Re: Minimal Logics in the 2020's: A Meteoric Rise --- Olcott doesn't understand about formal systems and meta

On 7/8/24 11:32 PM, olcott wrote:

On 7/8/2024 7:37 PM, Richard Damon wrote:

On 7/8/24 8:28 PM, olcott wrote:

On 7/8/2024 7:07 PM, Richard Damon wrote:

On 7/8/24 8:00 PM, olcott wrote:

On 7/7/2024 10:09 PM, olcott wrote:

On 7/7/2024 10:02 PM, olcott wrote:

>
Formal logic is a subset of this.
Not-a-logic-sentence(PA,g) ≡ (~True(PA,g) ∧ ~True(PA,~g))
There are no truth preserving operations in PA to g or to ~g
>

>
https://liarparadox.org/Tarski_275_276.pdf
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Within my analytical framework this Tarski sentence is merely
self-contradictory
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(3) x ∉ Provable if and only if x ∈ True. // (1) and (2) combined
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There are no truth preserving operations in Tarski's
theory to x if and only if There are truth preserving
operations in Tarski's theory to x
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>
There cannot possibly be an infinite proof that proves
that there is no finite proof of Tarski x in Tarski's theory

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Who says there needs to be a infinite proof, since there is no such thing.
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As I said, one example of such an x is Godel's G.
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The infinite proof of the Goldbach conjecture
(if it is true) continues to find more true
cases than it had before, thus makes progress
towards its never ending goal (if its true).

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or, it continue to show that there is no counter examples.
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"Progress" on an infinite path isn't really measurable.
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The cycles in the following two cases never make any progress
towards any goal they are merely stuck in infinite loops.

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Which just means you are on the wrong path. One wrong path doesn't me that there is no path.
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The Prolog unify_with_occurs_check test means that
LP is stuck in an infinite loop that makes no progress
towards resolution. I invented Minimal Type Theory to
see this, then I noticed that Prolog does the same thing.

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Which is irrelevent, since Prolog can't handle the basics of the field that Traski assumes.
>

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?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
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LP := ~(L ⊢ LP)
00 ~ 01
01 ⊢ 01, 00
02 L
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The cycle in the direct graph of LP is
an infinite loop that make no progress
towards the goal of evaluating LP as
true or false.
>
>

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So?
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Failure to prove by example doesn't show something isn't true.
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You are just proving you are stupid and don't know what you are talking about.

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Every expression of language that cannot be proven
or refuted by any finite or infinite sequence of
truth preserving operations connecting it to its
meaning specified as a finite expression of language
is rejected.
>

>
So?
>
Tarski's x like Godel's G are know to be true by an infinite sequence of truth preserving operations.
>

 "are *know to be true* by an infinite sequence"
"are *know to be true* by an infinite sequence"
"are *know to be true* by an infinite sequence"
"are *know to be true* by an infinite sequence"
"are *know to be true* by an infinite sequence"
 On 7/8/2024 9:59 PM, Richard Damon wrote:
 > No, infinite "proofs" determine TRUTH, not knowledge.
 

Right, G is known (by meta-F) that it is true (in F) because of an infinite sequence of truth preserving steps IN F.
By meta-system we can know something about a system that in that system it can only be know with an infinite chain.
This idea seems to be beyound your understanding, I think because you just don't understand how formal system work, and thus how meta-systems work.
These proof you have so much troble with all are dealing with systems and meta-systems, and I think you loose track of what is said about each and in what system shows it.