Can we communicate as effectively with language as we do with mathematics?

[pivoxa15]

We all know that it is possible to do mathematics for no practical purposes at all such finding a proof in number theory or exotic geometrical mathematics. The goal is to find internal relationship within the framework.

But consider a normal (social/culture) language such as English. Is it possible to do what you would with pure mathematics with regards to English? Such as doing English only for the purpose of establishing relationships within the language and not for any empiricial reasons. Although you might think about things that the language is describing. So you can think about justice, adverb, tool when using these words. For example, in pure math, you would think about different geometric shapes when you are only seeing mathematical symbols.

Just like pure math, there might be an empirical use for the new connections in English and possibly new words (that are essential) were introduced into English. You have made the English language more user friendly and more wide ranging in its practibility. More people, espeically lawyers are able to satisfactorily use English in their work. It is just like how physicsts borrow new developments/relationships made in mathematics.

 

[neurocomp2003]

i'm sure you could or possibly rearranging the letters themselves to make new words. Or if you were working with a pictographic language to make new drawings...OR the search for a universal language...

 

[Orefa]

The trouble is, a natural language grammar is a theory, not a formal set of rules. The theory tries to describe the usage and meaning of human sounds in a particular culture. But it frequently fails and must be re-written as the same human sounds keep changing meaning over time, and new human sounds keep being created and/or combined in new ways. It is hard to do anything formal with such an informal basis as the English language (or any other). It's not all bad, this problem actually helps lawyers and politicians pay for their yatchs.

 

[pivoxa15]

The trouble is, a natural language grammar is a theory, not a formal set of rules. The theory tries to describe the usage and meaning of human sounds in a particular culture. But it frequently fails and must be re-written as the same human sounds keep changing meaning over time, and new human sounds keep being created and/or combined in new ways. It is hard to do anything formal with such an informal basis as the English language (or any other). It's not all bad, this problem actually helps lawyers and politicians pay for their yatchs.

So you are saying that in a normal language like English, it is like applying a framework to the real world so when dealing with English, it must be all applied. It is like doing physics.

Good point on the yatchs but some language is better than no language at all. Look at how lower order animals settle things. Just like it is much better to study nature with mathematics than without it. But mathematics never perfectly matches nature just like how English never matches our human reality, that is we can never express fully what we have on mind. We can only approximate our feelings, views with the finite many number of words in a given language. Although this approximation is a very good approximation because otherwise many new words would need to be introduced.

 

[matt grime]

As I have no idea what 'We all know that it is possible to do mathematics for no practical purposes at all such finding a proof in number theory or exotic geometrical mathematics.' and 'Is it possible to do what you would with pure mathematics with regards to English?' mean really, since they are subjective, I can only offer some guesses as to answers.

Gerard Manly-Hopkins used a germanic method of creating new words, no hyphenation just concatenate. There's nothing to stop you creating new words like this. Indeed, many authors have imported from other languages to create artificial ones, and have done so to describe things that are purely invented, just as people have invented words possibly from scratch (jabberwocky). Other examples: Burgess (Spindrift is the name of one of his character, I leave it to you to figure out what it means); Huxley; Self and so on abound of people playing with languagein and of itself.

It is also possible to create new words from units to create things that might one day exist, and it is possible to create an artificial language with grammar rules that describes nothing physical. Bear in mind there is a latin word for helicopter.

But then this leaves itself open to the argument that once you create it and use it it becomes a language that is not merely theoretical anymore.

Indeed one might argue that language is that thing which we use to communicate; it is its usage. But as Wittgenstein isn't here let's leave that.

 

[honestrosewater]

I don't understand what's being asked either. Scientists have been and still are studying and doing all kinds of things with natural language. The field is called linguistics. I happen to be studying it. What do you want to know?

Current mainstream linguistics is in fact quite formal -- the leading school of thought, or whatever you'd call it, is even called Formalism. The main goal of theoretical linguistics is to discover the nature of a speaker's linguistic knowledge, or mental grammar (largely, what rules and constraints you follow when using language). There is lots of overlap with logic and computer science. The subfield of mathematical linguistics is concerned with the formal and mathematical properties of natural languages.

Gerard Manly-Hopkins used a germanic method of creating new words, no hyphenation just concatenate. There's nothing to stop you creating new words like this.

If word structure and formation is what you're interested in, its study is called morphology. I started to explain a little about some morphological processes here (a lexeme is basically one aspect of a word):

Derivational morphology, or word formation, creates new lexemes (SINGER) from old ones (SING); inflectional morphology determines the word forms in the paradigm of a lexeme (SINGER: singer, singers; SING: sing, sings, sang, sung, singing). The definitions and the distinctions they're meant to draw are rather hairy. Morphological processes include compounding (black + bird --> blackbird), incorporation (scare (verb) + crow (noun) --> scarecrow), affixation (un- + happy + -ness --> unhappiness), ablaut/apophony (goose --> geese; bath --> bathe), back-formation (editor --> edit + -or (edit + -er) --> edit), and reduplication (repeating the whole word or part of it, ?English example?, example from Pima: gogs 'dog' --> gogogs 'dogs'). A process can be used for inflection or derivation or both and can be used differently in different languages. As earlier examples show, English regularly inflects nouns for number (i.e., forms plurals) by affixation, specifically by suffixation, while Pima uses partial reduplication to do the same thing, and English also uses suffixation to derive nouns from verbs by affixing -er.

 

[loseyourname]

Well, I'll give my shot at an answer, and it seems the closest thing to what you're describing is ordinary language analysis, which is simply the process of looking at how speech-acts are used, and what they mean with respect to other speech acts, without regard to whether or not they have any empirical significance.

 

[pivoxa15]

As I have no idea what 'We all know that it is possible to do mathematics for no practical purposes at all such finding a proof in number theory or exotic geometrical mathematics.' ...

Why is this statement subjective? Hardy himself admits that he does mathematics for no application interests whatsoever.

I agree that doing pure language is subjective and the fact that I have no knowledge of linguistics dosen't help either.

 

[honestrosewater]

What do you want to do with the language? Or perhaps it would be better to ask what you think the difference is between a natural language (like English) and a formal language (like first order logic). There are obvious 'practical' differences between them: their origins and how they are used by humans. But if you only consider their abstract structure, or certain aspects of their structure, how could you tell the difference between a formal and a natural language?

From one perspective, a language, natural or formal, is just a set of strings, and a grammar is the formal device that determines which strings are in the set. From this view, in what way does a "grammatical sentence" of a natrual language differ from a "theorem" of a formal language? I can't think of any difference that holds necessarily. How would the natural v. formal distinction persist into the models? I think it's only relevant when the languages are the objects of scientific study.

 

[sameandnot]

mathematics with words. concepts... it seems that we would need to have the same kind of relationships, as we have in mathematics. numbers are conceptually whole, and yet can be applied to denote concpets, on a scale that ranges from the infinitely small, or simple, to the infinitely large, or complex (at least, this was the assumption of our intellectual tradition).
we can denote an electron numerically, or we can denote an atom with a number, or a molecule, or a galaxy... depending on the nature of the equation.
if it were possible to have (or to believe one had) the same kind of "conceptual integrity", with words, as is had with numbers, then it may be fruitful to explore mathematical linguistics, or something like that. i think that such a system would never yield truth, but it would, on the other hand" express many anomolies, paradoxes, hypocriticisms, alienations of meanings and other peculiarities that are characteristic of logical systems. over all i think that it would most probably do more harm that good, but i would like to ask one question, just to clarify the idea you have in mind:
would it be a kind of "mathematical system" that can logically adduce (or produce?) or deduce meaning, objectively/secularly? that is, founded in logic?

 

[pivoxa15]

What do you want to do with the language? Or perhaps it would be better to ask what you think the difference is between a natural language (like English) and a formal language (like first order logic). There are obvious 'practical' differences between them: their origins and how they are used by humans.

I like to say that mathematics and language (such as English) came from the same roots. They all started from pracital applications. People wanted to live their lives easier by inventing a system to deal with everyday necessary things like communication and counting things. Slowly math and language diverged because people needed math to do more and more specialised things that would be too slow or inefficient with language such as long additions or subtractions. Although it would be more appropriate to use language rather than math to express your feelings. However, math became a field on its own after the Greeks started to do it purely for intellectual reasons such as making proofs in numbers. Langauge though never went that route and has always been applied by people. Although it is not always the case that everything our language describe exists in the real world. It is sufficient if enough people feel the need for a new word such as in story telling.

A major difference between language and math is in the former's generality hence it is much more vague. And that is another reason why it did not take off like math in terms of doing it only for the pure sense purely for internal relationships. Langauge is so general and vague that if enough people use it in a certain way than that is the way to go - even if it did not make sense logically.

For example
Want to say: I don't have lollies
Actually Say: I don't have no lollies
Logically imply: I have lollies

 

[honestrosewater]

I still don't know what you mean by 'mathematics' and 'language'. How are they different? What IS a language? A system of abstract objects and rules for combining them? A set of utterances exchanged by a group of people? Do you want the physical system or the model of it?

You can study mathematics as a physical system, the language spoken by mathematicians, in the same way that you can study English as the language spoken by English speakers (I imagine you would define the set of speakers by extension if that seems circular).

What if I said that a model of the English language IS a formal language? It's the formalization of a language. ?? I realize that the languages that happen to be known to currently exist on this planet and are usually classified as natural tend to be more 'complex' than the languages that happen to be known to currently exist on this planet and are usually classified as formal. But I thought you weren't interested in the real world and accident. What's to stop me from creating a language that qualifies as a natural language and is less complex than any formal language? Anything? What's to stop me from creating a language that qualifies as a formal language and is more complex than any natural language?

I guess I'm trying to say that math and English might be essentially the same thing if you looked at them in the same way. And this would answer your question about whether anyone can or would want to do the same thing with English as is done with math.

Here, maybe a brief overview of formal grammars will interest you (and let you see the kind of modelling that I'm talking about).

 

[TheStatutoryApe]

Pivoxa15 came close to my personal view of the matter.

Math is an internally consistent language based exclusively on syntax (or grammer). 1 2 3 4 5 6 7 ect.. are all arbitrary symbols that can easily be replaced with others and the language loses none of it's meaning.
A + B = C makes just as much sense as 1 + 2 = 3 if I were to lay the ground work for the symbols as A B C D E F G instead of 1 2 3 4 5 6 7.

Languages like English on the other hand don't possesses that same internality of meaning. I can not randomly assign a set of new words in place of the traditional ones and expect any person to read them and find any understanding based solely on their syntax. I would have to supply pointers to objects outside of the language itself to provide a semantic property.

This is the difference I see between math and other languages.

 

[pivoxa15]

I still don't know what you mean by 'mathematics' and 'language'. How are they different? What IS a language? A system of abstract objects and rules for combining them? A set of utterances exchanged by a group of people? Do you want the physical system or the model of it?

You can study mathematics as a physical system, the language spoken by mathematicians, in the same way that you can study English as the language spoken by English speakers (I imagine you would define the set of speakers by extension if that seems circular).

What if I said that a model of the English language IS a formal language? It's the formalization of a language. ?? I realize that the languages that happen to be known to currently exist on this planet and are usually classified as natural tend to be more 'complex' than the languages that happen to be known to currently exist on this planet and are usually classified as formal. But I thought you weren't interested in the real world and accident. What's to stop me from creating a language that qualifies as a natural language and is less complex than any formal language? Anything? What's to stop me from creating a language that qualifies as a formal language and is more complex than any natural language?

I guess I'm trying to say that math and English might be essentially the same thing if you looked at them in the same way. And this would answer your question about whether anyone can or would want to do the same thing with English as is done with math.

Here, maybe a brief overview of formal grammars will interest you (and let you see the kind of modelling that I'm talking about).

There are strict rules in language (such as English) but most users are not aware of them (myself included). I could not tell you whether a given sentence is grammatically correct but I can still communicate with people. So when we speak English, we do not need to constantly think about the rules or grammar. However, when doing maths it is way different. I know that I am constantly thinking about the rules and seeing whether what I am writing down make sense. People cannot read a page of long arithmetic the same way as reading a page of Enligsh. That is one major difference between language and math. This could also mean that different parts of the brain process language and math.

 

[honestrosewater]

There are strict rules in language (such as English) but most users are not aware of them (myself included). I could not tell you whether a given sentence is grammatically correct but I can still communicate with people. So when we speak English, we do not need to constantly think about the rules or grammar.

Perhaps I'm not making clear the ways in which language is studied by these scientists called linguists. Linguists are not going to tell you, as your parents or grammar teacher might have, that you should or shouldn't end a sentence with a preposition or try to impose any other artificial rules on you, no more than any other scientist would tell, or try to tell, their subjects how they should or shouldn't behave. The point is not to impose artificial rules, but to discover the natural ones. Two types of data are used to determine whether a sentence or other linguistic unit is grammatical:

1) naturalistic data, which is what speakers are observed saying in normal, natural conversations. If a sentence appears under these circumstances, it is probably grammatical (people do make mistakes and such; speaking can get quite hectic).
2) experimental data, where speakers are presented with sentences or other units and asked to make judgements about their grammaticality, i.e. how they sound. Actually, the notion of acceptability is introduced because a speaker's judgement of a sentence may include things that don't affect grammaticality, and it's not necessarily possible to know what exactly is motivating those judgements; e.g. a sentence might be fine grammatically, but a speaker could find something in it offensive or morally repugnant, they just don't have the real world knowledge necessary to understand it, they want to please the experimenter, etc.

So linguists don't know all the rules either -- that's why they have to study it: to discover what rules are being used subconsciously by speakers and how the grammar of a language (which includes other things like all the words you know) is represented in a speaker's mind. And in the same way that English and other natural languages are studied, the language that mathematicians speak to each other can also be studied -- as a physical phenomenon.

However, when doing maths it is way different. I know that I am constantly thinking about the rules and seeing whether what I am writing down make sense.

I strongly suspect that you do the same thing with English -- you are producing strings of letters (or sounds) that behave regularly. You just probably aren't consciously aware of the rules that are being followed by other parts of your brain and nervous system. Yes, math has a formal foundation now, but is every mathematician even familiar with it? Certainly that isn't necessary since it was a development of the last century or so (for starters, see Hilbert's Program). Even logic hasn't always been as formal as it is now.

People cannot read a page of long arithmetic the same way as reading a page of Enligsh.

Sure, I'll agree, but why might that be the case? First, people's brains naturally work best with sound or gesture -- not with writing. It's spoken or signed language that is found in every human society; only around one third of the world's languages have written forms. So there's one disadvantage that I think math has: no sound rules, or phonology. Your brain might need to work harder because, let's say for the sake of argument, it was 'designed' to use languages that have a phonological component, which math is missing.

Second, natural languages may seem to be sloppy and ambiguous if you only look at one or some of their components, since components can work together to resolve ambiguities in each other. Lexical and structural ambiguities do occur and are of course the focus of logic and math, but they can easily be resolved by other means -- for example, knowledge about the meaning of words or extralinguistic knowledge about the worlds being referred to. So while

1) Would you like to watch paint dry and sip some tea?

may be structurally ambiguous, as

1a) Would you like to watch paint dry and would you like to watch paint sip some tea?
1b) Would you like to watch paint dry and would you like to sip some tea?

your knowledge of the world (or even the meaning of the words) includes the little tidbit that paint cannot sip tea, so (1a) is not an acceptable interpretation, thus (1) is not ambiguous.
Mathematicians may have to work harder when using only a subset of the components that have been available to speakers for millions of years, especially if that set includes components in which natural language allows (or takes advantage of) ambiguity, e.g. the formal, structural component.
Heck, our brains may just be used to using one these components more than the others.

That is one major difference between language and math.

I'm not denying that there are differences. I'm saying that math and English have fundamental similarities. They are the same kind of thing.

This could also mean that different parts of the brain process language and math.

Sure, it's possible, but I think that's a leap.

I'm still not quite sure what your original question was. Can new mathematical structures or logics be developed for the purpose of studying natural languages? Yes. Can people then study those new mathematical structures or logics for their own sake? Yes. Is this already happening? Yes.

 

[TheStatutoryApe]

So there's one disadvantage that I think math has: no sound rules, or phonology.

Why a disadvatage? If the point is communication I would think that forgoing the miscommunication issues that arise due to accents, pronounciations, speech impediments, ect would be an advantage. The lack of phonology makes it simpler and easier to communicate with in a certain sense doesn't it?

 

[honestrosewater]

Why a disadvatage? If the point is communication I would think that forgoing the miscommunication issues that arise due to accents, pronounciations, speech impediments, ect would be an advantage. The lack of phonology makes it simpler and easier to communicate with in a certain sense doesn't it?

Sure, but I think those kinds of complications are just part of real world communication. This isn't something I know much about yet, but I'll go out on a limb a little. The thing is that

1) you're transmitting abstract, or idealized, discrete units (e.g. a /t/ sound or the letter <t>) in a continuous signal (sound waves or EM waves) through a noisy channel (air, phone line, whatever). So what people understand as the same word on an abstract level can have various physical forms, as two people saying bat twice probably results in four physically distinguishable signals, and the same goes for writing, even disregarding their different positions in time and space. The same basic reason you can't draw a perfect circle or measure an inch exactly is at work here too. Also, the properties available through the medium can cause problems when they vary. For example, bat and pat, as abstract units, differ only in voicing: /b/ is voiced, while /p/ is not voiced -- it's discrete -- there is no 'in-between'. But as physical signals, you can start with a signal that is clearly bat and keep reducing the voicing in [ b] until you have a signal that is in a sense 'in-between' bat and pat (which, upon hearing, speakers might ask, 'Did you say bat or pat?'). The same can happen by, say, starting with a lowecase n and extending the left line upwards until you can't determine whether it's an n or h. So it also depends on how well your system was designed.

2) the sender and receiver (e.g. speaker-hearer or writer-reader) aren't even necessarily encoding and decoding the messages in the same way. For example, for each person, there is a point where bat changes from definitely bat to something between bat and pat and some point where n changes to something between n and h, and those points may not be the same for every person. So even without the problems in (1), since there aren't language police to enforce standards, problems can still crop up (unless the community polices itself, of course).

So writing introduces the same kinds of problems, though perhaps they are more manageable.

Anywho, I just meant a disadvantage with respect to how effortlessly your brain processes it. The advantages of working with your 'natural abilities' may outweigh any disadvantages inherent in communcating through speech. I mean, with all of its problems, I think natural language works amazingly well the vast majority of the time.