Then it sounds like we don't have a true definition of a fictional unicorn without a lot of work. In which case, is it analytic or synthetic? — Philosophim

We simply have the true definition of unicorn that already exists in the verbal model of the actual world. My purpose in this post is to unequivocally divide analytic from synthetic even if this requires defining analytic(olcott) and synthetic(olcott). Then on this basis an {analytic truthmaker} is merely a truthmaker that applies to analytic knowledge.

You misunderstand. I am not saying your "definition" of either the analytic statement or the synthetic statement is ambiguous. Instead, "tokens" of the statement "type" synthetic are more prone to ambiguity than "tokens" of the statement "type" analytic. — Arne

That is one reason why I am making sure to exclude them. The criterion measure for excluding them seems to have no boundary cases. The purpose of this post (of my several related posts) is to unequivocally divide analytic from synthetic even of this means that I am referring to analytic(olcott) and synthetic(olcott).

I understand that. But what is the true definition of a fictional unicorn? — Philosophim

Although the verbal model of the actual world already exists it may take millions of labor years to write this all down. This means that we simply understand that the fictional idea of a unicorn has fictional ideas as the root of its knowledge tree.

Well, no. The analogous question with "12" and the brownies would be, "How do we know that 'cat' represents those furry critters we like so much and not [insert wildly unlikely referent]?" We know this because we know how to use the word "cat", just as we know how to use "12". But in neither case is there some further, purportedly analytical fact about animals or integers. That, at any rate, would be how Kripke and others (including me, most of the time) would argue it. — J

In other words it may be the case that the {living animal} {cat} really is a {plate of brownies crushed on the floor} and everyone thinking otherwise is having a psychotic break from reality?

The only way that otherwise purely random finite stings of characters acquire any semantic meaning is that semantic meaning is assigned to them otherwise they remain meaningless gibberish.

In the BASIC programming language:
100 X = 50
There is zero doubt that the value of X is 50, after the assignment operation has been executed.
The assignment of meaning to words works this exact same way. That the different human
languages assign meanings to different finite strings proves this.

The truth value regarding analytic/synthetic statements detracts from your central point. It is a classic red herring that only illustrates what is already known, i.e., synthetic statements are more fraught with ambiguity. — Arne

We cannot have vagueness and ambiguity in the key terms that are being defined.
We must stipulate their precise definitions.

Sure. Replace all I said with actual encounters in the world with people's drawings. Is there a degree of bending we can do with a fictional creature and still keep its identity? When is a unicorn not a unicorn, especially if its a made up creature? — Philosophim

The axioms of the verbal model of the actual world stipulates that unicorns are fictional.

The truth value regarding analytic/synthetic statements detracts from your central point. It is a classic red herring that only illustrates what is already known, i.e., synthetic statements are more fraught with ambiguity. — Arne

We can call this the analytic(olcott) / empirical(olcott) distinction meaning that any expression of language that can be verified as true on the basis of the axioms of the verbal model of the actual world is analytical(olcott). Whereas empirical(olcott) cannot be verified as true on this basis and additionally requires sense data from the sense organs.

"Unicorns are horses with horns on their head" — Philosophim

Unicorns are fictional animals that are {horses} with {horns}.
The verbal model of the actual world is a set of mutually self-defining semantic tautologies.
This verbal model is stored in an inheritance hierarchy knowledge tree.
https://en.wikipedia.org/wiki/Ontology_(information_science)

I will call what I am saying the analytic(olcott) of the analytic/empirical distinction(olcott).
Analytic is typically general knowledge of the world. Empirical is typically knowledge of a specific situation that cannot be confirmed as true without sense data from the sense organs.

Can one know what cat is without ever having seen an actual cat? — Corvus

Blind people know that cats exist.
That cats exist is an axiom in the verbal model of the actual world.

Having seen the cat in the living room, I could come out of the living room, shut the door, and I can still say those statements from my memory without seeing the cat.
"A cat is in my living room right now." or "There is a cat in my living room right now." — Corvus

If we use Robert Heinlein's "fair witness" standard of truth you can not be sure that a cat is in the living room the moment after you have no sense data from the sense organs confirming this. You can correctly say that a cat was in the living room moments ago. The axioms of the model of the actual world only contain general knowledge. Having never seen a actual cat one can still say that cats are animals.

The controversy centers on whether part of the meaning of the word “cat” is indeed that a cat is an animal, — J

That seem to be like saying how do we know that "12" represents the integer twelve and not a plate of brownies crushed on the floor?

The meaning of the words that have been stipulated using Rudolf Carnap / Richard Montague meaning postulates. The same way that people must be told what words mean so does the formal system. A new born baby makes sounds yet knows no words.

Suppose “water” is a rigid designator in all possible worlds — J

I am only taking the idea of possible words as a verbal model of the actual world.
It is stipulated that water <is> H2O and anyone saying otherwise is wrong.

We don’t seem to need the concept of “animal” to refer to cats, or recognize them, or talk about them. — J

To know all of the general knowledge that humans know we must know that cats are animals.
I am dividing analytic from synthetic slightly differently. Previous divisions have been equivocal so I must correct their error. Anything that can be written down in language <is> stipulated to be analytical. Anything that cannot be written down such as the first-hand direct experiences of the taste of strawberries is empirical.

We can imagine a possible world where "water" is sulfuric acid, not-the-less {water} remains H2O.
The actual words in the BOAK are unique 128-bit integers and {water} is assigned to one of these. Every word in any language referring to the semantic meanings of {water} refers to this GUID.

Could it be the same meaning as
"There is a cat in my living room right now." or
"A cat is in my living room right now." or
"A cat exists in my living room right now."?
Above expressions don't require sense data? — Corvus

The only way that you can verify that a specific event is occurring at a specific location
right now generally requires that you are seeing this event occur.

So if listed, the listing might have to be refined as new knowledge is accrued. Still way to vague for me, but others may feel differently. I admire your tenacity on the subject. — jgill

It is simply the ordinary and common body of general knowledge known to mankind. It could be updated or static. Once the notions of {analytic truthmaker} is understood it is easy to see how this conquers Tarski Undefinability and Gödel's 1931 incompleteness. An expression of language either has an {analytic truthmaker} or it is untrue. Undecidable is no longer an option.

Unless you can describe this vague notion as it might appear in a computer program - that is to say a list with #1, #2, . . . - I can't get beyond it to the conclusions you draw. TonesInDeepFreeze is recognized as a go-to source on these kinds of subjects. — jgill

He seems to be disagreeing with Tarski.

https://en.wikipedia.org/wiki/Ontology_(information_science) is how the knowledge is stored.
It is easiest to simply imagine that all the [general] things known to humans that can be written down in language have already been written down. Now we have the {body of analytic knowledge}.

This is pages from his paper. I have taken them to be
the actual proof of the undefinability theorem.
https://liarparadox.org/Tarski_275_276.pdf
What do you think that they mean?

This sure seems to be talking about undefinability to me

From page 276
For every deductive science in which arithmetic is contained
it is possible to specify arithmetical notions which, so to speak,
belong intuitively to this science, but which cannot be defined
on the basis of this science.

And, for the third time: The incompleteness theorem pertains only to recursively axiomatizable theories. — TonesInDeepFreeze

The body of all analytical knowledge includes every recursively axiomatizable theory as a subset.

Tarski says no such thing as claimed two posts above. — TonesInDeepFreeze

Here is Tarski saying exactly that: "(3) x ∉ Pr if and only if x ∈ Tr"

The exact same thing is on the bottom of the first page of Tarski's actual text:
https://liarparadox.org/Tarski_275_276.pdf

Which means x is not an element of Provable if and only if x is an element of True.
I apologize for not making this 100% perfectly clear in my prior replies.

Perhaps this is why the analytic status of a statement like "Cats are animals" is controversial. (On my view, it isn't analytic at all.) — J

Since we can know that {Cats} <are> {Animals} on the basis of the meaning of these words then that makes is analytical according to the common and simple meaning of the term {analytic}. Think of this as explaining these things to a computer that has no sense data from sense organs.

grammar does not in and of itself make a general set of statements, even ones regarded as formalized by Montague grammar, a recursively axiomatizable theory. — TonesInDeepFreeze

I am not talking about Montague grammar per say. I am talking about some system like Montague Grammar that can explain every detail about human general knowledge such that a machine acquires a fully human level of understanding. The Cyc Project has been doing this for decades. It is known as a knowledge ontology inheritance hierarchy. Not words and a list of meanings. A knowledge tree having an enormous number of connections to and from each unique sense meaning of every word.

My advice is to drop the terminology entirely. Some words and concepts become so overloaded by debate, nitpicks, and lack of consensus that they're impossible to make head roads with and become worthless in discussion. You can convey your ideas that you want in an argument without using the terminology, so that's what I would do. — Philosophim

I am merely trying to define the term {analytic truthmaker} on the basis of the conventional meaning of those two terms. I can perfectly specify exactly what is and what is not {analytic} for all those people that have made up their minds that they don't believe in the analytic / synthetic distinction.

Or perhaps I'm not understanding what you want BOAK to do -- what its purpose is. — J

BOAK is the model of the actual world along with every detail of human general knowledge.
The BOAK also knows how to perform every aspect of human reasoning including all of mathematical and logical operations.

Tarski's proof makes no false assumptions, no matter whatever incoherent ersatz pseudo formulations a crank on the Internet wishes to cook up. — TonesInDeepFreeze

(3) x ∉ Provable if and only if x ∈ True. — PL Olcott

That is Tarski's line (3) that says that expression of language x is only true if x cannot be proven.

It seems that Tarski is saying: If Y is true and X follows from Y then X is not true.

deleted

The general problem is that as a word only has meaning in relation to other words, and as any such relation comes down to a personal judgement on behalf of the reader, whether an expression is analytic or not depends on personal judgements rather than absolute truths. — RussellA

I don't really want to delve into the trillions of details until after the architecture is understood and accepted, otherwise I won't be able to make my point until long after I am dead.

Analytic knowledge is entirely comprised of
(a) expressions of language that are stipulated to be true and
(b) expressions of language that are semantically derived from (a).
Try and prove otherwise

Synthetic knowledge is expressions of language that require sense data from the sense organs to verify that they are true. "I see a cat in my living room right now". This is stipulated to be true.

The incompleteness theorem applies to formal theories, — TonesInDeepFreeze

The first incompleteness theorem states that in any consistent formal system F
within which a certain amount of arithmetic can be carried out, there are statements
of the language of F which can neither be proved nor disproved in
https://plato.stanford.edu/entries/goedel-incompleteness/

The BOAK can perform every arithmetic and logical operations, thus qualifies for Gödel’s Incompleteness. Knowledge specified in natural language has been formalized using Montague Grammar.

For any model M for a language L, every sentence in L is either true or false, and not both, in M. — TonesInDeepFreeze

My system fully integrates the model directly within the formal system such that the system can perform deductive inference on the basis of semantics.

A theory T is complete if and only if, for every sentence S in the language L for T, either S is a theorem of T or the negation of S is a theorem of T. — TonesInDeepFreeze

I have changed this.
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
becomes
(¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
Incompleteness utterly ceases to exist.

True(L,x) ≡ (L ⊢ x)
False(L,x) ≡ (L ⊢ ¬x)

For any model M, there is the theory T whose theorems are all and only the sentences true in M. It was Tarski who proved "the undefinability of truth" theorem, which says that the set of sentences true in the standard model for the language of arithmetic is not definable in the language of arithmetic. — TonesInDeepFreeze

Thus step (3) of Tarski's proof is rejected as a false assumption:
https://liarparadox.org/Tarski_275_276.pdf
(3) x ∉ Provable if and only if x ∈ True. // derived from (1) and (2)

But Godel was speaking of a small finite collection of axioms, not an axiomatic system that continues to increase without end. At what point does one initiate the drawing of conclusions? Tacking on the axiom of choice took math into new dimensions, as did infinity axioms. BOAK seems bewildering rather than enlightening, imo. — jgill

The key change is the unprovable in BOAK simply means untrue in the BOAK, thus cannot means that BOAK is incomplete. BOAK is merely the actual body of general analytical knowledge as of now.

My question remains: show how exactly all axioms can be listed for reference. What is axiom #1?, #2?, . . — jgill

It is currently known that humans are the only life on the Earth that can understand analytic geometry.
Listing all the axioms make fill a book light years deep. The Cyc project spent 1000 labor years on this.

induction, or else you're begging the question. — tim wood

It in not probable that sheep need air to breath therefore it is not inductive inference. Inductive inference only deals with probabilities it never deals with certainties. The meaning of the words {Sheep} and {Mars} conclusively proves that sheep cannot survive in the Mars atmosphere.

"the conclusion of a deductive argument is certain given the premises are correct; in contrast, the truth of the conclusion of an inductive argument is at best probable, based upon the evidence given."
https://en.wikipedia.org/wiki/Inductive_reasoning

I think that's induction, the logic of which starts with "If.... That is, not proved but granted. Yes? No? — tim wood

It is deduction from true premises. The formal system required must have a human level of comprehension directly hard-wired into it. It must know every slight nuance of the meaning of every word. The word {human} may have a full definition that makes a book light years tall.

Some {humans} go to Universities. {Universities} teach from books. {Books} have knowledge. The knowledge that {Books} have is {the text of every book ever written}.

↪PL Olcott Ok. Is that in the BOAK? — tim wood

Every single detail of all of the general knowledge known to humans is in the BOAK. Can sheep live on Mars? is not general knowledge thus must be derived on the basis of general knowledge.

What I'm trying to get to is understanding whether the propositions of BOAK are there because they're provable or there only because they have been proved in the sense that a proof of them has been given. E.g. - and possibly not the best example - of "sheep can live on Mars," and, "sheep cannot live on Mars," — tim wood

All of the general knowledge known to humans derives that {sheep cannot live on Mars} on the basis that sheep must have an atmosphere that Mars does not provide. This same knowledgebase would also know that the atmosphere that sheep require could be artificially provided, thus the question: "Can sheep live on Mars?" is a different question than "Can sheep possibly live on Mars?"

It is possible the BOAK is just a kind of encyclopedia - is that what you're trying to say? — tim wood

No the BOAK is a knowledge ontology inheritance hierarchy having the same structure as the Cyc project. Unlike a mere dictionary the requires a human mind, the knowledge ontology connections create a human mind. The term {human} may have as many connections as there are millimeters to the nearest star.

What I mean by axiom is any expression of language that has been stipulated to be true
— PL Olcott
"True" by what measures? What of potential inferences not realized? — jgill

We know that dogs are animals and thus not fifteen story office buildings only because of the meanings of the words {dog} and {fifteen story office buildings} that have been stipulated. Unless these meanings are stipulated the words {dog} and {fifteen story office buildings} remain meaningless.

The body of analytic truth is only true on the basis of the connection of terms to the meanings that make the expression true. The lack of such a connection simply makes the expression untrue. Undecidability cannot possibly occur.

The BOAK can prove every instance that cannot be proved?

It is possible the BOAK is just a kind of encyclopedia - is that what you're trying to say? — tim wood

I don't know how I came up with that wording.
Every expression of the BOAK is either stipulated to be true (AKA axioms) or deduced from these axioms. Unprovable simply means untrue, thus undecidable cannot possibly exist.

Any further reading on that? As is, it seems there is some elaboration missing for this argument to pass. — Lionino

I simply define the term {analytic truthmaker} in on the the basis of the existing terms {analytic} and {truthmaker}. Because some analytic truths are unknown I subtract unknown truths from the {body of analytic truth} to derive the {body of analytic knowledge}.

So you have a collection of propositions that are trivially true (facts being excluded). In what sense is this an achievement and what does it achieve? — tim wood

Why would you think that facts are excluded?
The body of analytic knowledge is the subset of the body of analytic truth that is known to be true.
The only things that are excluded are unknown truths.

OK, this means an uncountable collection of "axioms". How could you organize these axioms in such a fashion they represent a data set in CS? What is axiom #1 ? — jgill

The body of all current analytical general knowledge is not only countable it is finite.

They would be organized as a knowledge ontology inheritance hierarchy.
https://en.wikipedia.org/wiki/Ontology_(information_science)

The Cyc project has already done this on a massive scale.
https://en.wikipedia.org/wiki/Cyc
The Cyc project has {Thing} at the root of its knowledge tree.

Some time back we had a promising theory of everything that started with the premise all facts could be catalogued within a program. But when asked "how?", things began to fade. — jgill

It is basically the model of the current world plugged into a knowledge ontology inheritance hierarchy.

I accept this as a definition. But what is the pair? — tim wood

(a) Formal system BOAK (b) Every expression of the language of BOAK can be proved in
(a) and (b) is the pair.

(a) The BOAK can prove every instance of (formal system /expression)
pair that cannot be proved making the BOAK complete. — PL Olcott

You stipulate axioms are true - but obviously not provable. Either there are no axioms in BOAK, or there are unprovable expressions in BOAK. Or perhaps you meant that every expression in BOAK is provable except the axioms. I take it then that every statement in BOAK is either an axiom or the conclusion of a proof in BOAK. Is there a method in BOAK for deciding whether, given an unproved expression, it is true? — tim wood

(1) Cats are animals is an axiom of BOAK.
(2) Any unprovable expressions in the language of BOAK are simply untrue.
Because it is the {body of analytical knowledge} every expression is BOAK is true.
(3) Every axiom is stipulated to be true and every expression deduced from axioms is true.

Mendelson represents theorems this way ⊢C, in other words C is provable from axioms, thus according to Haskell Curry that makes it true. https://www.liarparadox.org/Haskell_Curry_45.pdf

But G is about provability and not about truth. — tim wood

That is its mistake. Every analytic truth must have an analytic truthmaker connection to the formalized set of semantic meanings that make it true. When this provability semantic connection is missing then the expression is simply untrue. That G is unprovable in F merely means that G is untrue in F it does not actually means that F is incomplete.

Since this is generically the way that analytic truth really works mathematics is not free to override this.

Pair or pairs of what? This is not English. — tim wood

Every expression of the language of BOAK can be proved in BOAK, or it is simply untrue within BOAK.
This is the (expression of language / BOAK formal system) pair.

I wrote that per Godel there are an uncountable infinity of axioms, not that the proofs were of infinite length. — tim wood

This does not apply to BOAK.

What is it that you imagine completeness/incompleteness to be? Godel demonstrated that for systems at least as strong as arithmetic, complete implies inconsistent, with the consequence that every expression in that system is provable. By constructing his peculiar expression, he showed there were expressions that were unprovable but true in the system, therefore the system being incomplete. — tim wood

He never showed that there are expressions that are unprovable but true in the system.
He showed that G is unprovable in F and provable (thus true) in meta-mathematics.

This <is> that way that truth really works:
If there is no truth-maker in formal system F making G true in F then G is simply untrue in F.
We never misconstrue this as F is incomplete.

(Demonstrating in passing that if "truth" were definable, then he could create an expression that asserted its own untruth, being then both true and false at the same time.) — tim wood

It seems utterly ridiculous to me that people still fail to understand that the liar paradox is simply not a truth bearer. Is this sentence true or false: "What time is it?"
(Obviously neither because it is a question and not a statement).

And you might consider paying a little more attention to Godel - as well to the definition of any axiom. I.e., axioms are unprovable: does that mean that they're untrue? And are you confusing finite with infinite? — tim wood

I have been very diligently studying these things for two decades. I have written many papers.
What I mean by axiom is any expression of language that has been stipulated to be true. That cats are animals is stipulated to be true. Infinite proofs do not derive knowledge because they never reach their conclusion.