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Axioms in natural language

  1. Feb 22, 2014 #1
    In math, we have axioms that we assume to be true. We don't have proofs for it.

    Similarly english or any other natural language attempts to describe the world using words, alphabets etc.
    So there must be some axioms, right?

    Everything cannot be described / defined. But obviously, we can describe/define every word using other words.

    But if want to formalise it, is it possible that there would be certain words that are axioms(i.e. no definitions) and all other words would be defined using the axioms? Is such a thing possible?
  2. jcsd
  3. Feb 22, 2014 #2


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    You are misunderstanding a bit the role of axioms in math.
    A better analogy is to compare them as arbutrary rules, just like soccer has arbitrary rules, and poker has arbitrary rules.

    No-one has devised a natural language, so an analogy to axioms is unlikely to be found there. Rather, understanding the foundation of natural languages would be to UNCOVER governing principles, just like physicists seek to uncover the underlying rules.

    Do you see the difference here?
  4. Feb 22, 2014 #3
    Yes, right. Perhaps axioms were not a good analogy.

    But you still get the idea, right?
    Definitions of every word uses other words. Obviously it'll be circular. So, is it possible that we can have some set of words which have no definitions and every other word is defined using that set?
  5. Feb 22, 2014 #4


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    You can always define a word with other words, otherwise there would be words that could not be put in the dictionary. Do you know of any words that are not in the dictionary? Oh ... wait ... gullible is not in the dictionary :smile:
  6. Feb 22, 2014 #5
    I agree with the OP. I do not see how it is possible for there to be no undefined words.

    Just like we have undefined terms in geometry. It doesn't mean they are meaningless, it means that they cannot be defined because other concepts that could be used to define them, rely on its own very definition.

    Undefined does not mean "not in the dictionary" here. It means that its definition would eventually reduce to a tautology if you looked at the definitions of the words in its definition, and so on and so forth. It also doesn't mean that we don't know what the word means.

    Saying that you can always define a word with other words does not answer the question. How are the words used defined? With other words again. And how are those defined? Again, with other words. It is impossible for this to continue on, defining every word, and for there not to be some circularity.

    I completely agree that each dictionary contains a set of words that is not "defined" in that dictionary.
    Last edited: Feb 22, 2014
  7. Feb 22, 2014 #6
    Of course you can define every word. But that would mean definitions would be at some point circular? This is somewhat related to godel's incompleteness theorem (I guess).
    So what I am asking is:- Is it possible to have some set of words that do not have definitions and have every other word defined using this set?
  8. Feb 22, 2014 #7


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    If the words didn't have any definition how would anyone know what they meant? The whole concept just makes no sense to me.
  9. Feb 22, 2014 #8
    This issue seems to come up a lot. I've done a little thinking about it but have only come up with a general direction the solution should take, which is to consider the phenomenon of definition by example, or definition by demonstration. As babies we don't learn the meaning of words by recourse to other words. We learn them directly by experiential link between the word and what it stands for. This is, in fact, a prerequisite to later defining words by means of other words. The word "soft," for example, could be easily defined in an individual's mind by presenting that person with several examples of soft things for them to directly experience. The definition could be sharpened by contrasting it with the experience of "hard" things. All without using any other words. This is, obviously, how everyone starts out learning word meanings.

    Defining words with other words unconsciously assumes the "other words" are going to succeed in evoking memories of direct experience of examples and demonstrations, and that is where the circularity is broken. For understanding to occur, the link to be made must ultimately be between the symbol and the thing symbolized, with reference to no other symbols.
  10. Feb 22, 2014 #9


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  11. Feb 22, 2014 #10


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    You cannot "axiomatize" using only words-that makes absolutely no sense whatsoever. What you can do is usually break down words into free and bound morphological elements and phonological elements. Take a basic course in linguistics if you want to see the details because this is all very elementary linguistics.
  12. Feb 22, 2014 #11
    It makes no sense to you because you aren't quite realizing what he's talking about. "Not having a definition" in this context has nothing to do with "not knowing what they meant." It also doesn't mean it isn't listed in the dictionary. It also doesn't mean it doesn't have a meaning. It means that its definition uses words whose own definition will eventually use the undefined word.

    The fact is that learning words from the dictionary requires that you already have a set of known words. Zoobyshoe, I think, explained where this set of known words comes from beautifully.

    A demonstration: imagine I looked up "of" with Google dictionary.

    expressing the relationship between a part and a whole.

    But wait, what does "whole" mean?

    all of; entire.

    but wait, I am still trying to define "of" by learning what "whole" means! The definition of "whole" uses "of".

    Thus, one of these words, of and whole, must be taken as a "known," or axiomatic, or "undefined word" in order to define the other one.
  13. Feb 22, 2014 #12


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    That's natural language. Words evolve naturally, they don't start with a definition: they start with a linguistic association with feelings, events, or other precepts. And then, eventually, society settles on a definition (or several definitions, as different subcultures will sculpt their subjective experience that they associate with the word differently and sometimes words will be borrowed and retooled sharing some association with the original meaning).
  14. Feb 22, 2014 #13


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    That has been done. For example the Oxford English Dictionaries have created a list of 3000 words that cover the "basic" vocabulary of English, and produced dictionaries where all the definitions only use those 3000 words.


    This was an earlier attempt, based on 850 words: http://en.wikipedia.org/wiki/Basic_English
  15. Feb 23, 2014 #14


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    I think the OPs question is dealt with broadly by the study of semantics:


    We use words to describe things, feelings, sensory perceptions, ideas, but how do we really know if we are conveying what we mean to another party? Is what I consider to be the color 'red' the same as what someone else perceives? Clerk Maxwell did some important investigations in color perception and color blindness:

  16. Feb 23, 2014 #15
    That's exactly what I meant. I should've explained my question better in the first place.

    I was unsure whether my question would make sense but great to see something like that has been done. I'll give it a look.
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