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

On 4/5/2025 3:03 PM, Richard Damon wrote:

On 4/5/25 1:51 PM, olcott wrote:

On 4/5/2025 2:30 AM, Mikko wrote:

On 2025-04-03 18:59:15 +0000, olcott said:
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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.

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For that sort of system paraconsistency is possible, depending on
what else there is in the system.
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https://en.wikipedia.org/wiki/Paraconsistent_logic
Starting with a consistent set of basic facts (AKA axioms)
while only allowing semantic logical entailment thus
truth preserving operations does not seem to allow
any contradictions, thus paraconsistency.
Try to provide a concrete counter-example.
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 Your problem is you are making the error of assuming the concluion.
 You can't tell that you axioms ARE consistant excpet by proving that the system itself is consistant,

Counter-factual. A system with a consistent set of basic
facts can possibly have inference rules that derive
inconsistency because these rules are less than perfectly
truth preserving.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer