This is helpful. But you have omitted a critical qualification: "[C]annot be proven or refuted" from the axioms of the system. But that the sentence in question is absolutely a truth bearer is established by meta-system argument. — tim wood

We can determine that the Liar Paradox applied to itself is true:
This sentence is not true: "This sentence is not true" is true.

yet we can only do this on the basis that the Liar Paradox is not a truth bearer, thus would have rejected it before it gets to the meta-level of analysis.

"This sentence is not provable." — tim wood

To be proven requires a sequence of inference steps that prove that they themselves do not exist.

This is just like this adapted form of René Descartes: "I think therefore I am"
becomes: "I think therefore thoughts do not exist". (AKA nonsense).

But nowhere in that is Godel demonstrated wrong or foolish — tim wood

That he is simply too stupid to reject self-contradictory expressions makes him enormously foolish. On a related note he starved himself to death because he only trusted his wife's cooking. That he did not even trust his own cooking was quite psychotic.

I’m puzzled as to why you are posting on this amateur forum. Your ideas are groundbreaking and revolutionary. I urge you to submit your thesis to The American Philosophical Quarterly (or equivalent). If there is any validity to your ideas then of course they will print them and the name PL Olcott will be entered into the pantheon of famous philosophers along side with Aristotle, Kant, etc. Go for it PL!

↪PL Olcott I’m puzzled as to why you are posting on this amateur forum. Your ideas are groundbreaking and revolutionary. I urge you to submit your thesis to The American Philosophical Quarterly (or equivalent). If there is any validity to your ideas then of course they will print them and the name PL Olcott will be entered into the pantheon of famous philosophers along side with Aristotle, Kant, etc. Go for it PL! — EricH

When reviewing the actual publications in the field it seems that the greatest experts in the field are incapable of understanding that self-contradictory expressions are not true. This forum right here has proven to be the best forum for these things. People here (on this site) are generally very intelligent and thoughtful.

The world's leading experts all seem to be uniformly indoctrinated into believing that Gödel's words are utterly infallible. No one even bothered to notice that any expression asserting its own unprovability requires a sequence of inference steps that prove that they themselves do not exist.

That is not true at all. If someone says that a {dog} <is> a fifteen story office building this is ruled as false because there are no {dogs} that <are> fifteen story office buildings in the actual world. — PL Olcott

It sounds a weak argument for your point. Some surly confused guy calling an honest man dishonest doesn't make the honest man dishonest. Likewise some obtuse man making totally irrelevant claims wouldn't have anything to do with the fact that analytic truth is true or false.

You expect your interlocutor try to make the most reasonable inferences for the arguments. If they come with totally irrelevant barmy claims, then you know he is not worth for any discussions on truth or logic.

Likewise we can generalize cows eat house bricks into cows eat something.
Any nonsense sentence can be changed into a different sentence that is not nonsense. — PL Olcott

You know the cows eat house bricks is false from common sense.
https://en.wikipedia.org/wiki/Common_sense
You don't need to generalise it to find out it is false. But generalisation and abstraction is what FOL and HOL are for the computability of ordinary language.

I have the classic Clocksin and Mellish. https://www.amazon.com/Programming-Prolog-Using-ISO-Standard/dp/3540006788 — PL Olcott

I got this book as well. It just arrived. It seems Prolog is a great logic program language which is built on FOL and HOL. An ideal PL for AI applications.

It sounds a weak argument for your point. Some surly confused guy calling an honest man dishonest doesn't make the honest man dishonest. Likewise some obtuse man making totally irrelevant claims wouldn't have anything to do with the fact that analytic truth is true or false. — Corvus

The actual model of the world is the basis. Facts not opinions.

You know the cows eat house bricks is false from common sense.
https://en.wikipedia.org/wiki/Common_sense
You don't need to generalise it to find out it is false. But generalisation and abstraction is what FOL and HOL are for the computability of ordinary language. — Corvus

That set of facts that comprise the actual model of the real world is the basis.
This includes common sense and also details that almost everyone does not know.

I got this book as well. It just arrived. It seems Prolog is a great logic program language which is built on FOL and HOL. An ideal PL for AI applications. — Corvus

The key most important thing about Prolog is that Gödel's incompleteness can not be implemented in Prolog. Unprovable simply means untrue. Since this <is> the way that every expression of language that is {true on the basis of its meaning} derives its truth it shows that Gödel's incompleteness is a misconception.

...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
(Gödel 1931:43-44)

In Prolog epistemological antinomies are simply rejected as malformed:

?- LP = not(true(LP)).
LP = not(true(LP)).

?- unify_with_occurs_check(LP, not(true(LP))).
false.

BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:

equal(X, X).
?- equal(foo(Y), Y).

that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y,
which appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)

That set of facts that comprise the actual model of the real world is the basis. — PL Olcott

Which is exactly not the basis for mathematics. You might care to pause and consider just exactly what a fact is (and isn't). Agreed, if you compile a great list of facts, then you can distinguish between what is included in your list and what is not included, and presumably can test what is not included to see if it should be added or not. But it is a mistake to conclude that what is not a fact must be nonsense or a piece of stupidity; and that mistake arises out of either not understanding what a fact is and is not, or having a term-of-art definition of "fact" which you then misapply.

The distinction here is between what is a fact and what is true. Notwithstanding that the terms are often not distinguished and used interchangeably, they are not the same thing, and you are stumbling badly over that.

The distinction here is between what is a fact and what is true. Notwithstanding that the terms are often not distinguished and used interchangeably, they are not the same thing, and you are stumbling badly over that. — tim wood

This is ALL there is to expressions of language that are true on the basis of their meaning
(1) Some expressions of language are stipulated to be true thus providing semantic meaning to otherwise totally meaningless finite strings. These expressions are the set of facts.
(2) Some expressions of language are derived by applying truth preserving operations to (1).

Epistemological antinomies belong to neither (1) nor (2) thus are merely untrue.

Copyright 2023 and earlier PL Olcott

(1) Some expressions of language are stipulated to be true thus providing semantic meaning to otherwise totally meaningless finite strings. These expressions are the set of facts. — PL Olcott

Which is to say you simply do not know the difference between the two. Try this, 2+2=4. Repesenting a fact or a truth?

Which is to say you simply do not know the difference between the two. Try this, 2+2=4. Repesenting a fact or a truth? — tim wood

The ONLY way that we know that {cats are animals} is that it is stipulated to be true on the basis of the assigned meaning of the words.

2+2=4 is derived from Peano Arithmetic axioms, thus (2) derived from (1).

Ok. we'll plod. All facts are propositions that are historical in nature. A kind of hearsay, if you will. And this includes just about everything that can be said about the world. And you're right, we all agree on many facts - although sometimes we don't. Can you say election denier? Holocaust denier? Climate change denier? And with these we have to confront exactly what a fact is and is not.

And this opposed to truth. Propositions that are true are not temporal, not historical, not in any way hearsay. 2+2=4 is true and always and necessarily so (except for some engineers who make exception for large values of two). But anyone calling it a fact is simply in error, though a common enough mistake. Usually it's not important. But you, failing to distinguish the two, make outrageous and ridiculous claims about the thinking one of history's better thinkers, with neither evidence nor reason nor justification except for your own carefully applied ignorance. Yes it's granted that in your own limited application you can have what you like, but you've let that apply where it does not and should not, and that mistake makes everything else of yours suspect.

. .

All facts are propositions that are historical in nature. A kind of hearsay, if you will. And this includes just about everything that can be said about the world — tim wood

Actual facts are expressions of language that correctly model the actual world even if everyone in the universe disagrees or no one in the universe knows them.

And since 2+2=4 models nothing in the world, it's not a fact - what is it then? Ridiculous nonsense? And what does "correctly model" mean?

My point being that there is a whole barge-load of assumptions you're making, apparently without being aware you're making them. The Boston Red Sox won the 2003 World Series: if three out of three agree with that, does that make it a fact?

My point being that there is a whole barge-load of assumptions you're making, apparently without being aware you're making them. The Boston Red Sox won the 2003 World Series: if three out of three agree with that, does that make it a fact? — tim wood

I am making zero assumptions what-so-ever. Facts are expressions of language that are true
EVEN IF NO ONE KNOWS THIS OR EVERYONE IN THE WHOLE UNIVERSE DISAGREES.

This is ALL there is to expressions of language that are true on the basis of their meaning
(1) Some expressions of language are stipulated to be true thus providing semantic meaning to otherwise totally meaningless finite strings. These expressions are the set of facts. — PL Olcott

Here you seem to be saying that we can determine the set of facts from a well constructed dictionary.

Actual facts are expressions of language that correctly model the actual world even if everyone in the universe disagrees or no one in the universe knows them. — PL Olcott

And here you seem to be re-stating the Correspondence Theory of Truth.

Here you seem to be saying that we can determine the set of facts from a well constructed dictionary. — EricH

We can combine (1) and (2) and say that every expression of language that is true on the basis of its meaning is either a fact or derived from a fact. Facts are true even if everyone disagrees or no one knows.

Writing down every single detail of all of the general knowledge of the actual world would probably need a book at least a million miles tall. Since this is only 59 petabytes this is probably not nearly enough.

Facts are true — PL Olcott

*sigh* Anyone else want to take this on?

Facts are true
— PL Olcott
*sigh* Anyone else want to take this on? — tim wood

The reason for my persistence with correcting the notion of truth is that incorrect notions are resulting in the extinction of humanity through climate change and the end of Democracy through Nazi propaganda.

If we had a properly formalized notion of truth then it would be possible for a computer program to argue against the hired liar climate change deniers and Nazi propagandists so effectively that this people would look like complete fools even to themselves.

You're not correcting anything. But you are making a mistake plain and simple. Let's try a test. I'm a Holocaust denier (not, actually). How does your program handle that?

The mistake lies in an unnatural - and ignorant - restriction and confining of truth, in essence a misunderstanding of what truth is, to whatever you deem true, and then denying as ridiculous, stupid, mistaken anything that does not comport with your program. A very totalitarian scheme. Putin would approve.

All facts are historical (facts), and thus matters of agreement, if you will. All true statements are true, in respect of their being true, a priori. You can have your large listing of facts - such things already exist. And we can check them at need. But truth is not quite so simple - not least because being different.

But go ahead, prove the Holocaust - or anything else at your choice - is true. Or for that matter, any denial false.

You're not correcting anything. But you are making a mistake plain and simple. Let's try a test. I'm a Holocaust denier (not, actually). How does your program handle that? — tim wood

It will not focus its attention on every lie, only the ones that can have near term catastrophic consequences. I can't understand how 45% of the electorate can believe that election fraud changed the outcome of the 2020 presidential election when there has been literally no evidence of this.

The system that I propose would know 10,000-fold more about counter-propaganda than any human mind can possibly hold. The bad people that are pushing Nazi propaganda have had many decades perfecting their craft. The good people telling the truth don't have the slightest clue of how to effectively deal with this.

The good people telling the truth don't have the slightest clue of how to effectively deal with this. — PL Olcott

The Germans do, apparently.

The good people telling the truth don't have the slightest clue of how to effectively deal with this.
— PL Olcott
The Germans do, apparently. — tim wood

The Germans currently know how to counter-propaganda?
One of the things that they did that has worked is limiting free speech.

It does seem to me that counter-factual lies should come with civil liability.
To keep free-speech open you are allowed to assert any opinion as long
as you qualify it as only an opinion.

When you assert a counter-factual lie as a verified fact you can lose up to
all of your assets no matter how much you have. This would be especially
helpful for the fossil fuel industry's hiring of liars.

The actual model of the world is the basis. Facts not opinions. — PL Olcott

No one was talking about opinions here apart from yourself. Isn't it a typical case of the strawman?

That set of facts that comprise the actual model of the real world is the basis.
This includes common sense and also details that almost everyone does not know. — PL Olcott

But your example "cows don't eat house bricks" is neither a fact nor common sense. It is just an irrelevant daft statement, which is based on senseless reasoning. :)

The key most important thing about Prolog is that Gödel's incompleteness can not be implemented in Prolog. — PL Olcott

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.

But your example "cows don't eat house bricks" is neither a fact nor common sense. It is just an irrelevant daft statement, which is based on senseless reasoning. — Corvus

It is a concrete example of an expression of language that is true on the basis of it meaning. 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.