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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Sat, 9 Nov 2024 11:46:42 -0600
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On 11/9/2024 11:27 AM, joes wrote:
> Am Sat, 09 Nov 2024 11:09:02 -0600 schrieb olcott:
>> On 11/9/2024 10:04 AM, joes wrote:
>>> Am Sat, 09 Nov 2024 08:45:12 -0600 schrieb olcott:
>>>> On 11/9/2024 5:01 AM, joes wrote:
>>>>> Am Fri, 08 Nov 2024 18:39:34 -0600 schrieb olcott:
>>>>>> On 11/8/2024 6:33 PM, Richard Damon wrote:
>>>>>>> On 11/8/24 6:36 PM, olcott wrote:
>>>>>>>> On 11/8/2024 3:59 PM, Richard Damon wrote:
>>>>>>>>> On 11/8/24 4:17 PM, olcott wrote:
>>>>>>>>>> On 11/8/2024 12:31 PM, Richard Damon wrote:
>>>>>>>>>>> On 11/8/24 1:08 PM, olcott wrote:
>>>>>>>>>>>> On 11/8/2024 12:02 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 11/8/24 12:25 PM, olcott wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> That formal systems that only apply truth preserving
>>>>>>>>>>>>>> operations to expressions of their formal language that have
>>>>>>>>>>>>>> been stipulated to be true cannot possibly be undecidable is
>>>>>>>>>>>>>> proven to be over-your-head on the basis that you have no
>>>>>>>>>>>>>> actual reasoning as a rebuttal.
>>>>> Gödel showed otherwise.
>> Gödel had a different f-cking basis.

> Where is the difference?
> 

True is only provable from axioms
thus ~Provable(PA, G) == ~True(PA, G)

>>>> That is counter-factual within my precise specification.
>>> What Gödel did is a fact.
> 
>>>> When truth is only derived by starting with truth and applying truth
>>>> preserving operations then unprovable in PA becomes untrue in PA.
>>> No, unless your system is less powerful than PA.
>>> Untrue means the negation is true, but ~G is also unprovable.
>> It is not any less powerful than PA in the same f-cking way that ZFC is
>> not less powerful than naive set theory.
> Then it is incomplete or inconsistent.
> 
>>>>>>>>> But, as I pointed out, the way Meta-Math is derived from PA,
>>>>>>>> Meta-math <IS NOT> PA.
>>>>>>>> True in meta-math <IS NOT> True in PA.
>>>>> Yes it is. If MM proves that a sentence is true in PA, that sentence
>>>>> is true in PA.
>>>> Within my model: Only PA can prove what is true in PA.
>>> PA can’t prove anything about itself.
> 
> ^
> 
>>>>>>> But MM has exactly the same axioms and rules as PA, so anything
>>>>>>> established by that set of axioms and rules in MM is established in
>>>>>>> PA too.
>>>>>>> There are additional axioms in MM, but the rules are built
>>>>>>> specifically
>>>>>> One single level of indirect reference CHANGES EVERYTHING.
>>>>>> PA speaks PA. Meta-math speaks ABOUT PA.
>>>>>> The liar paradox is nonsense gibberish except when applied to
>>>>>> itself, then it becomes true.
>>>>> What is "the liar paradox applied to itself"?
> 
> Open question.
> 
>>>> Can yo please add a newline so that you comments are no buried in my
>>>> comments?
>>> How does your newsreader mark quotes?
>> Instead of replying immediately after my comment, skip a line. Leave a
>> freaking blank line inbetween.
> Does your reader not mark quotes?
> 
>>>> This sentence is not true: "This sentence is not true" is true because
>>>> the inner sentence is nonsense gibberish.
>>> I think you missed some quotation marks there. The outer sentence is
>>> true, but the inner is perfectly wellformed and syntactically correct.
>> https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously is
>> also syntactically well formed and semantic gibberish.
> "This sentence is true" however has a welldefined meaning.
> 

No it does f-cking not. WTF is it true about?

>>> Gödels sentence isn’t exactly this, because formal systems don’t speak.
>>> It is just a number that happens to encode itself.

Richard Montague's formal system speaks complete English.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer