Since words are defined in terms of other words in dictionaries, leading to infinite loops, does it mean natural languages are meaningless? Are infinitely recursive definitions valid? If we visualize the relationship graph of a dictionary, where vertices are words and there is a directed edge X -> Y from word X to word Y if X appears in definition of Y, we would see that such a graph is full of cycles. So if you pick any word and try to fully capture its definition from the dictionary, you will be looping in the dictionary forever. In order to avoid that, you would need a DAG (directed acyclic graph) of definitions. Correct? Do you agree with this? If so, would that mean that all natural languages are bound to be meaningless and we should state our logical proofs in formal logic / mathematically?
Natural languages do not depend in any fundamental way on our learning the meanings of words from dictionaries. No child I know learns to speak, read and understand meanings by memorising dictionary entries.
For one thing, a child must know some rules of grammar even to see the point of a dictionary. For another, children learn words by associating sounds with meanings; and meanings with written words only secondarily. Indeed I know some people who can speak a foreign language, understanding fully the meanings of its standard words, without being able to write or read a word of the language. They do not appear to be whizzing around in infinite loops.
Sounds can be connected with meaning by ostension among other ways. X says to child Y : 'Cat jumps down' as the cat jumps down. X later says to the child Y : 'Kim jumps down' as child Z jumps down. The semantics of 'jumps' dawns on the child. This is only a thumbnail sketch of how a child comes to understand the meanings of words but there's not a dictionary in sight.
Whatever the role of dictionaries, no feature of them renders natural languages meaningless.
The fact that a dictionary defines each word as a loop that includes other words doesn't mean there is no information present in the dictionary. The information about all the words together is encoded in a mangled form, namely in the structure of this network of relations and loops.
If an alien civilization received an English dictionary, there's a good chance they will eventually be able to decode large parts of it. The source of this information is the structure of the graph.
Unless you're a badly programmed robot, you just never get to the point where you're looping around ad infinitum.
Many linguists including Chomsky I believe have studied languages up to the point of realizing that there are no set rules as to how languages develop. They just do.
It's technocratic and overly formal philosophical view to think that natural language is structured like formal languages. Formal languages can model natural language, but it doesn't mean that natural language "reduces" to formal language, because they have developed through different means. Lojban is an attempt to a natural language that's both formal and natural, but as it's not adopted yet one cannot understand whether people have evolved to it or not. Due to formality it's also perhaps more complicated language, just like maths is "complicated" for some people, so it might be that it will never become broad. Natural language has other aspects than mere syntax for people. It's by very nature informal in many cases.
Also dictionaries are not a "formula" for how words form. It's just a map about language. It tells what exists, but it doesn't tell how they developed. So in natural reality the structure given in a dictionary, doesn't likely exist.
Natural language is a form of communication and communication is a basic necessity for (group) animals.
Humans do not initially learn language from the dictionary; they initially learn the first rudiments of language from ostensive definitions (also known as "definition by pointing"). A pre-linguistic child points to a cat, and his mother says "cat", and after repetition of this event, the child learns that the word "cat" describes the class of furry creatures he has been pointing to. Eventually he learns this well enough (and develops his speech sufficiently) that he points at a cat and says "cat" himself. Once a child has formed a language of nouns from ostensive definitions, he gradually moves on to higher concepts, with verbs, and then adjectives. He points to a jumping cat and says "cat", and now his mother says, "Yes, cat. Cat is jumping." Since he has already learned cat, now he starts to learn the ostensive definition of "jumping".
The purpose of a dictionary is to assist literate people (not pre-literate children) to relate concepts together, by describing each word in terms of others. The definitions in the dictionary are mostly in a descriptive hierarchy, where more complex higher-order concepts are described in terms of less complex lower-order concepts. However, due to the necessity of describing lower-order concepts, like "cat", without appeal to ostensive definitions, this hierarchy is reversed for simple ostensive concepts, and their description is given in terms of higher-order concepts. For example, one dictionary definition of "cat" (excluding slang) is:
a small domesticated carnivore, Felis domestica or F. catus, bred in a number of varieties.
any of several carnivores of the family Felidae, as the lion, tiger, leopard or jaguar, etc.
Obviously no pre-linguistic child would gain any assistance from this definition, since the concept of "cat" is described in terms of higher order concepts ("domesticated", "carnivore", etc.) that the child will learn later on, after they already know what a cat is. If his mother tried to describe this to the child by pointing to the cat and saying "small domesticated carnivore", it would lead to confusion. However, to a literate adult, this definition assists in relating "cat" to the broader concept "carnivore" and other concepts. (And the perceptive adult will presumably notice that the first definition refers only to the subclass of domesticated cats, since not all cats are domesticated.)
The infinite loop you are referring to would occur if you used the dictionary in isolation to try to learn language. If a thinking being (capable of forming language) was deprived of observation, and thereby deprived of ostensive definitions, it would not be able to form language from the dictionary. Without ostensive definitions, the dictionary would merely give a web of inter-related words, with no reference tying them to reality. Every definition would lead to a cycle in the dictionary, or an undefined term. (To deal with this shortcoming, some dictionaries have pictures, which gives some progress toward an ostensive definition, though a single picture is not really sufficient.)
Words are mapped to their "real world" physical objects as observed by humans, or "real" emotions felt by humans. Abstractions slowly depart from this but still follow the same form, as if they had some true "type" that exists somewhere we can't see.
The dictionary definition is a reflection of the word, using other words to define it inside the mind of the human reading it.
Yes, if you start looking at the definitions of words in the definition, the whole thing become an infinite loop, just like if you put 2 mirrors together. That's just a property of how the mirror works/how the dictionary works, not a property of the physical object/or the word inside the language.
I recap your question, then answer, based on my experience:
The purpose of natural language is to convey meaning. The mechanism by which natural language conveys meaning is use of words. A mechanism that allows words to convey meaning, thus endowing natural language with meaning is then necessary; this mechanism is the definition of a word.
Then, if a word's definition is, as you imply, an infinite loop, does the whole foundation for natural language's meaning crumble?
No. A word is not defined as an infinite loop. The relation of a word to an infinite loop is an emergent property of the word-definition system; it does not define a word. Thus, a word is not an infinite loop and therefore does not confer 'meaninglessness' to natural language.
In addition, it seems you assume that an infinite loop is meaningless. This is not an obvious truth, if a truth at all.
Regarding the validity of an infinitely recursive definition, a definition must impart a finite description of a given concept to be well-founded.
Your final question strikes me as recursive. I'm not clear on its meaning...
The trick is that you don't need any language to understand basic concepts or usual things which happen around you every day.
We as humans developed language to share information without the need of showing. Without language, if I wanted you to know that I have a dog, I would have to bring you to my place (or show you a photo or draw a picture of the dog) - instead we developed some basic words to describe basic things. Nobody asks what a dog is or what it means to "be" (leaving philosophical considerations of existence aside).
Anyways, naming basic things and activities is a second step, because as I said, you don't need language to understand them, which is the first step - babies interact with and understand their parents to a high extent, before they are able to understand the language (not to mention using it).
The third step is to use combination of words as sentences to carry and share infromation.
The fourth step is to use combination of words to define meaning of new words - to describe abstract concepts or the ones which would be hard to show otherwise.
There's no infinite loop. You basicly think that an advanced feature of language is a requirement for understanding and sharing information. Which is wrong.
You are asking two very different questions as if they were equivalent, which they are not:
Are all natural languages bound to be meaningless?
This depends entirely on your definition of meaningless. For nearly all commonly accepted definitions, the answer is "no." Empirically speaking, people do communicate meaning (by most definitions) through natural language. Conversely, much of what most people would consider "meaningful" cannot be expressed formally. I'm guessing you would consider (for example) love poetry to be "meaningless," but plenty of people would disagree.
Should we state our logical proofs in formal logic / mathematically?
Generally, yes. That's arguably the entire reason we have formal logic in the first place.
The map is not the territory.
A dictionary is a map of a language (actually just a partial map, as grammar, metaphors and many other details are missing). The fact that it is its own legend does not change the fact that the dictionary describes a language, but the language is not what is contained within the dictionary.
The meaning of words is a question of semantics. A dictionary is using the tool of words to convey this meaning in the same way that a factory of the right kind can produce another factory. But as you noticed, if you look for the meaning of the factory, you need to look outside of it. But you won't be able to express it with the machines and materials of the factory itself.
Words can be understood without a dictionary, and are in fact acquired by native speakers (i.e. as children) through use and observation rather than through rote learning of dictionary definitions. The dictionary comes second, not first. Arguing about a property of language through a property of a dictionary is rather backwards.
You're querying the definition of 'definition'! A non-human that communicates by other means than speech would ask how we know what words mean. The short version of a long answer is that our species is hard-wired to learn language. It's been proven many times. We may reasonably suppose that in-group communication is a massive survival advantage; we do it with language, thus we've evolved to be very good at learning it.
Dictionaries exist for further language learning, they don't specify meanings. Communities specify them by common consent.
This question's interesting in light of contemporary postmodernism. We are now asked to accept that everyday words mean only what the speaker says they do: language is socially constructed and thus changeable by any member of a society. By extension, nobody can be sure what anyone else means by "table" so there's no such thing as a table ... be careful when putting your drink down! (What is a drink?) If I could meet Foucault now, I'd bang his head against a wall until he understood that a wall is, indeed, an impermeable structure.
Yes. Natural languages begin with agreement for abstract usages. Do Words Have Inherent Meaning Each individual piece develops into larger structures based on the need to communicate content. Once the agreement on the content is made, the language develops by usage. And, by usage alone. Dictionaries attempt to give the most common usages. If you do not understand the initial base agreements for a language it is all meaningless, in your personal POV. Both language and mathematics are based upon agreed abstractions. Mathematics has a greater commonality and distribution well beyond most common languages. That does not make it more meaningful to those who have the base understanding for it. That is a basic, superficial answer. There is an inherent human need to develop and learn to communicate with abstractions. Both Mathematics and languages satisfy that need. And, that primal instinct to connect and create legacies, cannot be tossed away as 'meaningless'.
No. Definitions are fundamentally rooted either in our senses (for physical meaning -- e.g. "what does table mean?"), in our actions (for ethical meaning -- e.g. "what does rights mean?") or in the axioms of an abstract system (for mathematical meaning -- e.g. "what does triangle mean?").
So you have a basis on which stuff is defined. There is no circularity (when your semantics isn't rooted in these, that's when you have meaninglessness).
Although controversial within the field of linguistics, there are some linguists who believe that natural human languages are built from semantic primes, the base set of concepts which cannot be meaningfully reduced to other concepts. While it is difficult to determine what the primes are (one project, the Natural Semantic Metalanguage has been refining its set of primes for over 45 years), once you have determined your list of semantic primes you can in theory define every word in every human language without recursion.
People have expectations of the dictionaries they use however, and if a dictionary embraced a theory like NSM and left primes like I, YOU, GOOD or THINK undefined, it would probably get so many complaints that they'd have to quickly publish a revision defining the primes just to stop the complaints.
And in practice, as the language specific expressions of these primes have additional meanings, it is appropriate for dictionaries to define them. For example, the prime YOU is strictly only the singular second person pronoun, however the English word you means both the singular and plural second person.
In a dictionary and in the brain, words and concepts are defined on top of each other.
In the brain, at the bottom of the conceptual hierachy, words are bound to senses & feelings. That makes the brain definition of language non cyclical (and artificial intelligence difficult).
The traditional paper dictionary showed little pictures to save space (but encyclopedia showed more) and could not let you smell a dog or hear it bark. So yes the traditional dictionary was cyclical.
With the advent of multimedia, it doesnt have to stay so.