On 12/30/22 11:06 PM, olcott wrote:
> On 12/30/2022 7:09 PM, Richard Damon wrote:
>> On 12/30/22 6:04 PM, olcott wrote:
>>> On 12/30/2022 11:56 AM, Richard Damon wrote:
>>>> On 12/30/22 11:30 AM, olcott wrote:
>>>>> On 12/30/2022 10:15 AM, Richard Damon wrote:
>>>>
>>>>>> But the existance of ONLY an infinite sequence of semantic
>>>>>> connections for a sentence make it True but Unprovable.
>>>>>>
>>>>>> Thus your idea that all Truth is Provable is debunked, and you are
>>>>>> shown to be an idiot.
>>>>>>
>>>>>
>>>>> My prior claim that every true statement must be provable is either
>>>>> qualified to allow infinite proofs or changed to refer to semantic
>>>>> connections that may be finite or infinite.
>>>>
>>>> If you allow your "Proof" to be infinite, then you have broken the
>>>> link between provable and knowable, and have left the language that
>>>> everyone else is talking.
>>>>
>>>
>>> You and I already know that the possibility that an expression of
>>> language can only be confirmed as true by an infinite proof then the
>>> link between true and knowable was already broken.
>>
>> Right, which means that there are some things that are True that are
>> unknowable.
>>
>>>
>>>> Since some Semantic Statement DO require an infinite set of semantic
>>>> connections, but knowable requries a finite set of semantic
>>>> connections, we have that there exsits some statements that are True
>>>> but not knowable, and thus not Provable by the classical definition.
>>>>
>>>
>>> When infinite proofs are required to verify the truth of an expression
>>> of language and formal systems are not allowed to have infinite proofs
>>> then unprovable in no way means that the formal system is in any way
>>> incomplete.
>>
>> WRONG. The DEFINITION of "Incomplete" is that there exist statements
>> that are True that can not be Prove, with the definition of Provable
>> being a Finite Proof.
>>
>> In your modified terminology, Incompletenesss is DEFINED as the
>> existance of statements that are Analytically True but are Unknowable.
>>
>> THAT IS DEFINITION.
>
> In other words you are saying that unless a formal system violates its
> own definition and performs an infinite proof then the formal system is
> incomplete.
>

No, a formal system simple enough to be able to prove all true
statements in it is what is defined as "Complete".

It just turns out that most usable systems are incomplete, because it
turns out they are expressive enough to create Truth that can't be proven.

Nothing wrong with being "Incomplete" by this definition,

What the systems lack, is the ability to prove every true statement.

What is wrong with that?

Somehow you seem to not understand the meaning of that statement.

>>
>>>
>>>>>
>>>>> Thus an expression of language is never true unless it is connected to
>>>>> its truth maker.
>>>>>
>>>>
>>>> Right, but that connection might not be knowable, because it is
>>>> infinite, and thus not provable by the classical meaning.
>>>>
>>>
>>> Yet formal systems that are not allowed to have infinite proofs
>>> cannot be called "incomplete" because they lack an infinite proof.
>>
>> But that is the DEFINTION of the Term.
>
> That definition is incoherent. It is like saying that apples are
> incomplete because they are not oranges.

Nope, just means you don't understand the concept that it is talking about.

I suspect the issue is you are trying to use a colloqual English meaning
for the word in your mind instead of its actual Technical Meaning in the
Field.

Apples are logic systems, so this definition doesn't apply to them.

Maybe a better analogy would be that a grape that grew without seeds in
it could be considered incomplete because it is missing something that
was expected, and needed for the fruit to reproduce itself.

It just turns out that for grapes, this can be a FEATURE, not a defect.

In the same way, logic systems that are incomplete, are lacking a useful
feature, the ability to prove all truth statements in them, but come
with the advantage of being able to express concepts that can't be done
when you limit yourself to logic that allows all truths to be proven.

>
>>>
>>>> If you redefine your idea of "Proof" to include "infinite proofs"
>>>> you have just made you logic system incompatible with ALL standard
>>>> logic that requires it to be finite, so you need to restart at the
>>>> begining.
>>>>
>>>
>>> We can simply use my semantic version instead: True(x) ↔ (⊨x).
>>
>> So, start with your restart and see what you get. Make sure you fully
>> document you other definitions and axioms as you go.
>>
>> In particular, do you plan to redefine the implication operator?
>
> I am only specifying the natural preexisting way that analytical truth
> really works.

So you accept that it is a True Statement that "Unicorns being purple
implies that the world is flat".

>
>>
>> Note currently A -> B means that for every model where A is true, B is
>> also true, even if that truth of B is not directly connected to the
>> Truth of A.
>>
>
> That is an error. To say that
> cows give milk implies the grass is purple
> is false at the semantic level, thus not a truth preserving operation.

How is your example a proper counter to my statement?

Since it is not true that in every model where "Cows give milk" is true
that "Grass is purple" is true, that statement fails the definition of a
valid implication.

You are just showing you don't understand what you are talking about.

Are you saying that you are BANNING the implication operator because all
of the following are valid implications?

True -> True
False -> False
False -> True

and only if there is a case of

True -> False

is the implication invalid?

Good luck trying to develop your logic system if you remove the
implication operator from your system.

>
>> Note, PROVING a statement like A -> B, without knowing the actual
>> truth of A or B, will require building such a direct connection.
>>
>>>
>>>> You are going to need to define SOMETHING, to indicate actually
>>>> knowable due to having a finite proof. Knowable isn't actually a
>>>> good word for this, as we often want to include in knowable not just
>>>> things proven with a finite analytical proof, but also things
>>>> knowable by direct sensation.
>>>>
>>>> Thus, if you redefine "Provable" to include an infinite sequence of
>>>> steps, it becomes just a synonym for True, and we have lost the use
>>>> of it for its normal use, and need to replace it with something more
>>>> clumbsy like Analytically Knowable.
>>>>
>>>>
>>>> The claim you seem to want to make is that all Analytically True
>>>> statements are Anayltically Knowable, but that is a false statement.
>>>>
>>>> You try to hide the error by redefining the words and saying that
>>>> all Analytical True statements are Provable, and implying that this
>>>> means Analytically Knowable, but that is wrong because you are using
>>>> incompatible meanings of Provable.
>>>
>>> All analytically true statements have a semantic connection to their
>>> truth maker.
>>
>> Ok. But I don't think that actually establishs what you are trying to
>> make it establish.
>>
>
> It does, I spent 25 years on this and can finally say it succinctly.

Then do so.

>
>>>
>>>>
>>>> You need to actually DEFINE what you mean by your terms, and any
>>>> term that doesn't mean what it means what it actually means in
>>>> classical logic can not use any of the results from classical logic.
>>>>
>>>
>>> Hence my new idea of semantic connections using a knowledge ontology
>>> instead of model theory.
>>
>> So DO IT. Of course, changing the base means you have to redo
>> EVERYTHING to see what survives.
>>
>
> I am not going to write down every element of the set of all analytic
> knowledge. True(x) ↔ (⊨x) has the set of all known and unknown analytic
> truth as its formal system.

No, I wasn't saying write down all knowledge, I was saying SHOW that
your logic system is actually capable of doing something usefle.

Since you are redefining some core definition, that means going back to
the ultimate basics and show what you can actually still show of logic
as still applying.

I don't think you know enough to even know what you need to do.

(I'll admit, I would need to do some research to figure out how deep
into the basics you need to go).

>
>> Ultimately, my guess is you will find that with the restrictions you
>> are talking about, you are going to find that you logic system is not
>> able to handle much of the current logic families, but you system is
>> just going to put them outside what it can show.
>>
>
> The set of analytic knowledge can show everything that is analytically
> known.

But that doesn't show that you can know all analytic TRUTHS.

You keep making that mistake, It is like "Truth" doesn't actually mean
anything to you, only knowledge, and becaue you have lost track of
Truth, you accept as knowldge things that aren't actually True, because
you have let your system become inconsistent (which in a sense destroys
the meaning ot Truth).

>
>> That, or you system is going to fall into a massive mess of
>> inconsistencies because you fail to guard against it, and you ego is
>> unable to see these problems.
>>
>
> Expressions of language that are not coherently linked to the set of
> analytic knowledge are not members of this set.

Again, talking about Knowledge instead of Truth.

You are just proving your ignorance.

>
>>>
>>>> You seem to want to change the foundation, but then expect that the
>>>> whole structure built on it will stay mostly the same. That is a
>>>> false assumption. If you change the base, you need to work up from
>>>> that base and see what changes above it, but going through ALL the
>>>> steps, especially those that depend on the things you have changed,
>>>> to see what actually changes.
>>>>
>>>
>>> True(x) requires semantic connections to its truth maker, else we have
>>> ~True(x) or False(x). Semantically incoherent expressions of language
>>> (such as the Liar Paradox) are neither true nor false.
>>
>> Ok, so what.
>>
>
> Tarski's undefinability theorem fails. He claimed to have proved an
> incoherent expression of language is true, that is ridiculous.

No, he proved the incoherent expression CONDITIONALLY, based on the
assumption that a definitoin of Truth exsits.

You just don't understand how a Proof By Contradiction works.

>
>> It is accept that statements like the Liar's paradox are not truth
>> holders.
>>
>
> Tarski claimed to have proved that it is true, what a nut.

No, he showed that if you assume that a definiton of Truth in a system
of logic exists, that you can prove the Liar's Paradox.

YOU are just proving you are an IDIOT that doesn't understand the basics
of logic.

>
>> The problem is that it is absolutely TRUE that Some True Statements
>> are Unknowable in a sufficently powerful logic system (and that
>> sufficently powerful is a fairly low hurdle).
>>
>
> We cannot possibly correctly say that some statements are unknowable
> until we can prove that no finite proofs exist. Until then they are
> simply unknown.

Right, and Godel showed a statement that can not be proven but must be
true, because otherwise the system is able to PROVE a statement that is
FALSE.

>
>> You can't just try to make that statems be just the same as the Liar's
>> Paradox, because they aren't.
>>
>
> Gödel himself implied that his logic sentence is isomorphic to the liar
> paradox.

No, he said that you can ADAPT any statement like the liar's paradox
into his form of proof. The key is that rather than talking about the
Truth of the statement, that in the META-THEORY the statement refers to
its provability.

>
>> It is a fundamental property of Knowable/Provable for systems of any
>> reasonable power.
>>
>
> Gödel said that any epistemological antinomy will do, thus he limited
> his proof to be based only on self-contradictory expressions of
> language.

So you admit you just don't understand how is proof works.

yes, the proof starts looking at the FORM of the liar's paradox, and
transforms it in the meta-theory to a statement not about Truth but
about Provability. Since statments of Provability are always Truth
Bearer, and Provable statements are always True, the antinomy ends up
forcing the rovability statement to be True but Unprovable, because if
it was False, it would be Proven and thus must be True.

>
>>>
>>>> Many of your ideas you think of as "New" are not really new, just
>>>> you have failed to see their use in the past. They might not have
>>>> used your names, but they did use the same base ideas. The
>>>> limitations of these ideas have been long established.
>>>
>>> I have shown that Tarski Undefinability and Gödel Incompleteness are
>>> incorrect. Tarski "proved" that the Liar Paradox is true and we both
>>> know that it is not true so Tarski goofed.
>>
>> No, you haven't.
>>
>
> He you already admitted that he proved that the Liar Paradox is true and
> you also admitted that the Liar Paradox is not true hence you admitted
> that Tarski goofed.

You are just proving you aren't reading, or just can't understand English.

He proved that the Liar's Paradox would be True **IF** there existed a
definition of Truth in the logic system.

>
>> You just don't understand his proof.
>>
>> The fact is that Tarski PROVED (not in quotes) that the Liar's Paradox
>> is True
>
> Conclusively proves that Tarski did something wrong.

Nope, proves you don't understand it, or even basic logic.

>
>> IF A DEFINITION OF TRUTH EXISTS, this is actually proof that no such
>> definitio of truth can exist.
>>
>> Unless you find an actual ERROR in his proof, you haven't established
>> anything but to confirm his proof.
>>
>
> You already admitted that Tarski proved that a statement that is not
> true is true, thus Tarski goofed.

No, he proved, based on the assumption that Truth can be defined in a
system, the Liar's paradox is True.

>
>> Note, you probably need to look at the AcTUAL PROOF he gives, not just
>> the short summary you quote. Yes, that summary is not in itself a
>> proof, but references that actual proof that has been firmly established.
>>
>
> These two pages are his entire proof in his original verbatim words:
> https://liarparadox.org/Tarski_275_276.pdf

Nope. Read the footnotes, this is just a "Sketch" of the proof.

Further proof that you can't understand what you read.

>
>> This seems to be a common error of yours, you don't read the actual
>> proof (probalby because it is too complicated for you since you admit
>> you have avoid formal study of the field) so you can't actually come
>> up with a refutatioh of the proof, so you just say it must be wrong.
>>
>> In actuality YOU must certainly be wrong, since you are the one
>> claiming something without proof that is contradicted by an actual
>> vetted proof.
>>
>>>
>>> Because Gödel Incompleteness is an exact isomorphism to Tarski
>>> Undefinability the refutation of one is a refutation of both.
>>>
>>>
>>
>> Which you haven't done, because it seems you don't understand what
>> either one is doing, in part because it seems you don't actually
>> understand how logic works.
>>
>
> Gödel said this in his footnote 14
> 14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof
>
> In other words his proof requires self-contradictory expressions of
> language or it fails and the Liar Paradox can be used for a similar
> undecidability proof. Tarski did that.
>
>

Yes, and antimomy can be used as a FRAMEWORK, to transform it from a
statement of Truth to a statement of Provabilty that lead to the
concusion that the statement must be True and Unprovable, since if it
was False it would be Proven, and thus must be True.

The conflict that leads the statement to being not a Truth Bearer when
talking about Truth of the Statement changes due to the nature of
statements about Probabilty, that MUST be Truth Bearers, and if a
statement is Provable, it must be True.

This DISTINCTION between Truth and Provable (which you don't seem to
understand) means that a statement when directly used becomes
self-contradictory, but when transformed as described, becomes a Truth
Bearer that shows that it must be True but Unprovable in the system.

Note, we need to use the classical definition of Proof here, namely that
it is only provable if a FINITE proof exists.