XPost: sci.logic, comp.theory
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.
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