Synthetic expressions are expressions of language that also require sense data from the sense organs. Example: "I see a cat in my living room right now". — PL Olcott

Synthetic expressions are to add new knowledge or information to the expressions, but the example expression doesn't seem to add any new information or knowledge. Because it seems just reporting your visual sense perception.

"Your cat played with a mouse in the garden this afternoon". That would be more like giving you new knowledge that cats can play with mouse (not catching attacking mouse).

Why did you write down a meaningless gibberish? — Corvus

It is difficult to understand how words acquire meaning. That it is difficult to understand does not entail that my understanding is incorrect. The arbitrary identifier "rose" has a set of meanings to it that are assigned to different finite strings in different human languages.

Synthetic expressions are to add new knowledge or information to the expressions, — Corvus

That is not what Synthetic(Olcott) means. Actually seeing or smelling a {Rose} is the synthetic aspect of a {Rose}. Every detail about a {Rose} that can be described using words is the Analytic(Olcott) aspect of a {Rose}.

I am defining Analytic(Olcott) and Synthetic(Olcott) so that they can be unequivocally divided. — PL Olcott

That is fine but your definitions will not be picked up because that is not what analytic means neither is it for synthetic. When the word 'synthetic' is used it never implies sense data in any context. When the word 'analytic' is used it does not always imply language.

The words you are looking for are a posteriori and linguistic/semantic.

That is fine but your definitions will not be picked up because that is not what analytic means neither is it for synthetic. When the word 'synthetic' is used it never implies sense data in any context. When the word 'analytic' is used it does not always imply language. — Lionino

The only reason why there continues to be disagreement about whether or not the analytic/synthetic distinction exists is because it was not defined unequivocally. I cannot begin any discussion about {analytic truthmakers} with people that have chosen to disbelieve that {analytic} exists.

Only when we clarify that analytic excludes sense data from the sense organs can we know that the full meaning of a {red rose} is excluded from analytic. You have to actually see the redness of a rose to get its full meaning.

(a) Knowledge that can be specified using language and (b) those aspects of knowledge that cannot be fully specified using language is the most natural division of analytic/synthetic.

Maybe I could call this the analytic/empirical distinction.

You have to actually see the redness of a rose to get its full meaning. — PL Olcott

Fine, but that is called a posteriori knowledge.

Fine, but that is called a posteriori knowledge. — Lionino

No existing terms exactly match the ideas that I must communicate.

Every element of the body of analytic knowledge can be verified as true in that it is either an axiom of {BOAK} or is deduced from the axioms of {BOAK}.

The {body of analytic knowledge} (BOAK) is the subset of expressions of analytic truth that are known to be true. — PL Olcott

There is circularity here.
From 1): if an expression is part of a Body of Analytic Truth (BOAK), it is true and analytic.
From 2): if an expression is true and analytic, it becomes part of a Body of Analytic Truth (BOAK)

Given the proposition "X is Y", how do we know whether this is part of the Body of Analytic Truth (BOAK)?

That is not what Synthetic(Olcott) means. — PL Olcott

Then what is the formal definition of "Synthetic" in expressions? Are expressions correct here? Should they not be propositions or judgements?

There is circularity here.
From 1): if an expression is part of a Body of Analytic Truth (BOAK), it is true and analytic.
From 2): if an expression is true and analytic, it becomes part of a Body of Analytic Truth (BOAK)

Given the proposition "X is Y", how do we know whether this is part of the Body of Analytic Truth (BOAK)? — RussellA

Analytic(Olcott) is a lot like the conventional meaning of {Analytic} in that every expression is verified as completely true entirely on the basis of its meaning.

X is Y is a mere template until the variables are assigned values. Once they are assigned values then it becomes an axiom. The axiom must correspond to things in the actual world.

That is not what Synthetic(Olcott) means.
— PL Olcott
Then what is the formal definition of "Synthetic" in expressions? Are expressions correct here? Should they not be propositions or judgements? — Corvus

Analytic(Olcott) propositions can be verified as completely true entirely on the basis of their meaning. This includes many things that are typically construed as {Synthetic}. {Synthetic}(Olcott) only includes propositions that require sense data from the sense organs to verify their truth.

Analytic(Olcott) is a lot like the conventional meaning of {Analytic} in that every expression is verified as completely true entirely on the basis of its meaning. — PL Olcott

Consider "cats are animals".

However, there is no absolute meaning of "cat" and no absolute meaning of "animal", in that no two dictionaries will have the same definition, and even within the same dictionary the definition will change with time.

Therefore, if the expression "cats are animals" can only be analytic on the basis of the meanings of the words "cat" and "animal", but there is no absolute meaning of either "cat" nor "animal", then the expression cannot be analytic.

It is true that the National Geographic" wrote "As mostly nocturnal animals, cats have excellent vision and hearing, with ears that can turn like satellite dishes", but this is a synthetic judgement rather than an analytic truth.

Therefore, if the expression "cats are animals" can only be analytic on the basis of the meanings of the words "cat" and "animal", but there is no absolute meaning of either "cat" nor "animal", then the expression cannot be analytic. — RussellA

The meaning of those terms is the sum total of every detail of all of the general knowledge that applies to those terms (that can be written down using language). The body of analytic knowledge is simply a bunch of meanings connected together. They are connected in a tree of knowledge ontology inheritance hierarchy directed graph. https://en.wikipedia.org/wiki/Ontology_(information_science)

The meaning of those terms is the sum total of every detail of all of the general knowledge that applies to those terms (that can be written down using language). — PL Olcott

Can the expression "cats are animals" be analytic?

As you wrote "Analytic expressions are expressions of language that can be verified as completely true entirely on the basis of their connection to the semantic meanings that make them true."

To know that cats are animals I need to know the meaning of both cats and animals.

I cannot know the meaning of the word "cat" just from the word itself, but from the Merriam Webster Dictionary:
"cat" = "a carnivorous mammal (Felis catus) long domesticated as a pet and for catching rats and mice"

I cannot know the meaning of the word "carnivorous" just from the word itself

"Carnivorous" = "subsisting or feeding on animal tissues"

I cannot know the meaning of the word "subsisting" just from the word itself

"Subsisting" = "to have or acquire the necessities of life (such as food and clothing)"

However, as knowing the meaning of a single word ends up as an infinite regression, there can be no finite description of any word, meaning that no expression in language can be known to be analytic or not

The problem is that the "sum total" is infinite, negating the possibility of any analytic expression within language.

I cannot know the meaning of the word "carnivorous" just from the word itself — RussellA

All of the words have every slight nuance of their meaning assigned to them by Rudolf Carnap / Richard Montague Meaning Postulates.

All of the words have every slight nuance of their meaning assigned to them by Rudolf Carnap / Richard Montague Meaning Postulates. — PL Olcott

In his article Meaning Postulates in Philosophical Studies, Carnap writes that his Meaning Postulates only refer to a semantical language-system, not a natural language.

Our explication, as mentioned above, will refer to semantical language-systems, not to natural languages. It shares this character with most of the explications of philosophically important concepts given in modern logic, e.g., Tarski's explication of truth. It seems to me that the problems of explicating concepts of this kind for natural languages are of an entirely different nature.

When you write "Analytic expressions are expressions of language that can be verified as completely true entirely on the basis of their connection to the semantic meanings that make them true", it depends whether you are referring to a semantical language-system or a natural language.

As Carnap writes, a natural language is of an entirely different nature.

As Carnap writes, a natural language is of an entirely different nature. — RussellA

Rudolf Carnap derived the basis for Richard Montague to mathematically formalize natural language. https://plato.stanford.edu/entries/montague-semantics/

No existing terms exactly match the ideas that I must communicate. — PL Olcott

So why use existing terms whose definition is different and well known?

So why use existing terms whose definition is different and well known? — Lionino

It might take a whole book to define Analytic(Olcott) without any reference to anything else. To define Analytic(Olcott) in terms of the Analytic of the Analytic/Synthetic distinction is the most efficient and effective way.

I think Rorty actually uses something close to the example in the OP. "Cats are animals." But suppose we discover tomorrow that "all cats are actually very cleverly crafted androids introduced by ETs onto the Earth to spy on us." What then? It no longer seems to be true that cats are animals; they are actually androids. Different genus.

Maybe a more realistic scenerio might be the widespread belief that it was essential to triangles to have the angles add up to 180 degrees.

I've always been more interested in the "scandal of deduction," that analytical truths, deduction as a whole, and thus computation as well, should be completely uninformative according to most measures of information. Mill solved this by simply claiming that all deductions are really induction in disguise. Hittinka, and later Floridi tried all sorts of complex formal work arounds — surface versus depth information, virtual information, etc. (a real case of every problem looking like a nail if you're a hammer specialist IMO).

I've come around to thinking the problems with the scandal of deduction, and analytic truths, tends to actually come from mathematical Platonism and our tendency to mistake abstractions as "more real," than reality. E.g., Wittgenstein complains in the Tractus that people misunderstand implication in terms of cause and effect, and this is wrong because eternal implication is the more fundemental. I'd argue this is completely backward; toddlers learn cause and effect first, the idea of implication is just abstracting from this.

Analytical truths are informative because computation always occurs over time. But they are informative for precisely the same reason that sense data is informative, because there is an act of communication and semiosis undergirding the act of understanding either sort of truth. This makes them the same sort of thing from a physical/metaphysical perspective

So I'd rather say the difference with the analytical/deductive is that we work with a different methodology. We tend to be concerned with what is true assuming that other things are true, rather what is true vis-á-vis evidence. The epistemic difference would be one of appropriate methodology then, not one of confidence, as Hume had it with relations of ideas vs matters of fact.

I think Rorty actually uses something close to the example in the OP. "Cats are animals." But suppose we discover tomorrow that "all cats are actually very cleverly crafted androids introduced by ETs onto the Earth to spy on us." What then? It no longer seems to be true that cats are animals; they are actually androids. Different genus. — Count Timothy von Icarus

It is stipulated as an axiom that {cats are animals} even if cats are a mere figment of the imagination. If it is later proven that all cat's were only androids for the last 10,000 years then the axiom is updated.

One can easily get stuck in absurdity when one is too skeptical. One could propose that the integer {three} might have always only been a plate of burned brownies crushed on the floor, thus the entire notion of arithmetic was only ever a delusion.

Rudolf Carnap derived the basis for Richard Montague to mathematically formalize natural language. — PL Olcott

From the SEP article: Montague Semantics- the most important feature is the principle of compositionality, such that the meaning of the whole is a function of the meaning of its parts.

An example is given:

Consider the two sentences John finds a unicorn and John seeks a unicorn. These are syntactically alike (subject-verb-object), but are semantically very different. From the first sentence follows that there exists at least one unicorn, whereas the second sentence is ambiguous between the so called de dicto (or non-specific, or notional) reading which does not imply the existence of unicorns, and the de re (or specific, or objectual) reading from which existence of unicorns follows.

It seems to me that Montague Semantics is about how expressions are built out of the words used, not whether the expression is true or not. IE, as the expression "John finds a unicorn" may or may not be true, the expression "cats are animals" may or may not be true.

Montague Semantics may be able to analyse how expressions are constructed out of their parts, but not whether the expression is analytic or not.

It seems to me that Montague Semantics is about how expressions are built out of the words used, not whether the expression is true or not. IE, as the expression "John finds a unicorn" may or may not be true, the expression "cats are animals" may or may not be true.

Montague Semantics provides the basis to encode the current body of knowledge. This would exclude expressions that are not true facts or derived from true facts.

Montague Semantics may be able to analyse how expressions are constructed out of their parts, but not whether the expression is analytic or not. — RussellA

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.
https://en.wikipedia.org/wiki/Stipulative_definition

It is stipulated that Analytic(Olcott) means anything that can be encoded in Montague Semantics <is> Analytic(Olcott). More generally anything that can be encoded in language (including formal mathematical languages) <is> Analytic(Olcott). The actual taste of strawberries cannot be encoded in language.

More generally anything that can be encoded in language (including formal mathematical languages) <is> Analytic(Olcott). — PL Olcott

To know whether the expression "cats are animals " is analytic, one needs to know the meaning of "cats", "are" and "animals".

As an example, how is "cats" encoded in language?

As an example, how is "cats" encoded in language? — RussellA

Domain: Eukaryota
Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Carnivora
Suborder:Feliformia
Family: Felidae
Subfamily:Felinae
Genus: Felis
Species: F. catus
The above are the elements in the inheritance hierarchy for {cat}.
The only details about {cat} that are not encoded elsewhere in the
inheritance hierarchy tree of knowledge ontology are thing like {breed}.
https://en.wikipedia.org/wiki/Cat

We end up with every detail of all general knowledge about cats.
We can determine that a {cat} is an {animal} on the basis of the
above knowledge tree.

Kingdom: Animalia...We can determine that a {cat} is an {animal} on the basis of the above knowledge tree. — PL Olcott

True, if a cat is defined as part of the Kingdom Animalia , then a cat is an animal, and the expression "cats are animals" is true and analytic.

But then, if a cat is defined as an elephant, then a cat is an elephant, and the expression "cats are elephants" is true and analytic.

The problem is that there are an infinite number of possible analytic expressions including cats. For example, "cats are animals", "cats are elephants", "cats are part of the Kingdom Monera", "cats are part of the Kingdom Protista", "cats are trees", "cats are not anmals", etc.

I accept that analytic expressions are expressions of language that can be verified as completely true entirely on the basis of their connection to the semantic meanings that make them true, and synthetic expressions are expressions of language that also require sense data from the sense organs.

If cats are defined as part of the Kingdom Animalia, then the expression "cats are animals" is analytic and true. If cats are defined as part of the Kingdom Monera, then the expression "cats are animals" is analytic and false.

In the absence of sense data from the world, the expression "cats are animals" can be either true or false.

Only by sense data from the world can the expression "cats are animals" be verified as true, meaning it a synthetic rather than analytic expression.

The problem is that there are an infinite number of possible analytic expressions including cats. For example, "cats are animals", "cats are elephants", "cats are part of the Kingdom Monera", "cats are part of the Kingdom Protista", "cats are trees", "cats are not anmals", etc. — RussellA

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

I have already stipulated {the body of analytic knowledge} which necessarily excludes {cats are elephants} and includes {cats are animals}.

I have already stipulated {the body of analytic knowledge} which necessarily excludes {cats are elephants} and includes {cats are animals}. — PL Olcott

You have stipulated the definition of cat as an animal , meaning that the expression "cats are animals" is analytic and true.

I stipulate the definition of cat as "a very large plant-eating mammal with a prehensile trunk, long curved ivory tusks, and large ears, native to Africa and southern Asia", meaning that the expression "cats are elephants" is analytic and true.

You defined analytic expressions as "Analytic expressions are expressions of language that can be verified as completely true entirely on the basis of their connection to the semantic meanings that make them true. Example: "Cats are animals"".

If by "language" you are referring to PL Olcott's private language, then your definition of analytic expressions is true.

But if by "language" you are referring to the English Language, why do you have the authority to stipulate the meanings of words in the English Language rather than me, for example? :smile:

I stipulate the definition of cat as "a very large plant-eating mammal with a prehensile trunk, long curved ivory tusks, and large ears, native to Africa and southern Asia", meaning that the expression "cats are elephants" is analytic and true. — RussellA

I already said that expressions that are not elements of the body of analytical knowledge are excluded.

I will make it simpler for you ONLY known facts and expressions that are derived from known facts are included. If an expression if FALSE then it is excluded.

e referring to PL Olcott's private language — RussellA

The only way that any word ever obtains any meaning is that an otherwise random string of symbols is assigned a meaning. Then that word becomes an a part of a standard language. Since many words already have meanings we use the meanings of these words.

Only when we clarify that analytic excludes sense data from the sense organs can we know that the full meaning of a {red rose} is excluded from analytic — PL Olcott

I already said that expressions that are not elements of the body of analytical knowledge are excluded. — PL Olcott

Why can't the expression "cats are very large plant-eating mammals with a prehensile trunk" be part of the body of analytic knowledge?

It fulfils both your requirements: i) the expression excludes sense data from the sense organs and ii) being part of the body of analytical knowledge there's no reason to exclude it from the body of analytical knowledge.