Is a word a real thing which is out there in the world, or is a word a convention invented by people to facilitate communication?
I would like to begin this section with an ancient philosophical question called the Ship of Theseus.
The question, as often stated, goes something like this:
Theseus sets out on a voyage, taking with him a supply of spare wood and other parts for his ship. While at sea, he replaces, one by one, every single part on his ship, from his supply of spares. Another ship, following his, collects all the original parts and puts them back together. Theseus arrives at his destination in his rebuilt ship, and someone else arrives in the ship made of all the original parts.
Which ship, if any, is the one on which Theseus departed?
If it is the ship made of the original parts, how did Theseus change ships without ever getting off of his?
If it is not the ship made of the original parts, how did the ship lose its identity simply by being disassembled and reassembled?
If you have never encountered the Ship of Theseus before, I recommend that you spend awhile thinking about it and decide upon your opinion. If you would like some more detailed discussion, a web search for "Ship of Theseus" should provide as much as you could possibly want.
My purpose here, however, is not to actually address the questions posed in the Ship of Theseus paradox. In fact, though this particular example brings out questions related to "identity", another example involving ideas of "truth" or "existence" would serve just as well. I am interested in discussing not the answers to these questions, but instead the assumptions we make in attempting to answer the questions at all and the procedures we follow in doing so.
Specifically, I would like to examine the basic assumption that the ships either are or aren't the same; I would like to examine the assumption that objective is to find a rigorous definition of identity. Philosophers have been arguing about this for thousands of years, and they'll probably be arguing about it for thousands more. Are they really asking the right question?
What is the alternative? An alternative is to say that identity is an approximation - a mental and verbal shorthand. We could say "this object contains 99.99% the same materials as it did last week, arranged in the same location, and not having been rearranged in the meantime", but instead we say "this is the same thing" because it's shorter and we usually don't need the precision. We have an intuitive understanding of what we mean by "the same" instead of a rigorous one, so in certain pathological cases which meet SOME of our intuitive criteria, our understanding breaks down.
So, is that really a problem? Suppose we had a rigorous formal definition of identity, and could conclusively say in all cases that something was or was not the same. What could we do in that case that we couldn't do if we didn't have a rigorous definition?
Consider a parallel case. We have a general idea of what we mean by a "boot" and what we mean by a "shoe." Then, in the latest designer footwear catalog, we see something that's a strange cross between a shoe and a boot. So, being the good philosophers that we are, we gather all our equally philosophical friends, and argue tirelessly for three weeks about the definition of a "boot". In the end, we are able to say whether or not the item pictured in the catalog is a boot.
What, exactly, have we accomplished? What can we now do or think about with this rigorous definition of a "boot" which we could not have done by simply saying "it's like a boot in its sole and leatherwork, but like a shoe in its laces and shape" in the first place?
Consider another example. Suppose I go to work one day, get promoted, and get a 20% raise, and this makes me very happy. Then I come home, my wife tells me she wants a divorce, and this makes me very sad. Did I have a good day or not? I could argue about what exactly constitutes good, or I could just say that in some ways I had a good day, in other ways I had a bad day, and the common simplification of either having or not having a good day is TOO simplified for this case.
This latter approach has a great deal to recommend it. Most of our concepts - even things that may seem to be "really there" like boots - are better thought of not as "things" or "properties" but as approximations which allow us to think and communicate effectively by simplifying things until they're conceptually manageable. However, sometimes these simplifications will break down and be ambiguous. We could try to compulsively give rigorous definitions of every single concept, such that all possible cases can be shoehorned in somehow... or we could just recognize that sometimes even the best simplifications don't cut it, set them aside, and describe things in more detail instead.