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

On 4/2/25 10:51 PM, olcott wrote:

On 4/2/2025 8:56 PM, Richard Damon wrote:

On 4/2/25 9:30 PM, olcott wrote:

On 4/2/2025 5:05 PM, Richard Damon wrote:

On 4/2/25 11:59 AM, olcott wrote:

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 you can't do that unless you limit the system to only have a finite number of statements expressible in it, and thus it can't handle most real problems
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A system entirely comprised of Basic Facts and Semantic logical entailment cannot possibly be inconsistent.
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Sure it can.
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The problem is you need to be very careful about what you allow as your "Basic Facts", and if you allow the system to create the concept of the Natural Numbers, you can't verify that you don't actually have a contradition in it.
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It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.

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No, but any logic system that can support them

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Can be defined in screwy that has undecidability
or not defined in this screwy way.
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Basic facts and expressions semantically entailed
by the basic facts cannot have undecidability[math].
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 Wrong, Godel shows that having the properties of the Natural numbers is enough.
 

Show what property he uses that you can withhold and still have a reasonably usable mathematics.
 Your problem is you don't understand the power that basic logic gets from the basic nature of the Natural Numbers.