Re: How a True(X) predicate can be defined for the set of analytic knowledge

On 4/3/25 2:59 PM, olcott wrote:

On 4/3/2025 2:03 AM, Mikko wrote:

On 2025-04-02 15:59:47 +0000, olcott said:
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On 4/2/2025 4:20 AM, Mikko wrote:

On 2025-04-01 17:51:29 +0000, olcott said:
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All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.

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There already are programs that check proofs. But you can make your own
if you think the logic used by the existing ones is not correct.
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If the your logic system is sufficiently weak there may also be a way to
make a C program that can construct the proof or determine that there is
none.

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When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.

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But a proof of paraconsistency is required.
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 When it is stipulated that {cats} <are> {Animals}
When it is stipulated that {Animals} <are> {Living Things}
Then the complete proof of those is their stipulation.
AND {Cats} <are> {Living Things} is semantically entailed.

Which doesn't prove what was asked for.
You are just proving the fact that you don't understand what you are talking about.

 

A system entirely comprised of Basic Facts and Semantic logical entailment cannot possibly be inconsistent.

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It can if the set of basic facts is inconsistent or if the logical
entailment sematics is not sufficiently weak. Inconsistencies are
avoided if your system has no way to express logical negations
(which incudes negative quantification).
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 Stipulated basic facts + semantic logical entailment
guarantees True(X). When the basic facts do not contradict
each other then undecidability is impossible.
 

Nope. Tarski proved otherwise.
The problem is that your "assumption" that a True(x) exist creates an inconsistant set of "basic facts" when combined with the other basic facts that allow us to do arithmatic.