A re-definition of {analytic} that seems to overcome ALL objections that anyone can possibly have
An analytic expression x is any expression of language verified as completely true (or false) entirely on the basis that x (or ~x) is derived by applying truth preserving operations to other expressions of language that are stipulated to be true thus providing the semantic meaning of terms.
This seems to categorically address every objection that Quine or anyone else can possibly have.
Every truth entire contained within and totally verified by expressions of language analytic.
That I can see (with my eyes) that there is a small black dog in my living room right now requires eyes and eyes are not words, thus this expression is not analytic.
Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions.
https://en.wikipedia.org/wiki/Truth-conditional_semantics
This seems to categorically address every objection that Quine or anyone else can possibly have.
Every truth entire contained within and totally verified by expressions of language
That I can see (with my eyes) that there is a small black dog in my living room right now requires eyes and eyes are not words, thus this expression is not analytic.
Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions.
https://en.wikipedia.org/wiki/Truth-conditional_semantics
Comments (160)
As it stands, "expressions of language that are stipulated to be true"makes it appear that is saying that it is analytic if he says it is analytic.
:worry:
I'll leave you to it.
Problems with analytic expressions are possible tautology. They tend to repeat what is already contained in the subject of the expressions e.g. "A bachelor is an unmarried male." viz. they don't increase or add new knowledge.
All of the knowledge of the actual world is defined as the stipulated meaning of terms and stipulated relations between terms in an inheritance hierarchy knowledge ontology specified as Rudolf Carnap / Montague grammar meaning postulates. The term Bachelor(x) is stipulated to mean: Adult(x) & Male(x) & ~Married(x) defined in terms of the constituent parts that comprise it.
Still doesn't change the fact that it doesn't add any new knowledge or facts into the concept unless it was used with the real world situations or observations.
It doesn't add any new knowledge the same way that dictionaries and encyclopedias do not add any new knowledge. The purpose is not to add any new knowledge, it is to mathematically formalize existing knowledge. The Cyc project is named on the basis that it is an en-cyc-lopedia.
https://en.wikipedia.org/wiki/Cyc
That looks an interesting project. :ok:
Any data structure in hand for the project?
For example, the word bachelor's meaning "an unmarried adult male", Quine asks who on earth gave that meaning to bachelor, and why? Meanings of words are totally contingent and changeable. A single words can have also multiple meanings too which adds to the confusion. Hence without the empirical perception which reflects the situation, analytic words themselves have no meanings.
Finite strings are assigned semantic meanings in the same way that 5 is assigned to the value x in BASIC: 100 let x = 5
The CYC project uses 128-but GUID integers to reference each unique sense meaning. If they change over time a brand new GUID is created to reference the new meaning.
In a BASIC program when at line 100 we assign 5 to x like this 100 let x = 5, then we know that the variable x contains the value of 5. If we disagree then we are simply wrong.
It is the same way when semantic meanings are assigned to arbitrary finite strings.
?x ? ("Bachelor(x)" ? "Male(x) ? Adult(x) ? ¬Married(x)")
The stipulated relations between otherwise totally meaningless finite strings is 100% of the whole process that stipulates that finite strings have specific meanings. No one has authority to do this. We are merely following the arbitrary conventions that were mutually agreed upon long ago.
This is more clear when we understand that the above finites strings of {"Bachelor", "Male", "Adult", "¬Married"} are totally different across different human languages.
Yes, but Quine might ask, what about in the case of, when a married woman claims that she is a Bachelor, and you ask how is it possible? She replies "My names is a Bachelor."
That is an idiomatic reference that does not pertain to the same GUID.
I think his point is that an analytic system must be able to interact with the external world input data for it to be useful.
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.
SO, on the presumption that there is indeed a small black dog in your living room right now, and the view that facts are analytic, does it follow that it is not a fact that there is a small black dog in your living room right now? And this despite there being a small black dog in your living room right now?
Not following that.
SO facts divide into synthetic and analytic?
Quoting PL Olcott
There are synthetic facts, too. So what is it that Quine did not understand?
I don't know but he convinced a majority of philosophers that the analytic / synthetic distinction is problematic. He seemed to think that nothing about anything can be known without physical experience. He might not have known enough math to be challenged to provide the physical experience of the square root of two.
So the objections that you point to in the title of this thread - what exactly are they?
So what were his objections? The ones you refer to in the title of this thread?
Two Dogmas of Empiricism Willard Van Orman Quine (1951)
https://michaelreno.org/wp-content/uploads/2020/01/QuineTwoDogmas.pdf
What are his objections, specifically, and how does your account address them?
An analytic expression of language can be totally proved true or false entirely on the basis of other expressions of language.
That {dogs}
Sure, good, wonderful.
Now, can you set out the objections raised by Quine, and how it is that you address them?
Otherwise, it seems to me that your definition of analyticity is just the first one that Quine sets out -
No I cannot. Once I understood that he didn't understand that bachelors are unmarried I wrote him off as a nitwit. Do you know of any objections that are not already addressed by my definition?
I am assuming that a correct model of the actual world already exists in formalized natural language. How does anyone know that {dogs}
An axiom is a proposition regarded as self-evidently true without proof.
https://mathworld.wolfram.com/Axiom.html
Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. https://en.wikipedia.org/wiki/Truth-conditional_semantics
This stipulates the semantic meaning of expressions of language by assigning semantic meaning to otherwise totally meaningless finite strings.
Yeah, didn't think so.
I find that categorically exhaustive reasoning finds the optimal answer in minimal steps. Try bringing up any specific objection and I will address it. I have been using {categorically exhaustive reasoning} for two decades now it is quite effective.
My definition unequivocally divides analytic from synthetic. I have been going over it again and again for many years. It was reverse-engineered on the basis of several undecidable decision problems, the key one being the Tarski Undefinability Theorem.
Analytic sentences are known to be superfluous for the meanings are already in the sentence, and it is just repeating what is in it.
A bachelor is a man who is not married.
A bachelor = a man who is not married
A bachelor is a bachelor, or a man who is not married is a man who is not married.
It also creates some grammar confusions.
No bachelor is married.
No man who is not married is married.
A man who is not married is married.
Quoting PL Olcott
That dogs exist is ambiguous. It doesn't say where and when that dogs exist.
It only makes sense if that dogs exist in the real world, and if the sentence has been denoting for the info and also the evidence of the existence.
That dogs exist is analytic is ambiguous in another way that, it sounds like you are claiming that that dogs are analytic. I have not seen or heard analytic dogs. What breed are they? Or do you mean the dogs analyse something? Do the synthetic dogs exist too?
That is not the definition that I provided. I redefined {analytic} to eliminate all equivocation. Quoting PL Olcott
Quoting Corvus
The class {dog} is stipulated to be a subset of the class {animal}. The other details about {dogs} and {animals} are referenced in the axiomatic model of the actual world knowledge ontology inheritance hierarchy.
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. More simply, an ontology is a way of showing the properties of a subject area and how they are related, by defining a set of terms and relational expressions that represent the entities in that subject area. https://en.wikipedia.org/wiki/Ontology_(information_science)
Quoting Corvus
The formal semantic class {dogs} is a node in the above inheritance hierarchy.
Isn't axiomatic model for formalizing various branches of mathematical theory, including geometry, algebra, set theory? Applying that concept to linguistic topic sounds incorrect.
How does your system deal with the same words of the different meanings in the real world identification?
For example, a dog is an animal. But you also get a dog which has the following meanings.
1. A dog as a workbench tool.
2. A dog as a worthless or contemptible person.
3. Any of various usually simple mechanical devices.
4. The astronomical constellations - Canis Major or Canis Minor.
5. An an inferior one of its kind.
An axiom is a proposition regarded as self-evidently true without proof.
https://mathworld.wolfram.com/Axiom.html
An axiomatic model of the world is the only way that an AI mind can be created that is the functional equivalent to a human mind. It must be told that {cats}
The Cyc Project uses 128-bit GUID integers to identify unique sense meanings.
Cyc (pronounced /?sa?k/ SYKE) is a long-term artificial intelligence project that aims to assemble a comprehensive ontology and knowledge base that spans the basic concepts and rules about how the world works. Hoping to capture common sense knowledge, Cyc focuses on implicit knowledge that other AI platforms may take for granted. https://en.wikipedia.org/wiki/Cyc
When one definition simultaneously addresses every possible objection
then it also addresses any and all objections that Quine could possibly
have. I updated my OP to reflect this.
That Quine could not possibly understand that the term Bachelor(x) derives all of its semantic meaning from (Male(x) & Adult(x) & ~Married(x)) seems so ridiculous that accusing Quine of simply lying seems reasonably plausible. This definition is clearly acyclic.
So, a bachelor's degree is equivalent to an "unmarried man's degree?" But then how do married men and women have bachelor's degrees? It seems like the semantic meaning of the term bachelor is modified by the context here.
I would just consider that the question of analyticity was more focused on if facts could be analytic simpliciter. The fact that, if something is defined as true, then given that definition it is true, is trivial.
The Cyc project addresses this by providing a unique 128-bit integer (GUID) for each unique sense meaning in the world. 6ae8d0b5-be3e-4f0d-aaea-d37395ba4207 for {unmarried male adult} and
23abe8b5-4df1-4d63-a3ca-b436472a6e0e for a {bachelors degree} cannot be mistaken for the same thing.
But then all the semantic meaning of the word bachelor isn't derived from (Male(x) & Adult(x) & ~Married(x)). If it were, you wouldn't need multiple unique integers to encode its multiple distinct meanings.
Made me think of an interesting question though. The unique encoding for each meaning seems like it would resolve the need to distinguish between equivocal and univocal predication. But how would it deal with analogical predication? E.g. "Jake is a snake," meaning "Jake is slippery and devious." Trying to reduce analogy to unique encodings seems like it might be a limit, rather than a benefit for intelligence.
...one should proceed with extreme scepticism.
You have not understood Quine. I don't think you have understood the analytic/synthetic distinction. And I don't think that on this topic you are "open to learning", as teachers sometimes say. You have produced the answer without first making sense of the question - something you already did in your previous threads.
{Male, Adult and Married} have their own unique GUIDs.
Quoting Count Timothy von Icarus
We can assign sets of meanings to arbitrary finite strings idiomatically.
I have spent five full time years carefully thinking through how an analytic distinction could over-ride, replace and supersede the current one such that this new one has the full spirit of the original {true entirely on the basis of its meaning} yet would be 100% unequivocal.
The set of expressions of language that can be verified as completely true (or false) entirely on the basis of other expressions of language that are stipulated to be true meets this unequivocal requirement.
Most people have a problem with the {stipulated to be true part} because they have no idea how humans know that "cats are animals" is true, so they simply disbelieve what I say entirely on the basis of their own ignorance.
Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. https://en.wikipedia.org/wiki/Truth-conditional_semantics
Isn't it exactly the point Quine disagrees with? Some self-evident knowledge without proof can be also self-deceiving too.
Quoting PL Olcott
What if {cats} was someone's nick name, or name of a rock band? They are also cats too, no? In that case , the AI would fail to tell the truth, wouldn't it?
Not sure how the AI could know anything about the world, if they are locked up in the analytic cave. Doesn't sound very convincing in the system operandi.
As I told you before, because I have carefully studied all of these things in my mind for five years full-time I really can address and possible objection that anyone (including Quine) can possibly have. {cats} means the unique concept of the living animal and has an associated 128-bit GUID integer. Any other usage has its own different 12-bit GUID integer. "cats" may or may not be associated with {cats}.
It is told that {cats}
What can the system tell us about the cat next door? The grey coloured cat keeps coming into our garden looking for something often.
The sum total of all of the general knowledge of the world is finite.
Every detail about every atom of the cat next door's location at
every point in time is infinite.
The relevant details of the cat next door could be stored in a temporary
discourse ontology.
If we have this sort of nearly infinite database that [I]corresponds[/I] to all facts about the world, why even bother with genus and species? What is the value of encoding "cats are contained in animals?" and in virtue of what does the database decide that a given entity should be contained in a given category? Questions like: "are 'pet rocks' really 'pets?'" would seem to need to be answered to allow for a full categorization of all "facts."
In scholastic philosophy genus and difference are predicated of things as known by us, as conceptualized or as present in the mind. They arise when the intellect reflects on itself and on what it contains. But it seems like the system you are envisioning:
A. Has no mind.
B. Could simply contain all the facts uniquely specifying each individual cat, or each atom in each cat, etc.
Getting into species and genus seems difficult because people disagree about them and they disagree about how they relate to actual ontological differences. For example, "do species actually exist?" is a topic of debate in the philosophy of biology. What it means to be "living" is itself contested. Do viruses fall under the category of "living?"
Amorphous terms like "post-modern," "fascism," etc. don't seem to clearly map to entities in any sort of definitive fashion. Rather, it would seem that the database would need to incorporate each individual's beliefs and judgements vis-á-vis species and genus across time as independent facts. Facts like "Mount Washington is the tallest mountain in the Presidential Range," are based on evolving social conventions, and even what constitutes a distinct mountain and not just another peak on the same mountain is not based on firm criteria.
Yet without categorical distinctions, the database seems to turn into nothing but a phase-space map of the universe, or a Le Place's Demon, in which case it seems hard to see how it is easier to get facts out of it than simply observing the world (unless we also envision a computer of unlimited computational power attached to it).
Secondly, essences appear to be able to evolve over time. "Communism," today is not the same concept/category that it was in 1848. "Essences" are not what they were for Aristotle. Would the database need to have time/culture dependent categorization?
Further, we can consider the problem of defining superveniance relations. In virtue of what will a given subatomic particle be said to be "part of" a given candle flame or cat, and won't this change moment to moment?
Isn't it an objection to say that the definitions of the terms in play are arbitrary and not tied to reality? Or more to what I think Quine's point was, you would have to do a lot of empirical work to figure out what definitions to put into your database. That is, they aren't actually analytical truths because what you have put into the database has been determined not by definitions, but by empirical inquiry.
Otherwise it's just saying something like: given A is true, and given A = B, B is true. But the interest in analytical [I]a priori[/i] truths was generally motivated by the idea that they were aspects of reality that could be known with certainty, and which might act as a foundation for the justification of knowledge, not by the truism that "anything defined as true by definition is true by definition, given we accept that definition."
Going out and cataloging a bunch of non-analytical truths (empirical facts), throwing them into a database, and then saying "I have now defined every fact as true by definition," doesn't solve the problem. Particularly, it fails to solve the problem if you embrace any theory of truth other than completely deflationary ones. For, "cats are a type of sailboat" could no doubt be defined as an "analytical truth," by fiat and entered into a database, but this would not make it true that cats are a type of sailboat. This would, under most theories of truth, just make it a falsehood.
There is a reason facts were not considered analytical, why Hume's Fork, which kicks off the distinction, distinguishes between "relations of ideas" (analytical) and "matters of fact." You could make innumerable databases purporting to be "true models of the world," that vary in what they define as true. How would one compare these databases and determine which "analytical truths" are actually true? They would have to go out and observe the world... which means, in point of fact, the truths aren't analytical because determining their truth value does not depend on their definition (because empirical facts aren't analytical).
With my redefinition of the {analytic} side of the analytic/synthetic distinction any and all knowledge
that can be completely verified as true entirely on the basis of text
That "cats are animals" is verified as true on the basis of the axiom {cats are animals}.
The only way that the finite string "cats are animals" is associated with the semantic
meaning {cats are animals} is that this is stipulated. If you ask a person that only speaks
Chinese "are cats animals?" they will say: "No speak English" (in Chinese).
Yes, and most (arguably all) facts fail to actually fall into your category.
No, "cats are animals," is verified by experience. Consider that we could just as easily stipulate "cats are racecars," "cats are robots," and "cats are rocket ships" as axioms. Then, using the same processes, we could "verify" that these are analytical truths entirely on the basis of the text/axioms.
Your concept of what makes things analytical truths would entail that literally any arbitrarily chosen axiom is "an analytical truth." But this is clearly nonsense, cats are not racecars just because we have stated an axiom that "cats are racecars." How does one distinguish between a bad "axioms" that are clearly nonsense, such as "cats are sailboats," and good axioms that are true, like "cats are animals?" Through experience of what cats are.
No one thought of solving the distinction by advancing the solution that "if you arbitrarily declare all true things to be true by definition and all false things to be false by definition, then every truth becomes analytical," because it totally misses why the distinction is useful in the first place. It presupposes that you already know what is true and what is false. But then how do you find out which "axiom" is true so as to posit it in the first place? Certainly not on the basis of the word' meanings alone. Nothing about the term "Ravena" entails, "capital of the late Western Roman Empire," for instance.
That is not true. No amount of experience tells us that "cats are animals" means "los gatos son animales"(Spanish) which means "????"(Chinese).
One wonders then what the utility of language classes are then, or how it is that people living in a foreign country come to speak its language. :roll:
But it seems like the point stands, how does one differentiate between true and false axioms such as: "Michelle is the tallest woman in the room," "Springfield is the capital of Illinois," "Mogadishu is the capital of Florida ," "weed is a slang term for marijuana," "Alfred the Great is a slang term for cocaine," or "Helium has an atomic number of 8," etc. These aren't going to be shown to be true of false analytically, and you could make any of them "axioms" even though some are false.
"Michelle is the tallest woman in the room" is not analytic because it requires sense data from the sense organs to verify that {Michelle is in the room}.
The way that it currently works for humans is that all of the facts of the world are stipulated as axioms. When we look up: "Is Paris the capital of the planet Mars"? We find that it is neither an axiom nor derived from axioms thus it is not true.
No one figures out that "Paris is the capitol of France". No one experiences the physical sensation that "Paris is the capitol of France". They merely memorize that "Paris is the capitol of France" is true.
My ultimate purpose of redefining {analytic} is to abolish undecidability such as this:
Since "This sentence is NOT true." is not an axiom and cannot be derived from axioms thus we correctly determine that it is not true, yet this does not make it false.
Ah, so when the Roman capital moves to Milan people learn about this to memorize it... how exactly? How exactly did people come to memorize the fact that Senator Obama has become President Obama? Your solution involves totally ignoring how facts are actually know and you still haven't explain why/how false axioms wouldn't be added. In virtue of what are facts verified as true so that they can be stated as true by definition? The periodic table wasn't a given to humanity, it had to be discovered, etc.
Hume's Fork is about how we come to know truths. The distinction is about how people can come to know things. A magical inviolable database where all true statements exist and no false ones sort of misses the point of debate.
The only way that people learn that expressions of language are true is that they are told or they are derived from expressions of language they they are told are true. Without the infrastructure of the conventions of language they could not possibly know that "dogs bark". They would hear "noise" not even knowing that it is called "noise".
You are disagreeing that there can be a correct model of the world because you don't understand
how it is updated? How did humans find out that Obama is no longer president?
Interesting! I think Leibniz would approve Cyc project.
So the discovery of the period table occured because one day someone said "this is by definition true?" We know water is H2O because someone happened to declare "this is true by definition?" People don't know that dogs bark by hearing dogs bark, but rather because one day someone declared the "dogs bark is axiomatically true?" Come on.
The empirical fact/analytic distinction relates to how facts are discovered/verified. Things like "water is composed of hydrogen and oxygen, were discovered empirically."
You're fundementally misunderstanding what the distinction is and why it is important. Even assuming some sort of magical list of all true statements, it would still be the case that the way one verifies that fact statements on the list are true is through sense experience. There is a reason the distinction is literally between analytical truths and facts, because they are not the same thing, and what makes them different is what is required to verify them.
Water is H2O is a good example in that this was not known for human history. Establishing the synonymy of "water" and "H2O" requires matters of facts, which is part of Quine's point.
But more to the point, even if you don't buy those critiques, it still remains the case that "analytic" never referred to matters of fact. Kant's definition of an analytic truth are those truths whose negation is a contradiction. "Ravenna is not the capital of the Roman Empire," is not a contradiction, even though Ravenna was one capital of that empire. "Ravenna" defines a city in northern Italy, it is not a synonym for "capital of the Roman Empire."
Analytic(Olcott) is a stipulative definition that retains the essence of the original {proven completely true or false entirely on the basis of its meaning} and adds that this proof must be entirely contained within expressions of language.
This stipulative definition specifies that "Cats are animals."
In other words when-so-ever the truth of an expression of language S can be determined by analyzing the relation of S to other expressions of language then S is Analytic(Olcott).
A stipulative definition is a type of definition in which a new or currently existing term is given a new specific meaning for the purposes of argument or discussion in a given context. When the term already exists, this definition may, but does not necessarily, contradict the dictionary (lexical) definition of the term. https://en.wikipedia.org/wiki/Stipulative_definition
How about "There is a cat or there is not a cat in my living room right now." ? Is this sentence analytic or not?
Every expression of language that can be verified as true or false entirely on the basis of textual analysis is Analytic(Olcott), thus your expression is Analytic(Olcott).
Yes correct. It is true regardless a cat is or is not in the living room.
Cats are my favorite kind of sailboat, because they are fast.
The database that I referred to has always been the the set of general knowledge of the current actual world that can be expressed using language. For example it is true that "cats are animals" thus disagreement is simply incorrect.
Why is what is "general knowledge" so important? Typically, when I am talking about sailboats, I am talking with fellow sailors who understand "cat" is short for catamaran, and what a cat looks like:
Sounds like a wildly unrealistic goal to me.
Quoting PL Olcott
I'd have to say that there is a lot of variation from human to human and subject to subject.
The first step of this is to correctly refute the Tarski undefinability theorem. With the new LLM AI technology encoding knowledge of the world becomes feasible. It really needs Boolean True(L,x) to be computable to stop it from telling lies. https://en.wikipedia.org/wiki/Hallucination_(artificial_intelligence)
Well, another problem would be that human experts tend to be continually learning, so the system you describe would seem to inevitably lag behind human expertise. So unless the system is going to have a perceptual system, enabling it to become the world's leading expert at everything, how can it avoid lagging behind human experts?
The system would be hooked up to reliable online sources of news and academic articles. This would make it "the world's leading expert at everything" especially because it could cross correlate between differing academic disciplines. My plan is to merely design the architectural infrastructure so that Boolean True(L, x) could be eventually fully implemented.
So far I can't even find hardly any people that are totally sure that the Liar Paradox: "This sentence is not true" is simply not a truth bearer.
My whole point in this thread is to establish a definition of {Analytic} truth that forms the basic foundation of Boolean True(L, x).
Analytic knowledge is still limited in a sense that it doesn't add any new information to the knowledge. If you knew the meaning of cat, then you don't need the AI system to look at what it means. If you didn't know the meaning of cat, then you can look up a dictionary or google it.
Therefore, why do you need the AI analytic info system?
What about the case where cat means a plant?
"What is a cat plant?
Chamaedorea Cataractarum, also known as a Cat Palm, is a small, bushy palm tree that is native to Southern Mexico and Central America. It's an easy-to-care-for houseplant with beautiful foliage!" - Google
You have an analytic expression in your system, which says, cat is animal.
But when someone asks about cat (to mean the plant), the system will say cat is animal.
The answer from the AI "Cat is animal." is a wrong answer. The answer must be "Cat is plant." is right.
So you update the system after the complaint.
Cat is animal.
Cat is plant.
But after the update, the system has two expressions for the same word cat, which are contradictory.
https://en.wikipedia.org/wiki/Stephen_Yablo
It is the same as asking someone to count to infinity, invalid input.
At some point everyone must some how be told the semantic meanings of otherwise meaningless finite strings. That "cats are animals" is stipulated to be true, thus an axiom of natural language. The entire body of Analytical(Olcott) truth is comprised of axioms and expressions derived from axioms. The Prolog computer language has this same architecture of Facts and Rules.
Axiom is a proposition regarded as self-evidently true without proof.
https://mathworld.wolfram.com/Axiom.html
Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. This approach to semantics is principally associated with Donald Davidson, and attempts to carry out for the semantics of natural language what Tarski's semantic theory of truth achieves for the semantics of logic.
https://en.wikipedia.org/wiki/Truth-conditional_semantics
Analytic(Olcott) provides the provides the foundation to make True(L, x) computable thus refuting the Tarski Undefinability theorem. The current issue with LLM AI technology is that it has no way to tell the difference between truth and lies. This causes it to tell lies. https://en.wikipedia.org/wiki/Hallucination_(artificial_intelligence)
Quoting Corvus
Referring to a "Cat Palm" as a "Cat" is a type mismatch error that can be overridden by a temporary idiomatic expression.
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"
Is it self-evidently true that Moscow must be the capital of Russia?
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.
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.
Quoting 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.
Quoting 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.
Quoting 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.
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?
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:
The database is currently hypothetical as merely the set of finite strings that encode semantic truth.
Quoting Count Timothy von Icarus
The set of finites strings that encode semantic truth is neither arbitrary nor capricious.
Quoting 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).
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".
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 don't currently know how to handle contentious knowledge.
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)
Does it handle / process abstract concepts such as God, souls, freedom or immortality?
Quoting PL Olcott
This is a good link for the concept "Ontology in Information Science". Thanks.
In theory is can process any knowledge known to humankind that can be encoded as text strings.
How is it different from ChatGPT?
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
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.
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.
So this whole project is merely the embodiment of people's imagination.
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.
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.
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.
3ab2c577-7d38-4a3c-adc9-c5eff8491282 stands for the living animal dog, this is the same way that the Cyc project identifies unique sense meanings,
Quoting PL Olcott
I still can't make any sense of this. Does the Cyc project identifier refer to
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."
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 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.
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
(2) The proof in the article handwaves past the crucial lemma, thus appearing to commit a serious non sequitur.
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
Quoting PL Olcott
I still can't make any sense out of this. What is the difference between a "sense input" and a "sense meaning"? The only way we can even know that there are such things as dogs is through sense input.
I am providing the means for a computer to compute Boolean True(L, x) where L is a language such as English and x is an expression of that language. When I show how this can be coherently accomplished then the Tarski Undefinability Theorem is refuted.
This is a very ambitious project - if you succeed then the name PL Olcott will become world famous.
But so far I can't make any sense of what you're saying - this is why I'm trying to get some basic terminology clear. I'll ask again. What is the difference between a "sense input" and a "sense meaning"?
That you can hear dogs actually barking with your ears is a sense input from your
ears to your mind. Hearing dogs bark is the sense meaning of "dogs bark". These
things cannot be expressed using words thus are not Analytic(Olcott).
Analytic sentences, such as Pediatricians are doctors, have historically been characterized as ones that are true by virtue of the meanings of their words alone and/or can be known to be so solely by knowing those meanings. The Analytic/Synthetic Distinction
When we exclude those aspects of meanings such as the actual sound of dogs barking and include every element of human general knowledge that can be expressed using words expressly including that some Pediatricians are rich then we have the subset of human knowledge that can be processed by a computer program.
How do the users know the unique ID? How does the Cyc Project know that is the ID it has to select the answer for the query?
It's Wikipedia, so you can always edit it.
I would estimate that the users use ordinary English and the Cyc lexical analyzer converts words into GUIDs. The parser can determine which of the multiple GUIDs for the same word is most probably from context. My cat drank of bowl of milk would not refer to Caterpillar Earth moving equipment or Harvey Milk.
I'm not in the practice of editing Wikipedia articles. Meanwhile, my points about the article stand. More generally, a good amount of caution is warranted when referencing Wikipedia.
I have studied these things in my mind continuously for decades. Mathematics uses the term "theory" to mean a set of axioms. Everyone else means a set of ideas that might be true.
My current understanding of a subset of undecidable decision problems is that this undecidability can be easily abolished the same way that ZFC conquered Russell's Paradox. ZFC prevents self-contradictory expressions from coming into existence by forbidding the creation of sets that are members of themselves.
It is a common misconception on Internet forums that ZFC avoids inconsistency by disallowing sets to be members of themselves.
Yes, the axiom of regularity, which is adopted in ZFC, disallows that a set can be a member of itself. But the axiom of regularity does not block inconsistency. What avoids inconsistency is not having the axiom schema of unrestricted comprehension. If we have the axiom schema of unrestricted comprehension, then we get inconsistency, no matter whether we also have the axiom of regularity or not, and no matter whether there may be sets that are members of themselves or not.
Indeed, since the logic is monotonic, adding an axiom cannot avoid inconsistency. The only way to avoid inconsistency is to delete the axioms that provide inconsistency.
ZFC is undecidable. That means that there is no decision procedure to determine whether a given sentence in the language of ZFC is or is not a theorem of ZFC.
You just contradicted yourself. I will be more precise. ZFC eliminates the possibility
of inconsistency that is caused by allowing sets to be members of themselves.
An isomorphic solution would solve the halting problem. A halt decider is not allowed
to be applied to any input to refers to itself.
And, again, as I just explained, disallowing sets from being members of themselves does not avoid inconsistency. Again, as I just explained, inconsistency can be avoided only by deleting axioms (such as unrestricted comprehension) and not by adding them (such as regularity).
The fact that ZFC avoids inconsistency by not having unrestricted comprehension does not contradict that ZFC also has the axiom of regularity that disallows sets from being members of themselves. Moreover, the purpose of the axiom of regularity is not to avoid inconsistency but rather to facilitate the study of sets as in a hierarchy indexed by the ordinals. It is a nice feature of the axiom of regularity that it disallows sets being members of themselves, as many people regard it counter-intuitive or against the basic concept of 'set' that there are sets that are members of themselves. But the axiom of regularity, even with that feature, is not how set theory avoids inconsistency.
When we ask the question: Does a barber shave everyone that does not shave themselves? is allowed to be rejected as an incorrect question then the paradox goes away. ZFC prevents this question from even being expressed as sets.
Quoting TonesInDeepFreeze
Thereby preventing inconsistency in the same way that type theory prevents inconsistency.
And we don't even need any set theory to prove that, for any property P, there is no x such that, for all y, Pxy if and only if ~Pyy. We prove that by pure logic alone. So, perforce, we prove it in set theory too.
/
The hierarchy of sets is not type theory nor higher order logic. ZFC is a first order theory. The context here is not type theory nor a higher order logic, but rather first order set theory:
The main point here could not be more clear: The logic is monotonic, so adding an axiom can't block inconsistency.
Said another way:
Let G and H be sets of formulas, and P a formula:
If G proves P, then G union H proves P.
So, if set theory without the axiom of regularity proves a contradiction, then set theory with the axiom of regularity proves a contradiction.
The schema of unrestricted comprehension proves a contradiction. So the schema of unrestricted comprehension with also the axiom of regularity proves a contradiction.
So the contradiction can't be avoided by adding the axiom of regularity to any set of axioms, but rather the contradiction can be avoided only by not having the schema of unrestricted comprehension.
My post is about a single coherent way around all of these issues.
The key mistake of decision theory is that the notion of decidability requires a decider
to correctly answer a self-contradictory (thus incorrect) question otherwise an input
is construed as undecidable.
The key issue with decision theory is that deciders are required to correctly
answer a self-contradictory (thus incorrect) questions.
[b]The key difficulty with resolving this issue that most modern day philosophers
do not understand that both of these questions are equally incorrect:[/b]
(a) Is this sentence true or false: "What time it is?"
(b) Is this sentence true or false: "This sentence is not true."
They do not understand that the Liar Paradox is simply not a truth bearer.
The decision problem form of a formal proof
The formal proof shows the steps of how X is derived from Y in Z.
The decision problem version answers the question: Can X be derived from Y in Z?
When X is a theorem of Z then the premises are empty.
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yesno question of the input values.
Decision problem
Huge amount.
Proofs always have the provability question associated with them:
Whether or not a proof exists is.
I have found that it always succinctly and clearly presents an accurate view of
every technical subject that I have ever referenced as measured by its correspondence
with many other sources.
But a proof of T does not have questions in it.
That is a degree of detail that is totally irrelevant to my point so I did not
examine it at all. My point is the Tarski anchored his Undefinability
Theorem in the actual Liar Paradox.
So far hardly any modern or ancient philosophers seem to understand
that the Liar Paradox is not a truth bearer thus has no truth value thus
is not in the domain of any decision problem or formal proof.
Is the question associated with every formal proof or lack thereof.
Tarski's proof doesn't work the way you describe it.
/
For any sentence T, set of axioms S and set of rules R, we may ask the question "Is T derivable from S with R?" That fact doesn't entail the counterfactual that there are questions in proofs. Tarski's proof does not have questions in it.
This correctly recognizes that the Liar Paradox is not a truth bearer.
LP = "This sentence is not true."
Boolean True(English, LP) is false
Boolean True(English, ~LP) is false
I imagine that that happens because you learn from there. I find nonsense there all the time. The people who run it are oligophrenic. So I avoid it like a plague.
Most people can't understand his original proof
https://liarparadox.org/Tarski_275_276.pdf
so I use the Wikipedia simplification.
This is where Tarski anchors his proof in the actual Liar Paradox
https://liarparadox.org/Tarski_247_248.pdf
But to address that article, here are the proofs without ""liar"" (scare quotes in original), "ask", "truth bearer" or anything else extraneous to the mathematical proofs:
In this context, 'formula' and 'sentence' mean 'formula in the language of first order arithmetic' and 'sentence in the language of first order arithmetic'.
In this context, 'true' and 'false' mean 'true in the standard model for the language of first order arithmetic' and 'false in in the standard model for the language of first order arithmetic'.
For every formula M, let g(M) be the numeral for the Godel number of M.
/
Theorem: There is no formula T(x) such that for every sentence S, T(g(S)) is true if and only if S is true.
Proof:
Toward a contradiction, suppose there is such a T(x).
So, there is a formula D(x) such that for every numeral m, D(m) is true if and only if m is the numeral for the Godel number of a formula P(x) such that P(m) is false. (The steps in obtaining this line from the previous line are not included in the article.)
D(g(D(x))) is true
if and only if
g(D(x)) is the numeral for the Godel number of a formula P(x) such that P(g(D(x))) is false.
Toward a contradiction, suppose D(g(D(x))) is true.
So g(D(x)) is the numeral for the Godel number of a formula P(x) such that P(g(D(x))) is false.
g(D(x)) is g(P(x)), so D(x) is P(x), so D(g(S(x))) is P(g(S(x))), so D(g(S(x))) is false. Contradiction.
Toward a contradiction, suppose D(g(D(x))) is false.
So it is not the case that g(D(x)) is the numeral for the Godel number of a formula P(x) such that P(g(D(x))) is false.
So D(g(D(x))) is true. Contradiction.
So there is no formula T(x) such that for every sentence S, T(g(S)) is true if and only if S is true.
/
Theorem: There is no formula T(x) such that for every sentence S, S is true if and only if T(g(S)) is true.
Proof:
Lemma: For every formula P(x) there is a sentence D such that D <-> P(g(D)) is true.
Toward a contradiction, suppose there is a formula T(x) such that for every sentence S, S is true if and only if T(g(S)) is true.
So, for every sentence S, S <-> T(g(S)) is true.
By the lemma, there is a sentence D such that D <-> ~T(g(D)) is true. But also, D <-> T(g(D)) is true. Contradiction.
So there is no formula T(x) such that for every sentence S, S is true if and only if T(g(S)) is true.
I don't think they're stupid. Rather, I find that there is complacency and sloppiness in the writing of certain articles, sometimes to the extent that there are plain falsehoods in them. But in the case of the article being discussed, I'm not pointing out falsehoods, but rather the confusions the article opens.
Personally I love Wikipedia it always gives me a succinct clear gist of the whole idea in the first couple of sentences. When used this way it seems to be a very high quality standard.
I always go on the basis that his true predicate struggles with the Liar Paradox.
and concludes that no True (Language, Expression) can exists because would
have to handle the Liar Paradox incorrectly.
This is how I propose to handle the Liar Paradox correctly
LP = "This sentence is not true."
Boolean True(English, LP) is false
Boolean True(English, ~LP) is false
That sounds like a cumbrous task for normal users to go through for using the system. They would want just type in the expressions in their ordinary use of the language or words into the system, and expect to get the correct definitions for their queries. Somehow the Cyc Project must be able to convert the expressions or words into the unique GUID to narrow down and select the correct definitions for them. Would you agree?
I personally think so. I am convinced Wik***dia and Reddit have the same userbase.
Quoting PL Olcott
That is always the excuse given by users of that site. It is either "a good summary", when there are often mistakes right in the header and the site itself is rotten to the core, or to "check the sources on the bottom". Nobody who says that actually checks the sources on the bottom of course, otherwise they would notice the users there frequently misquote the sources they use. Especially because they have little understanding of the topic they are writing about.
The Cyc project converts the words of the users into multiple GUIDs and then from context narrows down to list to the intended meanings.
I examine many original sources and then quote Wikipedia as a verified summation of the technical ideas involved. The key point here is that the Tarski Undefinability theorem is anchored in the Liar Paradox and that by itself is its big mistake. Tarski himself shows that his proof is anchored in the Liar Paradox yet does this in a somewhat convoluted way that would be too difficult for most people to follow.
I directly understand his actual proof.
https://liarparadox.org/Tarski_275_276.pdf