## Does Tarski Undefinability apply to HOL ?

• 536
It can be implemented in C or Java in modified form with abstraction and generalisation. It cannot be implemented because you are seeing it in the propositional logic rather than predicate or first-order logic.

Gödel Incompleteness can only be implemented in systems that implement Boolean True(L, x) incorrectly. It cannot exist in systems where True(L, x) means that x is provable from L and False(L, x) means ~x is provable from L and for everything else x is simply untrue in L.

This same reasoning also conquers Tarski Undefinability.
When Tarski anchors his undefinability in the Liar Paradox:
x = "This sentence is not true" we get
Truth-Bearer(L, x) ≡ ∃x ∈ L ((L ⊢ x) ∨ (L ⊢ ¬x)) // x is not a Truth-Bearer
• 3k
Quine objected to true on the basis of meaning trying to get away with saying there is no such thing as meaning. The stupid nitwit could not even begin to understand that bachelors are not married.

Quine was not a stupid. He was very academic and famous. He wrote many Logic and Philosophy books. I have some Quine books.

Bachelors can mean different things. Bachelor is also "a person who holds a first degree from a university or other academic institution" - Oxford Dictionary

Hence a woman can be a bachelor, so could a man married many times. I am sure there are surnames called "Bachelor", hence some married old folk could be a Bachelor, Mr Bachelor, or if for a woman, Ms Bachelor. They are all B(b)achelors.
• 536
Hence a woman can be a bachelor, so could a man married many times. I am sure there are surnames called "Bachelor", hence some married old folk could be a Bachelor, Mr Bachelor, or if for a woman, Ms Bachelor. They are all B(b)achelors.

A person with a 50 million IQ that cannot understand that (one the the sense meanings of) the term {bachelor} is assigned the semantic meaning of {unmarried + male + adult} is ridiculously stupid about this one point.
• 3k
A person with a 50 million IQ that cannot understand that the term {bachelor} is assigned the semantic meaning of {unmarried + male + adult} is ridiculously stupid about this one point.

I think Quine did understand what bachelor meant. But his point was that a word can mean different things, the meanings of words can change through time and culture, and for a word to convey clear meanings, it needs the context in the expressions in grammatically correct sentence reflecting the reality situations.

It sounds naive to say that a word means just the simple definitions in a bracket in tautological form, and that is the only truth in all cases under the sun.
• 536
I think Quine did understand what bachelor meant. But his point was that a word can mean different things, the meanings of words can change through time and culture, and for a word to convey clear meanings, it needs the context in the expressions in grammatically correct sentence reflecting the reality situations.

No that it not it. He used the term {synonymous} 98 times. He did not understand that the term {bachelor} is simply assigned the semantic meaning of {unmarried + male + adult}.
• 583
every expression of language that is true on the basis of its meaning is either a fact or derived from a fact.

Are there expressions of language that are true but are NOT true on the basis of their meaning AND also are not derived from other facts? Put slightly differently - is there another mechanism/method to determine the truth value of expressions of language?
• 536
is there another mechanism/method to determine the truth value of expressions of language?

Yes there is a TV in my living room right now is true on the basis of eyesight.
• 3k
No that it not it. He used the term {synonymous} 98 times.
Really? In which book or article did he do that? I have his Mathematical Logic, Method of Logic, Elementary Logic and The Significance of New Logic, total 4 books. But cannot recall seeing it.

He did not understand that the term {bachelor} is simply assigned the semantic meaning of {unmarried + male + adult}.
Bachelor is a rather simple term. There are many other words in English which are more abstract to define. Try to define "Self", "Soul" and "Existence". Let's see if analytic truths can define them without contradiction or obscurity.
• 3k
Gödel Incompleteness can only be implemented in systems that implement Boolean True(L, x) incorrectly. It cannot exist in systems where True(L, x) means that x is provable from L and False(L, x) means ~x is provable from L and for everything else x is simply untrue in L.

This same reasoning also conquers Tarski Undefinability.
When Tarski anchors his undefinability in the Liar Paradox:

As I said before, will say again. The whole confusion with the paradox and undefinability have been originated from the single narrow perspective seeing the problems in propositional logic, which only allows a proposition must be either True or False.

If you think about the real world situations and objects, there are cases where things are neutral i.e. neither true nor false such as Number 0. And there are the real world cases where things are both True and False, read on QM or some Metaphysical topics.

If you open up the perspective wide and accept all these possibilities in the real world, it is quite normal for some cases to be either True or False, neither True nor False, or both True and False. If you apply FOL and HOL into your program languages bearing that point in your mind, and design the programs to deal with the particular cases in the real world examples, they deal all the case quite fine (Quine).
• 536
Really? In which book or article did he do that? I have his Mathematical Logic, Method of Logic, Elementary Logic and The Significance of New Logic, total 4 books. But cannot recall seeing it.

Two Dogmas of Empiricism Willard Van Orman Quine
https://www.theologie.uzh.ch/dam/jcr:ffffffff-fbd6-1538-0000-000070cf64bc/Quine51.pdf

Bachelor is a rather simple term. There are many other words in English which are more abstract to define.

Yet he wrote a whole paper on his failure to understand that the term {bachelor} is simply assigned the semantic meaning of {unmarried + male + adult}.
• 536
As I said before, will say again. The whole confusion with the paradox and undefinability have been originated from the single narrow perspective seeing the problems in propositional logic, which only allows a proposition must be either True or False.

If you think about the real world situations and objects, there are cases where things are neutral i.e. neither true nor false such as Number 0. And there are the real world cases where things are both True and False, read on QM or some Metaphysical topics.

The term {true bearer} is very widely know throughout philosophy. That declarative sentences can be {truth bearers} and questions cannot be {truth bearers} is known by everyone that knows what {truth bearers} are. It takes very little additional understanding to know that {self-contradictory expressions} are not {truth bearers}.

That Tarski and Gödel did not understand something as simple as this makes them totally incompetent.
• 8.8k
That Tarski and Gödel did not understand something as simple as this makes them totally incompetent.
From the web
https://plato.stanford.edu/entries/truthmakers/
"This much is agreed: “x makes it true that p” is a construction that signifies, if it signifies anything at all, a relation borne to a truth-bearer by something else, a truth-maker.But it isn’t generally agreed what that something else might be, or what truth-bearers are, or what the character might be of the relationship that holds, if it does, between them, or even whether such a relationship ever does hold. Indeed sometimes there’s barely enough agreement amongst the parties to the truth-maker dispute for them to be disagreeing about a common subject matter. This makes navigating the literature about truth-makers a treacherous undertaking but a necessary one because of the significance the debate about truth-makers bears for contemporary metaphysics." (Bold, italics added.)

The article is long, comprehensive, and in parts very interesting - I won't pretend to have read it all. But to you, PL, I commend it as necessary for your understanding. As for your quote above, it simply establishes - as a truth-maker - that someone is totally incompetent.
• 536
The article is long, comprehensive, and in parts very interesting - I won't pretend to have read it all. But to you, PL, I commend it as necessary for your understanding. As for your quote above, it simply establishes - as a truth-maker - that someone is totally incompetent.

A {truth-maker} is a more difficult subject than a {truth-bearer} It took me 20 years of primary and secondary research to fully understand exactly what a {truth-maker} is for expressions of language that are true on the basis of their semantic meaning. It turns out that the final analysis of this is very simple.

On the other hand a {truth-bearer} is much simpler than this:

A truth-bearer is an entity that is said to be either true or false and nothing else.
https://en.wikipedia.org/wiki/Truth-bearer

In other words a {truth-bearer} is any expression of language that can possibly have a semantic value of true or false. This generally includes declarative sentences and generally excludes questions.

I have focused 20 years of primary and secondary research on the relationship between epistemological antinomies and expressions of language that are true on the basis of their semantic meaning.

At this point it does seem very very stupid that people cannot understand that self-contradictory expressions are not {truth-bearers}.
• 8.8k
At this point it does seem very very stupid that people cannot understand that self-contradictory expressions are not {truth-bearers}.
I think everyone gets it as something that is defined in a particular way. But having defined it, you then misapply it where it doesn't apply, leading you to make foolish claims.

I submit to you - to anyone - that if your claims lead to your calling some of humanity's better thinkers stupid, ridiculous, foolish, totally incompetent, then a decent respect even for yourself should require you to do more than just rant. And again, you might try reading the article.
• 583
Are there expressions of language that are true but are NOT true on the basis of their meaning AND also are not derived from other facts? Put slightly differently - is there another mechanism/method to determine the truth value of expressions of language?

Yes there is a TV in my living room right now is true on the basis of eyesight.

So there are two distinct mechanisms to determine the truth value of a language expressions, yes?
• 536
I think everyone gets it as something that is defined in a particular way. But having defined it, you then misapply it where it doesn't apply, leading you to make foolish claims.

That almost everyone including the greatest experts in the field do not fully understand that self-contradictory expressions are not {truth-bearers} does seem ridiculously stupid to me. To me it seems like the same thing as a PhD mathematics professor that disagrees with first grade arithmetic because they simply "do not believe in" numbers.
• 536
So there are two distinct mechanisms to determine the truth value of a language expressions, yes?

Yes. There is expressions of language that are true on the basis of their semantic meaning and there are expressions of language that are true on the basis of direct observation by the sense organs. The first kind boils down to relations between expressions of language.
• 8.8k
That almost everyone including the greatest experts in the field do not fully understand that self-contradictory expressions are not {truth-bearers} does seem ridiculously stupid to me.

I think you have said that a truth-bearer is a proposition that is true, or if false then its negation is a truth-bearer. Yes? Or if no, then what, exactly, do you say a truth-bearer is?
• 536
I think you have said that a truth-bearer is a proposition that is true, or if false then its negation is a truth-bearer. Yes? Or if no, then what, exactly, do you say a truth-bearer is?

Very close. A proposition / logic sentence is defined to always be a {truth-bearer}. This means that it is either true or its negation is true.

A truth-bearer is any expression of language that can have the semantic value of true or false. That after 2000 years people do not understand that the Liar Paradox (and other self-contradictory expressions) are not {truth-bearers} seems as ridiculous as a PhD math professor that simply "does not believe in" numbers.

Tarski's Undefinability theorem still stands even though its basis is that a Truth predicate cannot correctly determine that the actual Liar Paradox is true or false. To me this is like all of the bakers in the world trying again and again to bake an angel food cake using only house bricks for ingredients and never having any idea that this can't possibly work.
• 8.8k
You get right to the point so will I. There are a whole lot of so-called
"contradictory" sentences that are true. As described in the Stanford article referenced above and to be sure proved to the satisfaction of all* by Godel, Tarski, and others. And until you can do better on this topic than just your claims and incidental rants; that is,until you make some substantive contribution or argument, this ought to be an end of it.

*One exception noted.
• 536
↪PL Olcott You get right to the point so will I. There are a whole lot of so-called "contradictory" sentences that are true.

That is the same as saying there are a whole lot of integers that are greater than five and less than three, utterly ridiculous nonsense. That logicians make sure to never pay any attention at all to philosophy of logic makes them complete ignoramuses. There there are no mistakes within their false assumptions DOES NOT MEAN THERE ARE NO MISTAKES.

That actual self-contradictory sentences (not the deliberate double-talk of so-called) cannot possibly be true or false should have been universally accepted thousands of years ago shortly after the Liar Paradox was created.
• 536
↪PL Olcott You get right to the point so will I. There are a whole lot of so-called "contradictory" sentences that are true.

Please provide one example. Contradiction is a very well-known and certain measure of falsity in classical logic, symbolic logic, predicate logic.
• 8.8k
A proposition / logic sentence is defined to always be a {truth-bearer}. This means that it is either true or its negation is true.
The sentences in question say one way or another - and the article makes clear that exactly how they speak can be important - that they are not true, or not provable. And the analysis shows that whatever else might be true, it is self-evident and provable that they are true. Which is to say that they are, according to your exact definition, truth-bearers, which in turn makes all of your claims absurd.

Edit. Examples: "This sentence is not provable/ is not true." Or Godel's sentence G, or the liar. Or read the article! Or the introductory informal proof at the start of Godel's 1931 paper.
• 536
The sentences in question say one way or another - and the article makes clear that exactly how they speak can be important - that they are not true, or not provable. And the analysis shows that whatever else might be true, it is self-evident and provable that they are true. Which is to say that they are, according to your exact definition, truth-bearers, which in turn makes all of your claims absurd.

Gödel's Incompleteness use diagonalization that show G is not provable in F yet totally hides why it is unprovable. When reasoning is entirely hidden behind mathematical operations there is no basis for rebuttal.

...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...
(Gödel 1931:43-44)

Exposes the actual reasoning that is hidden behind the mathematical operations.
I just recently figured out that the proof of any "proposition which asserts its own unprovability"
requires a sequence of inference steps that prove that they themselves do not exist.

That would be the same as converting René Descartes famous: "I think therefore I am"
into "I think therefore thoughts do not exist", ridiculous nonsense.

Russell's Paradox was solved by simply correcting the incoherent definition of a set.
We can solve Tarski Undefinability this same way: Truth_Bearer(F, x) ≡ ((F ⊢ x) ∨ (F ⊢ ¬x))
• 3k
questions cannot be {truth bearers} is known by everyone that knows what {truth bearers} are.

Your statement here sounds nonsense. Some questions can be for true or false. For example, "You lied, didn't you?" This means you lied, and it is true. It is also to mean you should be aware of the fact that you lied.
• 536
Your statement here sounds nonsense. Some questions can be for true or false. For example, "You lied, didn't you?" This means you lied, and it is true. It is also to mean you should be aware of the fact that you lied.

That is a great counter-example. It seems to me that is actually a declarative sentence that is phrased as a rhetorical question. It is comprised of two distinctive parts: The statement: (a) "You lied." and the question: (b) Did you lie? When we break it down to its constituent parts (b) is still not a truth bearer.
• 3k
The statement: (a) "You lied." and the question: (b) Did you lie? When we break it down to its constituent parts (b) is still not a truth bearer.

I am not sure if you are allowed to modify the given example sentence under the process of breakdown.
If it is allowed, then virtually all questions can be truth bearers.

For instance, "What time is it now?"
One could modify it into "It is true that she asked what time it is now.", hence one can say it is true.

"How are you doing?" - one can modify it again - "It is true that she asked him how he was doing." Therefore "How are you dong?" is a truth bearer.

Are modifications, inferences and breakdowns on the original sentence allowed for TF values?
• 536
I am not sure if you are allowed to modify the given example sentence under the process of breakdown. If it is allowed, then virtually all questions can be truth bearers.

Sentences with ambiguity must be disambiguated before that can be properly analyzed.
For example asking a man that has never been married: Have you stopped beating you wife?
Would be rejected as semantically incorrect on the basis of the false presupposition.

An expression of language that is both a question and a statement would also have
to be rejected until it is translated into one or the other. The sentence: "Did you lie?"
is not a truth bearer thus would be rejected by a correct Truth Predicate.
• 2.3k
Contrary to a claim made in this thread (and made by the same poster several other times in this forum), it is not the case the Godel sentence requires that there is a sequence of inference steps that prove that they don't exist (as has been explained several other times in this forum).

More generally, Godel's and Tarski's proofs do not have the defects claimed in this thread (and claimed by the same poster several other times in this forum). That can be verified by reading an introductory textbook on mathematical logic in which the groundwork and proofs of Godel-Rosser incompleteness and Tarski undefinability are provided.
• 2.3k
"Did you lie?" doesn't have a truth value, because it is not a declarative sentence. Indeed, interrogatory sentences do not appear as lines in proofs.
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