On Philosophy

November 23, 2007

The Myth Of The Perfect Language

Filed under: Logic — Peter @ 12:00 am

Language, especially written language, has always fascinated people. Its expressive power strikes some as magical, and the idea that somehow with the right language the world could be controlled is one that reoccurs in many myths. Even in this modern age many people trust without thinking whatever is written, possibly because once the idea expressed in writing is entertained it seems real. But obviously no language can possibly convey only true ideas, and words certainly can’t exercise any form of control over reality. Still, the idea that many problems could be dissolved with the right language remains, that somehow if we could just express our ideas in the right way that everything would become clear. And usually it is supposed that some kind of logical/mathematical language could fill this role if anything could. But is such a language possible, and would it really be useful?

Before we can turn to those questions we must first examine more closely what exactly a perfect language is supposed to do, which will place limitations on the form it can come in. Three common requirements are that: statements made using the language must be completely unambiguous, the meaning of words must be completely captured or capturable, and that every claim that must follow from a set of claims expressed in the language can be deduced in a completely mechanical way, without any need to special intuition. Let’s consider unambiguity first since it is the simplest. Ambiguity is a problem in our normal languages because the things we say can be taken in more than one way, and it is quite possible that some of the things they can be taken to mean are true while the others are false. Not only does this raise problems for the communication of ideas, but there is the possibility that the ambiguity will infect our thinking about the matter as well, where we will proceed first on the basis of one meaning and at some later point switch to a second, so that we might reach conclusions that are impossible if the statement was taken to have a single fixed meaning. But it is not entirely clear how ambiguity can be avoided. It is true that we may attempt to provide precise definitions for all the terms we use, but those definitions must themselves involve words that are undefined at some point, because the chain of definitions must come to an end, obviously. And while contextual or circular definitions are possible these guarantee the existence of ambiguity rather than remove it. It is possible, however, to construct a language that is completely unambiguous so long as a certain facts hold, although those facts themselves can never be conclusively verified. Suppose, for example, that we were considering a term defined in such a way that the definition directs us at some part of the world, and that it can direct us only at one particular thing, at most. If this language is to be unambiguous then it must be that there is such a thing that we are actually directed at, and, if this language is to be more than private, that everyone is directed at the same thing by their understanding of the definition. And, although we can test these assumptions, we can never completely verify them, because it is always possible that other people are directed at something slightly different and that the difference has simply yet to be revealed. But if they do hold then those terms are completely unambiguous and so will be any terms defined on the basis of them.

The next task for the perfect language is to capture completely the meaning of words. Now obviously there is a sense in which even our ordinary language captures completely the meaning of words. After all, if I write “justice” down that word captures completely the meaning of justice, at least for me. So what is desired is something more than this, something connected to unambiguity, namely that by writing a word down we somehow fully expose its meaning, or that if we can’t do so then we can’t even write it down. Obviously for convenience any language will contain symbols that are taken to refer to things, because it would take to long to write down the complete meaning for every word every time we use it. Still, in the perfect language such symbols would be by themselves meaningless until a complete meaning is given for them that they can be said to stand for. As I mentioned previously the idea that the complete meaning is to be expressed when we use words in the perfect language is connected to unambiguity because to be unambiguous definitions must be provided that pin down the meaning of the word, and some expression of the word’s complete meaning would fill that role perfectly. However, this requirement does ask something of the perfect language over and above unambiguity; the language must also be able to capture the meanings of the words we use ordinarily. And this is where the perfect language is something above the logical languages that already exist, because while we can simply stipulate that a particular letter stands for some property and another for some object it isn’t the case that we can also express the meaning of the words we usually refer to those properties and objects with, or at least it’s not obvious how to do so in any remotely straightforward way.

And our third requirement is that the perfect language must come with rules for exploring the connections between claims, such that if one claim follows necessarily from another, or is incompatible with another, it can be determined in a purely mechanical way with no need for intuition. The idea is, I suppose, that once the meanings are completely revealed that there is no barrier to manipulating them to come to these conclusions. Again logical languages can be held up as an example of this, because given any collection of statements we can apply a number of rules to arrive at further statements that must hold given them. Of course such languages are limited in some ways, with the rules for deduction being a completely separate from the statements themselves. That, I suspect, is a bit of an error in language design. How truth works with respect to a given domain is as much a part of the meaning of the terms as are other facts about them. And thus if a perfect language could be constructed I would suspect that for the most part that the deduction rules would somehow be embedded in the complete meanings, which also allows for different deduction rules to apply in different domains.

So, can we possibly construct such a language, and if we could would we want to? With respect to the first part of the question there are a number of people who believe that the kind of language I have described is an impossible one, in part because of certain limitations concerning logical languages. For example, it is well known that logical languages, which seem simple enough, are incomplete, that their rules for deduction will necessarily fail to arrive at every possible statement or its negation no matter how many statements we begin with, even if it would appear that there must be some fact of the matter about them. And it is known that more expressive logical systems must be either inconsistent or that there can never be enough rules to express all the valid patterns of deduction. But I don’t take these results as necessarily defeating the possibility of a perfect language. Certainly they do express limitations about what formal languages can do, but who is to say that those limitations are in some way detrimental to the project? Incompleteness need not bother us if we simply accept that there is not a determinate fact of the matter about every possible statement, despite initial appearance to the contrary, and I think there are good reasons to think exactly that, which I won’t go into here. Similarly, there is no need to be bothered by the limitations on more powerful deduction systems. We might suppose that only a limited number of deductive rules are really needed, and that the statements that can’t be reached by them aren’t really true at all. Obviously this reduces the power of the system, but, again, who is to say that the more powerful system really reflects the kind of truth and necessity we are interested in? Or, we might accept inconsistency, so long as we are working with deductive rules that are able to contain it. Again, going into all the details is somewhat tangential to the topic at hand, so I will omit them. It suffices to point out that limitations on formal languages may be taken not as failings, but on real limitations on truth and necessity that overthrow certain faulty intuitions we had about them previously. And, with these considerations aside, the perfect language seems to be a live possibility. Although it might be quite difficult to construct it there don’t seem to be any necessary barriers to doing so, given that every meaning seems expressible in ordinary language, and that we might very well simply go through the dictionary replacing terms with their perfect language equivalents, it appears that with enough dedication we could bring the language into existence.

But would the perfect language really be useful to us, or would it simply be a curiosity? It seems obvious from a certain perspective that the perfect language is desirable; we want to eliminate any ambiguity in order to better evaluate our claims. And it would certainly be nice to have all the valid rules for deduction laid out in front of us for complex topics, since they can be often a matter of dispute. But, on the other hand, while the perfect language might be helpful it doesn’t seem to solve our real problems. The real problems are not in determining which claims follow from each other or what exactly the meaning of words are, the real problems are in determining the correctness of claims and how well our terms actually track what we suppose them to refer to. And these are problems that the perfect language simply can’t help us with, it can only proceed from the claims and definitions we provide, not validate them. And so, while the perfect language probably wouldn’t hurt us, there is an argument to be made that focusing on it is to direct our attention at the wrong problems, and so that actually trying to bring it into existence would be a waste of our energy given the other more pressing issues that demand our attention.

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