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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 12:50:48 -0600
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On 11/9/2024 12:35 PM, joes wrote:
> Am Sat, 09 Nov 2024 11:46:42 -0600 schrieb olcott:
>> 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)

> The metatheory proves otherwise. If G were not true, ~G would need to
> be provable.
> 
The meta-theory does not and never has proved otherwise.
People simply stupidly assume that true in the meta-theory
is the same as true in the theory. It is not, that it merely
a stupidly false assumptions.

>>>>>> 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.

ZFC is neither incomplete nor inconsistent.

Stipulating that True(L,x) only means Provable(L,x)
from the axioms of L simply gets rid of incompleteness
and undecidability nothing else is changed.

> 
> 
>>>>>>>>>>> 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"?
> 

*This is the Liar Paradox applied to itself*
This sentence is not true: "This sentence is not true" is true.

*This is the Liar Paradox applied to itself*
This sentence is not true: "This sentence is not true" is true.

*This is the Liar Paradox applied to itself*
This sentence is not true: "This sentence is not true" is true.

*This is the Liar Paradox applied to itself*
This sentence is not true: "This sentence is not true" is true.

*This is the Liar Paradox applied to itself*
This sentence is not true: "This sentence is not true" is true.

I told you this many times before and you didn't bother to notice.
I told you this many times before and you didn't bother to notice.
I told you this many times before and you didn't bother to notice.
I told you this many times before and you didn't bother to notice.
I told you this many times before and you didn't bother to notice.

>>>>>> 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?
> Are you reading in plaintext?
> 
>>>>>> 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 not true" however has a welldefined meaning.
>> No it does f-cking not. WTF is it true about?
> 
> Itself?
> 

This sentence has words, is true.
This sentence is true. is infinitely recursive thus has no truth value.

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