When we redefine the architecture of formal systems to be an extension
of the notion of a syllogism such that conclusions are required to be a
semantically necessary consequence of all of their premises then
incompleteness is no longer possible. All unprovable expressions are
simply deemed to be invalid arguments. This makes them no longer
available to show incompleteness. Copyright 2023 PL Olcott

https://en.wikipedia.org/wiki/Syllogism#Basic_structure

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 8/22/2023 11:07 AM, olcott wrote:
> When we redefine the architecture of formal systems to be an extension
> of the notion of a syllogism such that conclusions are required to be a
> semantically necessary consequence of all of their premises then
> incompleteness is no longer possible. All unprovable expressions are
> simply deemed to be invalid arguments. This makes them no longer
> available to show incompleteness.

This transforms mathematical incompleteness into the non sequitur error

Copyright 2023 PL Olcott
>
> https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 8/22/23 12:07 PM, olcott wrote:
> When we redefine the architecture of formal systems to be an extension
> of the notion of a syllogism such that conclusions are required to be a
> semantically necessary consequence of all of their premises then
> incompleteness is no longer possible. All unprovable expressions are
> simply deemed to be invalid arguments. This makes them no longer
> available to show incompleteness. Copyright 2023 PL Olcott
>
> https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>

If you want to do that, fine.

Now, show what you can do with such a system.

Remember, you just pulled the foundation out from mosdt of logic, so you
can't use any of it until you re-establish it.

You need to start by trying to actually DEFINE your statement.

From the way you talk, it seems a necessary conclusion of your
statement is that you logic system can't actually handle abstract
statements.

Otherwise, what does it actually mean?

After all, standard logic doesn't let you make a conclusion that isn't
true by necessity from the previous shown truths and the rules of logic.

Or, are you confusing "conclusions" (things that are proven) with
"facts" (things that have a truth value).

For instance, the Truth or Falsity of Collatz Conjecture is a fixed
value, even if we don't know it, or maybe even CAN'T know it.

Your inability to understand that, just shows the limitations of your
mind, and the logic system you are trying to create.

On 8/22/23 6:56 PM, olcott wrote:
> On 8/22/2023 11:07 AM, olcott wrote:
>> When we redefine the architecture of formal systems to be an extension
>> of the notion of a syllogism such that conclusions are required to be a
>> semantically necessary consequence of all of their premises then
>> incompleteness is no longer possible. All unprovable expressions are
>> simply deemed to be invalid arguments. This makes them no longer
>> available to show incompleteness.
>
> This transforms mathematical incompleteness into the non sequitur error
>
>
> Copyright 2023 PL Olcott

No, it shows that your logic is insufficient to handle that level of
Mathematics.

But then, that just shows your level of comprehension.