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What was left out?
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If there exists no contiguous sequence of semantic deductive inference
steps from the basic facts of a system establishing that the semantic meaning of this expression has a value of Boolean true in this system then this expression is simply not true in this system even if it may be
true in other more expressive systems.
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The system is incomplete in the artificially contrivance way of
deliberately defined system to be insufficiently expressive.
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And what about the fact that ther *IS* a contiguos sequence, infinite in length, that makes the statement true that you don't understand.
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"Incomplete" means that there is no contiguous sequence of inference
steps within the expressiveness of this specific formal system.
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No, "Incomplete" means that there is some true statement that can not be proven.
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Within empirical truth this is possible.
Within analytical truth this is impossible.

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No, you only think it is impossible, becuase you don't know what you are talking about.
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Unless there is a semantic connection with
a truthmaker to what makes the expression
true IS IS NOT TRUE.

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Right, and that can be an INFINITE series of connection, which thus don't form a proof.
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It does make a {proof} within the foundational base meaning
of the term {proof} even though it may not meet the idiomatic
term-of-the-art meaning from math. The generic notion of {Truth}
itself is only defined in terms of base meanings. When math
diverges from this it is no longer talking about actual truth.
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 The "foundational base meaning" of a proof in Formal Logic is a FINITE series.
 

True[0] cannot possibly exist for any expression of language that
is only made true by a semantic connection to its truthmaker
WITHOUT SUCH A CONNECTION.
This makes the notion of provable[math] essentially a misnomer
because it attempts to override and supersede the most basic
foundation of the notion of truth itself.

I know of no standard theory of logic that admits an infinite series of steps as a "proof", as we can not do an infinite series of steps, and a proof is normally about knowledge, and thus needs to be about something that we can actually do.
 We can do a finite series of steps to show that an infinite series of steps exist in another system by the properties of meta-logic, but that is not a "proof" in that other system, only in the meta-system, again something that seems to be beyond your understanding.
 And, you are wrong that "truth" only has a single base meaning, as Truth is established by several different meanings each given a different "class" of Truth.
 I'm sorry, but you are just showing that you don't really understand the terms you are using, and tha that you don't even have enough of a basis to understand that you don't understand the terms.
 You HAVE been shown this, and your repeatedly repeating the same proven false claims just shows that you are totally ignorant of what you talk about, and have no concern about the actual meaning of Truth. This shows that you native tounge is that of your "father", the tounge of lies, which you try your best to sprea.
 Sorry that you are sealing your fate, which you are likely going to see sooner than you want.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer