More of them coming up...

We exist as linguistic beings, embodying our experience through language. Every linguistic event occurs as an attempt to embody meaning/s arising from the context/s we are in. The context/s are endlessly varied, for no two contextual situations are ever identical in this spatio-temporal world, depending on everything from the will of the speaker, through spatial conditions and temporally based experience, to emotive states, levels of attention or distraction, what was last eaten for dinner, and so on (indeed, we are always unaware of nearly all the contextual influences acting in any given linguistic event). The meaning/s arising out of the context/s are unique to that situation, but the purpose of language is to embody the meaning/s sufficiently well to communicate them to another human being. These embodiments are always approximations of the original meaning/s, and language employs its forms of expression in order to approximate the original meaning/s in this way. The language has at its disposal a wide array of possible forms of expression and brings them into play to do so. The language assigns an expression its parameters, and brings it into play when the meaning arising from the contextual situation falls within those parameters. The parameters of an expression are not hard, however, nor are they exclusive. Bounds on an expression may be stretched, and they are fuzzy. They may overlap with those of other expressions (which allows synonymity). Because any expression is defined by its open-ended parameters, not a discreet "point" of meaning, they are of necessity ambiguous, though not absolutely fluid. It is only by painting with a broad brush that language can function at all -- remove the ambiguity, and language cannot function. Meaning is assigned to an expression by the language in regard to the contextual meaning, according to the rules and bounds the language imposes upon it.
All of those are just characteristics of the common languages of today. Look at what a language in the generality really is - forget about today's common languages and think in more abstract terms. As I said earlier, any system that symbolizes ideas into a form of simpler representation (for communication, deduction, etc.) is a language. Languages were designed to express ideas through symbolic representations, and any consistent system that does this qualifies perfectly as a language. The computer programming languages are therefore just as much languages - never mind that they are called "languages," they can be called shivans for all we care (

) - since they satisfy the required conditions. (they express ideas in symbols) Even random markings in the dirt are a language if there exists a set of precise rules for interpreting them into ideas. The "math language" I had in mind will be basically the same thing as a programming language; different syntax, but the same general structure.
Now you say that no two contextual situations are ever identical, which is true, but it is not saying much. (it is like saying that no two distinct numbers are equal) They may not be equal, but the important thing is that patterns exist that determine their inequalities. The very fact that language is capable of "assigning expressions [their] parameters," regardless of how fluid those parameters may be, means that the meanings must have patterns, or else language would not be able to do anything whatsoever. As for the fluidity of the parameters of expressions, it may well be so, but it does not
have to be so. All of the common languages have it so, but then we have the programming languages for which this does not hold, and they work equally well. (better, in fact) We know that ideas cannot be partitioned into quantized parts due to the concept of ideal continuity but that is not at all necessary here; we need only seperate them into intervals defined by functions, and these can be fine-point intervals that do not overlap. In regards to the last sentence, that is absolutely correct, but the
contextual meaning is just as much of a part of the expression as its constituent words are. (no, it does not have to be actually written in there to be a part of it, as you should well know) What you are saying here is the equivalent of asserting that, say, English is the only "true" language, and if you remove English words and conventions out of the language system, you would have no language. (actually, there are people who claim just this

)
Thus, expressions cannot mean absolutely anything, but only anything within the bounds of their applicability.
Oh, so now they
do have bounds to their applicability. So such bounds exist, and the words/contexts/whatever can thus be classified.
So you ask me what my point is, and I tell you: ambiguity cannot be eliminated from a language, or is ceases to be a language. Any project to eliminate the ambiguity of language, of which your idea of a mathematical language is a very radical (and fairly innovative) example, cannot end in anything but the destruction of language. Reduce language to nothing but math, and you are left with nothing but math -- language will have disappeared.
You are telling me that a language should deliberately be made ambiguous?

In that case, the ultimate language would be to have, say, the same symbol mean everything.

First, re: partitioning: you will see in the above that seperation of meaning/s is obviously still included in our understanding of language. But the lines of division are not set in stone -- they move, blur, and sometimes even collapse.
Exactly, and that is the main flaw with the common languages. This, however, is
not a necessary characteristic of language in general insofar as it contributes to the purpose and utility of language.
Second, re: the "50%" mark: perhaps I did not elucidate my objection clearly enough. We have no measuring stick for niceness. Say I give a friend a sweater, and I give another friend five dollars. Which was more nice? How do we measure it? Or again, what is the absolute maximum of niceness? To what do we point as the embodiment of absolute niceness? Perhaps if we can find that, and also find somthing to point to as the embodiment of the absolute lack of niceness, we will be able to devise a method for measuring degrees between them. But unless we can do so, we cannot identify anything that lies 50% of the way between them. We cannot call niceness quantitative until we have some way to measure it as a quantity. Gravity can be measured, and is thus quantitative, but how do we measure "nice?"
You don't, unless the differences between the applied test situations lie within a certain interval. Again, you need to establish exact and precise conditions for a "niceness test" to be valid, and give equally precise "niceness" intensity values based on the parameters of the test. Heck, how else would you judge this "niceness" anyway? I said this before: even the
common languages have such standards, even if they are not explicitly "set in stone," because the words would otherwise have no real meaning in common usage. Of course, these standards are very messy due to the way they have come into usage and need to be rewritten from the ground up, but that is a mere technicality. Either one of two conditions must hold here: such standards exist in some way, or the word is completely meaningless. Of course, the word "nice" is indeed a pretty meaningless term today since it could mean just about anything, but that is because the standards need to be revised.
Third, re: sarcasm: no, no, no, the incongruity lies in the relationship between the symbols and the meaning. I understand what you are trying to say, but think of it this way: adding a "sarcasm symbol" would be roughly analogous to placing brackets around a mathematical expression and putting a negative sign out in front of it all. But in so doing, I am only negating the statement. Sarcasm is not the negating of the statement; negation does that. ("I am so happy," becoming "I am not so happy.") Sarcasm is the using of the symbols -- all the symbols, collectively -- to communicate the opposite of what they should communicate. So the statement is negated, but precisely on a level other than the symbolic one. Sarcasm is thus a relationship between symbols and meaning, not a symbol itself.
A relationship like this is
just another symbol. It by no means has to be explicitly written down to qualify as a symbol. All aspects of language are like this, and sarcasm is no exception. Adding a symbol of sarcasm somewhere in sentence will be no different than the current symbol for those who are used to it. We have all been brought up with one of the languages in popular use (e.g. English), and these all have the same symbol for this particular idea; we thus are much more used to seeing and interpreting this particular symbol as sarcasm, but we do not want to lose sight of the fact that other, radically different methods of symbolizing ideas exist are equally "good" at whatever purpose they serve.