Re: This makes all Analytic(Olcott) truth computable --- truth-bearer

On 8/21/24 8:47 AM, olcott wrote:

On 8/20/2024 9:43 PM, Richard Damon wrote:

On 8/20/24 9:45 AM, olcott wrote:

On 8/20/2024 4:53 AM, Mikko wrote:

On 2024-08-19 12:58:12 +0000, olcott said:
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On 8/19/2024 3:14 AM, Mikko wrote:

On 2024-08-18 11:26:22 +0000, olcott said:
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On 8/18/2024 5:37 AM, Mikko wrote:

On 2024-08-17 15:47:51 +0000, olcott said:
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On 8/17/2024 10:33 AM, Richard Damon wrote:

On 8/17/24 11:12 AM, olcott wrote:

On 8/17/2024 9:53 AM, Richard Damon wrote:

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I guess you consider all the papers they wrote describing the effects of their definitions "nothing"
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Not at all and you know this.
One change had many effects yet was still one change.
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But would mean nothing without showing the affects of that change.
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Yet again with your imprecise use of words.
When any tiniest portion of the meaning of an expression
has been defined this teeny tiny piece of the definition
makes this expression not pure random gibberish.
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Meaningless does not mean has less meaning, it is
an idiom for having zero meaning.
https://www.britannica.com/dictionary/meaningless

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You are lying. According to that page the word "meaningless"
has two meanings. The other is 'having no real importance or value'.
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OK. I always use the base meaning of a term as its only meaning.
That makes things much simpler if everyone knows this standard.

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People have different opions about which meaning is the "base"
meaning.
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The most commonly used sense meaning at the first
index in the dictionary.

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If you want to use this you should say so and specify the dictionary
in the beginning of your opus. You shold not choose a dictionary
that presents obsolete and archaic meanings first.
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Base meaning as in the meaning in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
basis that all other sense meanings inherit from.
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For example a liar must be intentionally deceptive not merely mistaken.

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For example people may regard you as a liar if you say something untrue
when you were too lazy to check the facts.

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I am redefining the foundations of logic thus my definitions
are stipulated to override and supersede the original definitions.

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If you want to use definitions other that the first meaning given
by the dictionary, you must present the definition before the
first use in each opus that uses it.
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The key term that I am slightly adapting is the term {analytic}
from the analytic synthetic distinction. That is why the
title of this post says Analytic(Olcott)

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Which, as I pointed out elswhere, basically means you aren't actually talking about formal systems, as they don't have that distinction, because there is no sense based truth to be synthetic.
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  Formal systems kind of sort of has some vague idea of what True
means. Tarski "proved" that there is no True(L,x) that can be
consistently defined.

Right, there is not PREDICATE that always answers if a given statement is True.
That doesn't mean that truth doesn't have a definition.
The issue is that sometimes truth is unknowable, and the predicate can't handle some of those cases.

 https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem#General_form

Which just means we can't create a predicate that TELLS us if a statement is true or not.

 *The defined predicate True(L,x) fixed that*

So, what is your value for True(L, x) where x is defined to be the expression ~True(L, x)
If for this x, True(L, x) was FALSE, because the predicate determined that there was no sequence of truth perserving operations to x, then x, being defined as the negation of that value, must be a TRUE, and thus, your predicate has ERRED, and gave an answer that it was not actually able to establish, as it has said that a TRUE statement could not be es shown to be true.
The problem is that the predicate, to exist, must mean that the system is Decidable, but if the grammer of the system allows creation of undeciable forms, it is stuck. By its definition, the predicate doesn't have the option of saying its argument is undecidable, but must decide on it, and thus traps itself if the grammer allows for undecidable statements, this means it can only exist in system with very restricted grammers, and thus systems not suitable for a lot of the work that is desired.

Unless expression x has a connection (through a sequence
of true preserving operations) in system F to its semantic
meanings expressed in language L of F then x is simply
untrue in F.
 Whenever there is no sequence of truth preserving from
x or ~x to its meaning in L of F then x has no truth-maker
in F and x not a truth-bearer in F. We never get to x is
undecidable in F.

But then True(F, x) would, by the definition be FALSE.
But if x is itself the expression ~True(F, x), then that makes x true and the answer wrong.
So, you system must not allow the expression in its grammer of a statement like that.
Not just by its semantics, but in the syntax, as the domain of the predicate is expression in the grammer of the language.

 

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It took a long time to reverse-engineer the subtle nuances of
the exact details of what needed to be changed.

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It seems that you have not yet completed that task.
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I have competed the architecture of the task.
We cannot move on to further elaboration until
people quite rejecting the architecture out-of-hand.

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No, you haven't, because you haven't sat down an listed the axioms of your Formal System, so you haven't "completed"  (or even really strated) your architecture.
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*This abolishes the notion of undecidability*
As with all math and logic we have expressions of language
that are true on the basis of their meaning expressed
in this same language.
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Unless expression x has a connection (through a sequence
of true preserving operations) in system F to its semantic
meanings expressed in language L of F then x is simply
untrue in F.

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But Godel's G *IS* an expression that has a connection through an INFINITE sequence of truth preserving operations in PA. It just can't be proven in PA, as proofs require finite sequences in the system.
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Whenever there is no sequence of truth preserving from
x or ~x to its meaning in L of F then x has no truth-maker
in F and x not a truth-bearer in F. We never get to x is
undecidable in F
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Wrong.
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Truth allows an infinte sequence of steps.
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Decidability requires a FINITE sequence of steps.
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That difference is where undeciability comes into existance.
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Requiring Truth to be only established by finite sequences breaks too much logic, and greatly limits what can be exressed. In particular, you lose mathematics. Things that we could show must be true or false, but we can't show which, end up being non-truth-bearers.
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We also end up with a system that can't talk about what it doesn't know yet, as not-yet-known might be unknowable, and thus neither true or false.
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And, you can't let "proofs" use infinite sequences, as that breaks epistomolgy, as we are finite, and can only know what can be shown with a finite proof.