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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 ---
Date: Sat, 9 Nov 2024 11:01:50 -0000 (UTC)
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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.
>>>>>>>> No, all you have done is shown that you don't undertstand what
>>>>>>>> you are talking about.
>>>>>>>> Godel PROVED that the FORMAL SYSTEM that his proof started in, is
>>>>>>>> unable to PROVE that the statement G, being "that no Natural
>>>>>>>> Number g, that satifies a particularly designed Primitive
>>>>>>>> Recursive Relationship" is true, but also shows (using the Meta-
>>>>>>>> Mathematics that derived the PRR for the original Formal System)
>>>>>>>> that no such number can exist.
>>>>>>> The equivocation of switching formal systems from PA to meta-math.
There’s no such thing happening. They are very clearly separated.
>>>>>> No, it just shows you don't understand how meta-systems work.
>>>>> IT SHOWS THAT I KNOW IT IS STUPID TO CONSTRUE TRUE IN META-MATH AS
>>>>> TRUE IN PA.
MM doesn’t even contain the same sentences as PA.
>>>> 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.
>>> This sentence is not true: "This sentence is not true"
>>> is only true because the inner sentence is bullshit gibberish.
It’s a perfectly wellformed sentence.
>> 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"?

-- 
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.