Overcoming all objections to the Analytic / Synthetic distinction
It seems to me that after pondering this for many years that there is a simple and precise way to divide analytic from synthetic.
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".
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".
The Analytic/Synthetic Distinction https://plato.stanford.edu/entries/analytic-synthetic/
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".
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".
The Analytic/Synthetic Distinction https://plato.stanford.edu/entries/analytic-synthetic/
Comments (63)
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?
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.
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."
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.
Can one know what cat is without ever having seen an actual cat?
Blind people know that cats exist.
That cats exist is an axiom in the verbal model of the actual world.
"Cats are plants" may be an incorrect analytic statement but it is still an analytic statement. Similarly, the statement "there is a cat in my living room" when there is no cat in my living room may be an incorrect synthetic statement but it is still a synthetic statement.
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.
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.
We cannot have vagueness and ambiguity in the key terms that are being defined.
We must stipulate their precise definitions.
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.
A precise definition of "synthetic statement" will not render synthetic statements less prone to ambiguity than analytic statements. The world to which synthetic statements refer is more ambiguous than the world to which analytic statements refer. And you cannot define that difference away. You can try to account for it.
And besides, I think the definitions implicit in your original post are precise enough.
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).
or verified as not true. Cats are rocks. An analytical statement that is verified false is still an analytical statement. And the same can be said of synthetic statements. So again, whether a statement is true/false does not determine whether it is analytic/synthetic. Instead and consistent with your original post, the true difference between analytic or synthetic statements is the need for sense data.
If its truth value cannot possibly be determined entirely on the basis of its meaning then it is not analytic.
My bad.
I mistakenly presumed your post was about "Overcoming all objections to the Analytic / Synthetic distinction."
Good luck with that.
I have three different related posts. The purpose of this post is to unequivocally establish that the analytic / synthetic distinction definitely exists. People like Quine seem to simply "not believe in" this distinction.
I don't want to go into every subtle nuance of detail of synthetic, I merely want to unequivocally divide it from analytic. Too many people simply "do not believe in" analytic and this prevents me from even starting a conversation about the foundations of analytic truth.
Yes that is my key point, hence I cannot begin to understand how anyone could possibly disbelieve in the analytic/synthetic distinction. Quine seemed to disbelieve that words have meaning yet to even say this he had to use the meaning of words.
I suspect Quine would consider the process by which words are attached to meaning is far more organic than people prefer.
The meaning of the words of a specific human language simply assigns meanings to finite strings. When these meanings are analytic then it merely assigns a set of finite strings to a finite string. It gets much more complicated when the meanings are experiential.
Analytic(olcott) means all the things that a computer can possibly understand entirely on the basis of the relation of finite strings to other finite strings. A computer never need taste an actual strawberry to explain all of the details of strawberries that can be explained using language.
Quoting PL Olcott
Starting with the expression "X is Y", let the meaning of X be the same as the meaning of Y. The expression "X is Y" is then an analytic expression as it can be verified true .
As long as it is known that two words have the same meaning, analytic expressions are possible, meaning there is a distinction between the analytic and synthetic.
However, in order to know that two words have the same meaning, the meaning of each word must be known.
A computer could invent a language from scratch that was purely self-referential.
Stage one
For example, a simple language could consist of the proposition "X is Y", where X has the properties a and b and Y has the properties c and d.
So far, X and Y have been fully specified, but the properties a, b, c and d haven't. This means that it is impossible to know whether the expression "X is Y" is true or false, in which case it cannot be analytic.
Stage two
Let the property a be named A, the property b be named B, the property c be named C and the property d be named D
But as we still don't know what the names A, B, C and D refer to, we still don't know whether the expression is true or false, in which case it is still not analytic.
Fundamental problem
The fundamental problem is that at the end of the day properties cannot be described in words. How can the sensation of pain be described, the smell of a rose, the colour red, the feeling of missing an important appointment?
Therefore, even within a computer generated language, there will be some words whose meanings cannot be described using other words. The inevitable consequence will be that it is impossible to know whether expressions such as "X is Y" are true or false. IE, even a computer generated language will not be analytic.
Does he disregard justified "belief" as a ground for truth?
Do they know how cats look like?
Quoting PL Olcott
"That cats exist." is a statement, which needs verification to be true. It is only true if and only if the cats exist in the actual world of some place (in your living room, or your kitchen) at certain time duration T1 - Tn.
If you meant "Cats exist." in general terms, then it would be a tautology. The word "Cats" contain the concept "exist* as a property already.
No it is an axiom forming the foundation of the body of analytical knowledge.
Unless and until finite strings are assigned meaning they remain meaningless gibberish.
The assignment of meaning to finite strings
It is not at all that properties cannot be described using words. It is that some properties
require first-hand direct experience of sense data from the sense organs to be fully described.
The actual smell of a rose cannot be completely put into words, thus is not an element of
the body of analytic knowledge. We can still know that some {roses} are {red} even though
we lack the sense data from the sense organs showing exactly what {red} is.
I already corrected the gettier problem cases of the error of "justified true belief".
knowledge is a justified true belief such that the justification necessitates the truth of the belief.
Heinlein's "fair witness" merely refrains for forming conclusions based on sense data when
there is a pause in the continuity of the sense data.
Consider a computer generated language that does not depend on any external information. Rather than the expression "cats are animals", consider the more general case "X is Y". If it is possible to verify the expression as true, then the expression is analytic.
To know whether "X is Y" means knowing the meaning of "X" and the meaning of "Y".
It is impossible to discover the meaning of "X" just from knowing the name "X", similarly for "Y"
Suppose "X" can be described as "a, b, c"
It is impossible to discover the meaning of "a" just from knowing the name "a", similarly for "b" and "c".
Suppose "a" can be described as "d, e, f"
It is impossible to discover the meaning of "d" just from knowing the name "d", similarly for "e" and "f".
Suppose "d" can be described as "g, h, i"
But this ends up as an infinite regression, in that there is no name whose meaning is contained within the name itself .
IE, within a computer generated language that does not depend on any external information, as the meanings of X and Y cannot be established with absolute certainty, as the language would have to be of infinite length, it becomes impossible to determine whether "X is Y". The consequence is that it becomes impossible to know whether any expression within such a language independent of the senses is analytic or not.
"A triangle in Euclidean space has its angle sum up 180º degrees" is a synthetic expression that does not require sense data.
It seems you are conflating the synthetic analytic distinction with a priopri a posteriori one.
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 BOAK excludes photographs, videos, tape recordings, and the first hand direct experience of sense data from the sense organs.
https://en.wikipedia.org/wiki/CycL Is a language that can formalize the semantic meaning of any natural language expression. CycL uses 128-bit GUIDs instead of words so that every unique sense meaning of every natural language word has a unique identifier. The reasoning provided by CycL is basically sound deductive inference on the basis of the semantics of formalized natural language axioms.
I am defining Analytic(Olcott) and Synthetic(Olcott) so that they can be unequivocally divided.
Analytic(Olcott) is anything that can be explained using language.
Synthetic(Olcott) is anything that requires sense data from the sense organs:
photographs, videos, tape recordings, or the first hand direct experience of sense data from the sense organs.
Why did you write down a meaningless gibberish?
Heinlein's "fair witness"?? Is it a Philosophical term or idea of something? I did some google search on it, but it came up with some pop arty gibberish.
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).
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.
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}.
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.
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.
Fine, but that is called a posteriori knowledge.
No existing terms exactly match the ideas that I must communicate.
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)?
Then what is the formal definition of "Synthetic" in expressions? Are expressions correct here? Should they not be propositions or judgements?
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.
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.
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.
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)
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.
All of the words have every slight nuance of their meaning assigned to them by Rudolf Carnap / Richard Montague Meaning Postulates.
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.
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.
Rudolf Carnap derived the basis for Richard Montague to mathematically formalize natural language. https://plato.stanford.edu/entries/montague-semantics/
So why use existing terms whose definition is different and well known?
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.
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.
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.
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:
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 is stipulated that Analytic(Olcott) means anything that can be encoded in Montague Semantics
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?
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.
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.
I have already stipulated {the body of analytic knowledge} which necessarily excludes {cats are elephants} and includes {cats are animals}.
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 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. Quoting 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.
Quoting 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.
Do you understand that lies are not true and only truth is included in knowledge?
Who determines that the semantic meaning of cat is "animal" rather than "very large plant-eating mammals with a prehensile trunk"?
It could be that person A stipulates that "cats are animals" and person B stipulates that "cats are very large plant-eating mammals with a prehensile trunk".
Who determines whether person A or B is correct, if the person making the determination is not allowed to look at the world using their sense data through their their sense organs?
How can there be knowledge that cats are "animals" and not "very large plant-eating mammals with a prehensile trunk" without being able to look at the world?
It is difficult to understand how words acquire semantic meaning, perhaps this is too difficult for you? There is no guy named "Bill" that has complete authority to write all the dictionaries in the world. That is simply not the way that reality works.
In the correct body of analytical knowledge the attributes of {cat} are assigned to the otherwise totally meaningless finite string "cat". The same process works this same way for every human language.