Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct

Am Thu, 14 Nov 2024 20:58:40 -0600 schrieb olcott:

On 11/14/2024 8:42 PM, Richard Damon wrote:

On 11/14/24 9:26 PM, olcott wrote:

On 11/14/2024 5:53 PM, Richard Damon wrote:

On 11/14/24 6:40 PM, olcott wrote:

On 11/14/2024 2:39 AM, Mikko wrote:

On 2024-11-13 23:01:50 +0000, olcott said:

On 11/13/2024 4:45 AM, Mikko wrote:

On 2024-11-12 23:17:20 +0000, olcott said:

On 11/10/2024 2:36 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 11/10/2024 1:04 PM, Alan Mackenzie wrote:

I have addressed your point perfectly well.  Gödel's theorem
is correct,
therefore you are wrong.  What part of that don't you
understand?

>

YOU FAIL TO SHOW THE DETAILS OF HOW THIS DOES NOT GET RID OF
INCOMPLETENESS.

>
The details are unimportant.  Gödel's theorem is correct.  Your
ideas contradict that theorem.  Therefore your ideas are
incorrect. Again, the precise details are unimportant, and you
wouldn't understand them anyway.  Your ideas are as coherent as
2 + 2 = 5.
>

Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))

>
That's correct (although T is usually used instead of L).
Per this definition the first order group theory and the first
order Peano arithmetic are incomplete.

Every language that can by any means express self-contradiction
incorrectly shows that its formal system is incomplete.

That "incorrectly shows" is non-sense. A language does not show,
incorrectly or otherwise. A proof shows but not incorrectly. But
for a proof you need a theory, i.e. more than just a language.
That a theory can't prove something is usually not provable in the
theory itself but usually needs be proven in another theory, one
that can be interpreted as a metatheory.

When you start with truth and only apply truth preserving operations
then you necessarily end up with truth.

Right, but that truth might not be PROVABLE (by a finite proof that
establishes Knowledge) as Truth is allowed to be established by
infinite chains.

All of analytic truth is specified as relations between expressions of
language. When these relations do not exist neither does the truth of
these expressions.

But in FORMAL LOGIC, that analytic Truth is specified as the axioms of
the system, and the approved logical operations for the system.
You confuse "Formal Logic" with "Philosophy" due to your ignorance of
them.

This.

I am looking at this on the basis of how truth itself actually works.
You are looking at this on the basis of memorized dogma.

No, because you logic is based on LIES, because you are trying to
redefine fundamental terms within the system, as opposed to doiing the
work to make a system the way you want, likely because you are just to
ignorant to do the work,

Logic never has been free to override and supersede how truth itself
fundamentally works.

Logic is just a formal system. The semantics/interpretation might
be wanted to correspond to common-sense truth. Truth inside a
logical system can be totally unrelated. Is the philosophical
debate on what truth is even finished?

If Goldbach conjecture is true then there is some finite or infinite
sequence of truth preserving operations that shows this, otherwise it is
not true.

Yes. In the case of an infinite sequence we can not prove it.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.