Axiom is a proposition regarded as self-evidently true without proof.

Is it self-evidently true that Moscow must be the capital of Russia?

Cat is animal.
Cat is plant.

But after the update, the system has two expressions for the same word cat, which are contradictory.

It seems to me the larger issue is if you were simply to put something completely false in, e.g. "the US House of Representatives has 572 members."

This is false. How do we know it is false? Not because "The US House of Representatives," fails to be synonymous with "has 572 members." In is a contingent fact. If something like the Wyoming rule was ever passed, the House very well could end up with that many members, but it still wouldn't make the fact true by definition. It isn't an analytic truth. Most true propositions are not analytic.

We could debate about propositions related to natural kinds, e.g., if Carbon was synonymous with "the element with 6 protons in its nucleus" before "element" had its current definition and before anyone knew what a proton was. However, the more obvious case where this breaks down are propositions like "Moscow is the capital of Russia." Well, it is right now. It wasn't when Saint Petersburg was the capital though, and it might not be in the future. Moscow simply is not synonymous with "the capital of Russia;" "Moscow is the capital of Russia," is not a tautology, it is not analytic.

Saying, "what if we collected all possible non-analytical truths, and then declared them true by axiom, won't that will turn them into analytical truths," is totally missing what an analytical truth is. It turns non-analytical truths into tautologies only in the context of our made up language. But our made up language could just as easily contain false axioms. How would we determine which is which? How do we determine which true "axioms" to include in our language? Well, for all those truths that aren't real tautologies, it would still require sense data, because they are simply not analytical truths. You can't "turn a truth analytic," by axiom (at least not in the context in which the distinction is remotely useful).

The distinction was about truths simpliciter, not about "what can be made analytical in some arbitrary system." Absolutely no one denies that you can make a system where "Paris is the capital of Mexico," is true by definition, and that in that system, that proposition will be true by definition, a tautology, and thus "analytical." But that's really missing the point of both why the distinction was ever relevant and Quine and others' critique of it, which is not about truth in the context of some one arbitrary system. You have to overdose on deflation and think of truth as just "what formal systems say about statements," to get to this.

Cat is animal.
Cat is plant.

But after the update, the system has two expressions for the same word cat, which are contradictory.

Not at all the system rejects the incorrect use of {Cat} as a type mismatch error or is able to determine from context which {Cat} is being referred to.

This is false. How do we know it is false? Not because "The US House of Representatives," fails to be synonymous with "has 572 members." — Count Timothy von Icarus

The system reads everything that anyone ever wrote and detects inconsistences. It knows to use the US constitution to determine the number of members of congress. It also understands all of the details of how the constitution is amended thus any purported amendments must have a complete audit trail.

Saying, "what if we collected all possible non-analytical truths, and then declared them true by axiom, that will turn them into analytical truths," is totally missing what an analytical truth is. — Count Timothy von Icarus

{Analytic}(Olcott) is intended to retain {proven completely true entirely on the basis of its meaning} and is free to override and supersede every other detail of the conventional meaning of {Analytic}.

It boils down to the fact that I am defining True(L, x) the way that it actually works and rejecting any and all misconceptions of this.

But our made up language could just as easily contain false axioms. How would we determine which is which? — Count Timothy von Icarus

Expressions of language that are stipulated to be true are from the current correct model of the actual world. If someone says that the current number of members of congress is {a stale bologna sandwich} then they are wrong.

Expressions of language that are stipulated to be true are from the current correct model of the actual world. If someone says that the current number of members of congress is {a stale bologna sandwich} then they are wrong.

Are they wrong in virtue of the fact that a bologna sandwich was never elected to Congress or are they wrong in virtue of the fact that the database hasn't included that as an axiom?

proven completely true entirely on the basis of its meaning

Ok, so you can have your magic database, and I will make my own. In mine, the current congressman for the 12th District is a stale bologna sandwich. This is axiomatic and can be "proven completely true entirely on the basis of its meaning."

Is it now the case that it is both completely true and also false that a bologna sandwich is a member of Congress? Or is your database right and my database is wrong? If yours is right and mine is wrong, in virtue of what is your database correct and mine incorrect? It can't be in virtue of the meanings of terms alone, for I have a unique integer code that says that a bologna sandwich is a member of Congress by definition.

Might it be that yours is correct because it is true in virtue of how the proposition relates to states of affairs and not the meaning ascribed to some code? :chin:

Are they wrong in virtue of the fact that a bologna sandwich was never elected to Congress or are they wrong in virtue of the fact that the database hasn't included that as an axiom? — Count Timothy von Icarus

The database is currently hypothetical as merely the set of finite strings that encode semantic truth.

Ok, so you can have your magic database, and I will make my own. — Count Timothy von Icarus

The set of finites strings that encode semantic truth is neither arbitrary nor capricious.

Might it be that yours is correct because it is true in virtue of how the proposition relates to states of affairs and not the meaning ascribed to some code? — Count Timothy von Icarus

"this sentenced has words" is semantic meaning encoded in symbols.
https://www.liarparadox.org/Communication_Process.png

"state of affairs" includes some expressions that are not Analytic(Olcott).

Just like the Cyc project each unique sense meaning has its own unique GUID
9824b3dc-7237-4b4b-9a71-fb788348bc9a for the living animal "Cat"
9f444cef-f49f-4aa8-89bf-248ee5976b92 for "Cat Palm" — PL Olcott

So how do the users know which is which? Do they have to type in the unique GUID into the system to get the correct definition they want?

Or can the Cyc project know which is the right one the user wants to know? How does it do that?
Some users could call cat palm as just "cat", and some may have a cat called "cat palm".

So how do the users know which is which? Do they have to type in the unique GUID into the system to get the correct definition they want?

Or can the Cyc project know which is the right one the user wants to know? How does it do that?
Some users could call cat palm as just "cat", and some may have a cat called "cat palm". — Corvus

Once a system like Cyc acquires all of the general knowledge of the world then it can disambiguate these things exactly as well as the best human experts. If there is no context to disambiguate it then it would do the same thing that a human would do and tentatively hypothesize one of them until this hypothesis is proven false.

He also agrees that Cyc project's flaw is the problem of handling contradictions in the input data.

I have understood that beliefs are a very terrible measure measure of knowledge when I was 16, 56 years ago. When I was 16 I saw this as the woeful fallibility of humanity to distinguish facts from opinions. Doug Lenat's approach is correct for the entire body of {analytical knowledge} meaning known truths that can be expressed using language.

I don't currently know how to handle contentious knowledge.

I don't currently know how to handle contentious knowledge. — PL Olcott

Any AI system needs some sort of reasoning logic based on the different domains and hierarchical structure of the data. It is more challenging to implement the reasoning logics onto the natural language based data, because computers cannot handle the human natural languages well, hence converting the data into the axiomatised symbolic formalisation using the semantic frames would be needed? Just guessing.

Here is some conceptual definition of the semantic frames in AI knowledge based system.

"In semantics, particularly in the context of knowledge representation and artificial intelligence, a frame is a data structure used to represent knowledge about a particular concept or domain. Frames provide a way to organize information hierarchically and capture both structural and procedural knowledge.

Here are some key components and characteristics of frames in semantics:

1. **Slots**: Frames consist of slots, which represent attributes or properties of the concept being modeled. Each slot can have a name and a value, where the value can be a simple data type (such as a string or number) or another frame, allowing for nested structures.

2. **Values**: The values associated with slots can represent various kinds of information, such as characteristics, relationships, or behaviors of the concept being modeled. For example, a frame representing a "car" might have slots for attributes like "color," "model," "manufacturer," and "engine type."

3. **Inheritance**: Frames can inherit properties and relationships from other frames, forming a hierarchical structure. This allows for the representation of generalizations and specializations within a domain. For example, a frame representing a "sedan" might inherit properties from a more general "car" frame.

4. **Prototypes**: Frames can serve as prototypes or templates for creating instances of concepts. By specifying default values for slots, frames can capture common characteristics shared by instances within a category.

5. **Scripts**: Frames can also include procedural knowledge in the form of scripts, which represent sequences of actions or events associated with the concept. Scripts provide a way to represent typical sequences of behavior or events related to a particular concept.

Frames are used in various applications, including expert systems, natural language processing, semantic networks, and knowledge-based systems. They provide a flexible and intuitive way to represent knowledge about complex concepts and domains, allowing for efficient reasoning and inference in AI systems." - ChatGPT

The original version of CycL was a frame language, but the modern version is not. Rather, it is a declarative language based on classical first-order logic, with extensions for modal operators and higher order quantification. https://en.wikipedia.org/wiki/CycL

In information science, an ontology encompasses a representation, formal naming, and definitions of the categories, properties, and relations between the concepts, data, or entities that pertain to one, many, or all domains of discourse. https://en.wikipedia.org/wiki/Ontology_(information_science)

The original version of CycL was a frame language, but the modern version is not. Rather, it is a declarative language based on classical first-order logic, with extensions for modal operators and higher order quantification. https://en.wikipedia.org/wiki/CycL — PL Olcott

Does it handle / process abstract concepts such as God, souls, freedom or immortality?

In information science, an ontology encompasses a representation, formal naming, and definitions of the categories, properties, and relations between the concepts, data, or entities that pertain to one, many, or all domains of discourse. https://en.wikipedia.org/wiki/Ontology_(information_science) — PL Olcott

This is a good link for the concept "Ontology in Information Science". Thanks.

Does it handle / process abstract concepts such as God, souls, freedom or immortality? — Corvus

In theory is can process any knowledge known to humankind that can be encoded as text strings.

In theory is can process any knowledge known to humankind that can be encoded as text strings. — PL Olcott

How is it different from ChatGPT?

In theory is can process any knowledge known to humankind that can be encoded as text strings.
— PL Olcott
How is it different from ChatGPT? — Corvus

ChatGPT is the huge breakthrough that makes populating the Cyc project's
knowledge ontology feasible. They spent about 1000 labor years manually
encoding the current teeny tiny fraction of knowledge known as common sense.
This took them 40 calendar years since 1984.

Getting from Generative AI to Trustworthy AI: What LLMs might learn from Cyc

Only in the sense that facts can be looked up in an encyclopedia and encyclopedias can be updated with new facts. Actual interaction with the world that requires sense input from the sense organs is specifically excluded from the body of analytic knowledge. That dogs exist is analytic. That there is a small black dog in my living room right now is synthetic. — PL Olcott

You'll have to forgive this bear of little brain, but i can't make any sense of this. How do we know that dogs exist? Can we rule out the possibility of an overnight canine pandemic that killed every dog on the planet via analytic statements? Not that I can see. The only way to determine this is via sense input.

You'll have to forgive this bear of little brain, but i can't make any sense of this. How do we know that dogs exist? Can we rule out the possibility of an overnight canine pandemic that killed every dog on the planet via analytic statements? Not that I can see. The only way to determine this is via sense input. — EricH

Dogs exist as conceptual objects even if all of reality is a mere figment of the imagination.
My purpose is to provide the foundation such that Boolean True(Language L, String x) becomes computable.

On Stack Exchange the foundation of analytical truth is rejected specifically because it is unpopular. Once we have the actual foundation of analytical truth then Boolean True(L, x) becomes computable.

Dogs exist as conceptual objects even if all of reality is a mere figment of the imagination. — PL Olcott

So this whole project is merely the embodiment of people's imagination.

Dogs exist as conceptual objects even if all of reality is a mere figment of the imagination.
— PL Olcott

So this whole project is merely the embodiment of people's imagination. — EricH

Not at all, exactly the opposite. Dogs are animals is absolutely true no matter what.
It is true in the same sort of way that we know that 5 is numerically greater than 2.
5 > 2 remains true even after the heat death of the universe when zero minds exist.

Dogs are animals is absolutely true no matter what. — PL Olcott

Something is true or false always in relation to some respect. Dogs are animals is false in case of the robot AI dogs. Dogs can be tools in wood carving toolbox. Dogs are pieces of the wooden material that get inserted in the holes of the workbenches to secure a plank of wood to be carved. In this case dogs are animals is false again.

5>2 is false in case of the amounts of electric current output of some electrical tools. When 1 is set to the highest, and 5 is the lowest, 2 is greater in the current output than 5. In this case, 2>5 is true. 5>2 is false.

5 > 2 remains true even after the heat death of the universe when zero minds exist. — PL Olcott

According to Carnap (Introduction to Semantics, 1941, Harvard University Press) , all sentences and expressions carry implied truth conditions for it being true i.e. 5>2 is true, iff 5>2 in all possible conditions of the universe.

Dog is animal is true, iff the dog is a living dog of the dog species.

Something is true or false always in relation to some respect. Dogs are animals is false in case of the robot AI dogs. Dogs can be tools in wood carving toolbox. Dogs are pieces of the wooden material that get inserted in the holes of the workbenches to secure a plank of wood to be carved. In this case dogs are animals is false again. — Corvus

3ab2c577-7d38-4a3c-adc9-c5eff8491282 stands for the living animal dog, this is the same way that the Cyc project identifies unique sense meanings,

3ab2c577-7d38-4a3c-adc9-c5eff8491282 stands for the living animal dog — PL Olcott

Dogs exist as conceptual objects — PL Olcott

I still can't make any sense of this. Does the Cyc project identifier refer to

- a conceptual object
- a collection of conceptual objects (i.e., how do we know that one person's conception of a dog is the same as another's)
- a particular existing living animal that happens to be a dog
- all living animals that happen to be dogs
- other?

The use of "analytic" here bears little resemblance to the normal usage. As far as I can tell, any fact is "analytic" so long as it can be defined as true by definition by some string. The analytic normally is "what is true by definition," and apparently non-analytic facts like "Moscow is the current capital of Russia," can become analytic despite the fact that "Moscow" is not synonymous with "the capital of Russia," by simply stipulating an axiom that says "Moscow is the capital of Russia, by definition."

But how would one determine if any such string is actually true? Wouldn't we need to look at the world and make sure the capital hasn't moved back to St. Petersburg again? No, because we have the "one true model of the world" in which all strings are true, by definition, and this makes everything analytic, because, given the model, you can point to an axiom for any fact that says "this is true by definition."

In virtue of what is the "one true model," true? In virtue of the fact that it stipulates that only true things are true (by definition). Why are these things true? Because they are stipulated as true by definition and they are also true because they are in the "one true model."

I still can't make any sense of this. Does the Cyc project identifier refer to
- a conceptual object
- a collection of conceptual objects (i.e., how do we know that one person's conception of a dog is the same as another's)
- a particular existing living animal that happens to be a dog
- all living animals that happen to be dogs
- other? — EricH

A 128-bit integer GUID refers to a single unique sense meaning, thus the class living animal {dog} has its own unique GUID. A particular individual {dog} could have its own unique GUID within the discourse context knowledge ontology, yet not a part of the general knowledge ontology.

In one person believes that the living animal {dog} has an elevator because it is a {fifteen story office building} then they are simply incorrect.

The use of "analytic" here bears little resemblance to the normal usage. As far as I can tell, any fact is "analytic" so long as it can be defined as true by definition by some string. The analytic normally is "what is true by definition," and apparently non-analytic facts like "Moscow is the current capital of Russia," can become analytic despite the fact that "Moscow" is not synonymous with "the capital of Russia," by simply stipulating an axiom that says "Moscow is the capital of Russia, by definition." — Count Timothy von Icarus

The current model of the actual world (that can be periodically updated) that includes all knowledge of mathematics and logic and is able to perform any mathematical and logical operations is defined to be Analytic(Olcott). This is the foundation of analytical knowledge that is used as the basis to define a True(Language, Expression_of_Language) predicate thus refuting Tarski that incorrectly "proved" this cannot be done.

Ah, right, I forgot , it also disproves Tarski's undefinability theorem somehow.

That article doesn't properly state the subject matter.

↪Count Timothy von Icarus

That article doesn't properly state the subject matter. — TonesInDeepFreeze

I think that it does a decent job.
Here is the most relevant part
As always diagonalization shows THAT an expression is unprovable and ignores
the reason WHY it is unprovable is that it is self-contradictory.

Here is his actual proof
Here is where he anchors it in the Liar Paradox

(1) The article conflates a language with a theory.

(2) The proof in the article handwaves past the crucial lemma, thus appearing to commit a serious non sequitur.

(1) The article conflates a language with a theory.

(2) The proof in the article handwaves past the crucial lemma, thus appearing to commit a serious non sequitur. — TonesInDeepFreeze

The whole Idea as I present it is whether or not the computable function
Boolean True(String Language, String Expression) can correctly and
consistently determine the truth value of every element of human general
knowledge on the basis of an accurate model of the current world.

When we construe that Tarski's Undefinability Theorem got stuck
on the Liar Paradox here is the resolution to that:

LP = "This sentence is not true"
Boolean True(English, LP) returns false for not true.
Boolean True(English, ~LP) returns false for not true.

The generic issue across many undecidable decision problems is that
epistemological antinomies (AKA self-contradictory expressions) are
not excluded from the problem domain.

Another issue with this is that most modern philosopher's do not understand
that self-contradictory expressions are not truth bearers thus have no associated
truth value.

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

Gödel, Kurt 1931. On Formally Undecidable Propositions of Principia Mathematica And Related Systems