Re: Mathematical incompleteness has always been a misconception

On 2/1/25 9:09 AM, olcott wrote:

On 2/1/2025 3:19 AM, Mikko wrote:

On 2025-01-31 13:57:02 +0000, olcott said:
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On 1/31/2025 3:24 AM, Mikko wrote:

On 2025-01-30 23:10:18 +0000, olcott said:
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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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If there is a misconception then you have misconceived something. It is well
known that it is possible to construct a formal theory where some formulas
are neither provble nor disprovable.

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This is well known.

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And well undeerstood. The claim on the subject line is false.
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 a fact or piece of information that shows that something
exists or is true:
https://dictionary.cambridge.org/us/dictionary/english/proof

Right, and to show to a person, it must be finite in length.
If the method of showing something is true is to evaluate a relationship at EVERY intergral value, and see it is satisfied for every value, but no methed exist to reduce that, in the system, to an induction or similar methods to make the process finite, does not "Show" that something is true, as we can't actually do it.

 When you disallow assigning different idiomatic meanings to terms-of the-art such that the term "proof" retains every nuance of its base meaning and not allowed to diverge from this meaning at all then every expression of language that is only made true (by a connection through its philosophical truth maker) to its verbalized semantic meaning must necessarily remain untrue when it lacks such a connection.

Except your attempt is to remove one of the core requirements, that is SHOWS that the statement is true, becuase that showing takes infinite work, which no person is able to do.
All you are doing is showing that you fundamentally don't understand the existance or properties of the infinite.
I guess this goes with your idea that you are God, as only God is able to do the infinite, but of course, you can't actually do that, because you are not God.
Sorry, you are just proving your stupidity,

 

What is not so widely known is that this is only possible because process
defining what is referred to as a math proof intentionally leaves out key
required elements that would otherwise make it complete.

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Wrong. The result is the same if the omission is unintentional. For example,
Peano did not intentionally leave anything out in order to make an incomplete
theory. Only later Gödel found out that Peano's theory is incomplete.
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