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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception --- Tarski
Date: Sat, 1 Mar 2025 11:14:05 +0200
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On 2025-02-28 23:51:54 +0000, olcott said:

> On 2/28/2025 5:13 AM, Mikko wrote:
>> On 2025-02-25 20:57:44 +0000, olcott said:
>> 
>>> On 2/25/2025 9:40 AM, Mikko wrote:
>>>> On 2025-02-24 22:44:03 +0000, olcott said:
>>>> 
>>>>> On 2/24/2025 3:04 AM, Mikko wrote:
>>>>>> On 2025-02-22 17:41:40 +0000, olcott said:
>>>>>> 
>>>>>>> On 2/22/2025 3:15 AM, Mikko wrote:
>>>>>>>> On 2025-02-21 23:19:10 +0000, olcott said:
>>>>>>>> 
>>>>>>>>> On 2/20/2025 2:54 AM, Mikko wrote:
>>>>>>>>>> On 2025-02-18 03:59:08 +0000, olcott said:
>>>>>>>>>> 
>>>>>>> 
>>>>>>>>> 
>>>>>>>>> Tarski anchored his whole proof in the Liar Paradox.
>>>>>>>> 
>>>>>>>> More specifically, to the idea that the Liar Paradox does not have a
>>>>>>>> truth value. Do you reject that idea?
>>>>>>> 
>>>>>>> This was not what Tarski was saying.
>>>>>> 
>>>>>> Yes, he was. He just assumed that his readers already know that the
>>>>>> Liar Paradox does not have a truth value so he didn't need to be
>>>>>> emphatically explicit about that point.
>>>>> 
>>>>> In other words you never read this:
>>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>> 
>>>> Did you? Nowhere on those pages he claims that the Liar paradox is true
>>>> nor that the Liar paradox is false.
>>> 
>>> We shall show that the sentence x is actually undecidable and at the 
>>> same time true.
>> 
>> At that point Tarski has alredy known that the sentence s can be constructed
>> and that it can be represented by an object that the theory can handle.
>> Later Tarski ideed shows that the sentence x is both undecidable and true.
>> But x is not the liar paradox.
> 
> If you don't muck up the meanings

That is hard to avoid in contexts where you do.

> of common terms
> with idiomatic term-of-the-art meanings then true
> and undecidable is the impossibility of true without
> a truth-maker.

Should this be interpreted according to the term-of-art menings or
common language meanings or some other meanings?

-- 
Mikko