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

On 4/3/25 3:21 PM, olcott wrote:

On 4/3/2025 2:08 AM, Mikko wrote:

On 2025-04-03 01:30:28 +0000, olcott said:
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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

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That is generally believed but not actually proven.
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they are essentially nothing more than an ordered
set of finite strings of digits.

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The "nothing more" part cannot be proven.

 It is a stipulated basic fact.
There is no way that elements of the set of natural
is anything more or less then an ordered set of
concepts that can be expressed in some way such as a
string of digits.

You can't stipulate that something is a fact.
You aren just proving that you don't understand what you are doing.

 When we ADD the notion of arithmetic this notion
is added on top of the notion of an ordered set
of concepts.
 

In first order logic one cannot

 We are still adding notions on top of the notion
of an ordered set of concepts.
 

even say that those strings must be finite.

 It would seem to be a stipulated aspect of the
definition of natural number: ∀n ∈ ℕ (n ≠ ∞)
 

But that can't be the definition of Natural Numbers, as it is recursive.
You are trying to define that set of Natural Numbers as the set of the Numbers that are Natural Numbers.
That doesn't work.
When we look at definitions of the Natural Numbers, as per things like ZFC, the properties of arithmetic just come out by labeling properties that exist in the set.
Sorry, you are just proving your stupidity.