Two weeks ago I wrote about the problem with definitions. At scienceblog.com, this post got over 11,000 hits and 41 comments, most of which had to do with answering the age-old challenge of defining the word "chair." There were some very good attempts, none of which ultimately work, which isn't surprising since may of the greatest minds in the 20th century have tried and failed to solve this problem.
It happens that this week I am reading from Greg Murphy's Big Book of Concepts, which contains an excellent explanation of the problem, one which I think is probably right.
He starts with a big-picture view of the problem of concepts:
We do not wish to have a concept for every single object--such concepts would be of little use and would require enormous memory space. Instead, we want to have a fairly small number of concepts that are still informative enough to be useful (Rosch 1978). The ideal situation would probably be one in which these concepts did pick out objects... Unfortunately, the world is not arranged so as to conform to our needs.
Translating this into the world of words, we don't want a different word for every single piece of furniture (that is, where each of your dining room chairs has its own name). That would be impossible to learn and pretty useless. We also don't want one single word to describe anything on which you might sit -- that would be too broad to be very useful in communication. He continues:
For example, it may be useful to distinguish chairs from stools, due to their differences in size and comfort... However, there is nothing to stop manufacturers from making things that are very large, comfortable stools; things that are just like chairs, only with three legs; or stools with a back. These intermediate items are the things that cause trouble for us, because they partake of the properties of both...
The gradation of properties in the world means that our smallish number of categories will never map perfectly onto all objects: The distinction between members and nonmembers will always be difficult to draw or will even be arbitrary in some cases.
I think Murphy makes a very plausible explanation of why, even in the best of cases, our words could never perfectly divide up the world. It's not possible to have words that pick out discrete categories of things, because there aren't discrete categories of things in the world.
This does leave open the question of what words mean, given that they don't have definitions, since they clearly mean something. I'm still on the second chapter of the book, but I suspect the answer won't be in chapter three, since this is still an active area of research and debate.