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

On 3/1/2025 3:14 AM, Mikko wrote:

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:
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On 2/25/2025 9:40 AM, Mikko wrote:

On 2025-02-24 22:44:03 +0000, olcott said:
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On 2/24/2025 3:04 AM, Mikko wrote:

On 2025-02-22 17:41:40 +0000, olcott said:
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On 2/22/2025 3:15 AM, Mikko wrote:

On 2025-02-21 23:19:10 +0000, olcott said:
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On 2/20/2025 2:54 AM, Mikko wrote:

On 2025-02-18 03:59:08 +0000, olcott said:
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Tarski anchored his whole proof in the Liar Paradox.

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More specifically, to the idea that the Liar Paradox does not have a
truth value. Do you reject that idea?

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This was not what Tarski was saying.

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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.

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In other words you never read this:
https://liarparadox.org/Tarski_275_276.pdf

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Did you? Nowhere on those pages he claims that the Liar paradox is true
nor that the Liar paradox is false.

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We shall show that the sentence x is actually undecidable and at the same time true.

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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.

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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?
 

When we use provable(common) that means
{shown to be definitely true by whatever means}
then incompleteness and undecidability cannot exist.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer