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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Fri, 15 Nov 2024 11:14:21 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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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.