Re: Mathematical incompleteness has always been a misconception

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.

What was left out?
It seems what is misisng is *YOUR* understanding of what you talk about.
Your claims are just based on lies based on your misunderstanding of what others have written, largely because you fail to study the material to actually know the meaning of the words being used, and their implications.

 What-so-ever makes an expression true <is> its philosophical
truth maker and thus is proof in the broadest sense of the
term {proof}, not the narrow mathematical idiomatic sense.

Yes, and if it is an infinite sequence, it isn't a proof.
You just have a blind spot to understanding infinity.

 

You are just so ignorant about the distinction between knowledge and truth, that you can't make that distinction.
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And this stupidity blinds you to the logic that you are trying to manipulate, so you just prove that stupidity.