Re: Mathematical incompleteness has always been a misconception --- Tarski

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